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-rw-r--r--src/algebra/strap/DFLOAT.lsp946
-rw-r--r--src/algebra/strap/OUTFORM.lsp858
-rw-r--r--src/share/algebra/browse.daase2200
-rw-r--r--src/share/algebra/category.daase3089
-rw-r--r--src/share/algebra/compress.daase1298
-rw-r--r--src/share/algebra/interp.daase9708
-rw-r--r--src/share/algebra/operation.daase32984
7 files changed, 25545 insertions, 25538 deletions
diff --git a/src/algebra/strap/DFLOAT.lsp b/src/algebra/strap/DFLOAT.lsp
index ec08fcad..bc21825f 100644
--- a/src/algebra/strap/DFLOAT.lsp
+++ b/src/algebra/strap/DFLOAT.lsp
@@ -1,77 +1,70 @@
(/VERSIONCHECK 2)
-(DEFUN |DFLOAT;doubleFloatFormat;2S;1| (|s| $)
- (PROG (|ss|)
- (RETURN
- (SEQ (LETT |ss| (|getShellEntry| $ 6)
- |DFLOAT;doubleFloatFormat;2S;1|)
- (SETELT $ 6 |s|) (EXIT |ss|)))))
-
-(DEFUN |DFLOAT;OMwrite;$S;2| (|x| $)
+(DEFUN |DFLOAT;OMwrite;$S;1| (|x| $)
(PROG (|sp| |dev| |s|)
(RETURN
- (SEQ (LETT |s| "" |DFLOAT;OMwrite;$S;2|)
- (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |DFLOAT;OMwrite;$S;2|)
+ (SEQ (LETT |s| "" |DFLOAT;OMwrite;$S;1|)
+ (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |DFLOAT;OMwrite;$S;1|)
(LETT |dev|
- (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 10))
- (|getShellEntry| $ 12))
- |DFLOAT;OMwrite;$S;2|)
- (SPADCALL |dev| (|getShellEntry| $ 14))
- (SPADCALL |dev| |x| (|getShellEntry| $ 16))
- (SPADCALL |dev| (|getShellEntry| $ 17))
- (SPADCALL |dev| (|getShellEntry| $ 18))
- (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$S;2|)
+ (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 7))
+ (|getShellEntry| $ 10))
+ |DFLOAT;OMwrite;$S;1|)
+ (SPADCALL |dev| (|getShellEntry| $ 12))
+ (SPADCALL |dev| |x| (|getShellEntry| $ 14))
+ (SPADCALL |dev| (|getShellEntry| $ 15))
+ (SPADCALL |dev| (|getShellEntry| $ 16))
+ (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |DFLOAT;OMwrite;$S;1|)
(EXIT |s|)))))
-(DEFUN |DFLOAT;OMwrite;$BS;3| (|x| |wholeObj| $)
+(DEFUN |DFLOAT;OMwrite;$BS;2| (|x| |wholeObj| $)
(PROG (|sp| |dev| |s|)
(RETURN
- (SEQ (LETT |s| "" |DFLOAT;OMwrite;$BS;3|)
+ (SEQ (LETT |s| "" |DFLOAT;OMwrite;$BS;2|)
(LETT |sp| (OM-STRINGTOSTRINGPTR |s|)
- |DFLOAT;OMwrite;$BS;3|)
+ |DFLOAT;OMwrite;$BS;2|)
(LETT |dev|
- (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 10))
- (|getShellEntry| $ 12))
- |DFLOAT;OMwrite;$BS;3|)
- (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 14))))
- (SPADCALL |dev| |x| (|getShellEntry| $ 16))
- (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17))))
- (SPADCALL |dev| (|getShellEntry| $ 18))
+ (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 7))
+ (|getShellEntry| $ 10))
+ |DFLOAT;OMwrite;$BS;2|)
+ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 12))))
+ (SPADCALL |dev| |x| (|getShellEntry| $ 14))
+ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 15))))
+ (SPADCALL |dev| (|getShellEntry| $ 16))
(LETT |s| (OM-STRINGPTRTOSTRING |sp|)
- |DFLOAT;OMwrite;$BS;3|)
+ |DFLOAT;OMwrite;$BS;2|)
(EXIT |s|)))))
-(DEFUN |DFLOAT;OMwrite;Omd$V;4| (|dev| |x| $)
- (SEQ (SPADCALL |dev| (|getShellEntry| $ 14))
- (SPADCALL |dev| |x| (|getShellEntry| $ 16))
- (EXIT (SPADCALL |dev| (|getShellEntry| $ 17)))))
+(DEFUN |DFLOAT;OMwrite;Omd$V;3| (|dev| |x| $)
+ (SEQ (SPADCALL |dev| (|getShellEntry| $ 12))
+ (SPADCALL |dev| |x| (|getShellEntry| $ 14))
+ (EXIT (SPADCALL |dev| (|getShellEntry| $ 15)))))
-(DEFUN |DFLOAT;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $)
- (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 14))))
- (SPADCALL |dev| |x| (|getShellEntry| $ 16))
+(DEFUN |DFLOAT;OMwrite;Omd$BV;4| (|dev| |x| |wholeObj| $)
+ (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 12))))
+ (SPADCALL |dev| |x| (|getShellEntry| $ 14))
(EXIT (COND
- (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 17)))))))
+ (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 15)))))))
(PUT '|DFLOAT;checkComplex| '|SPADreplace| 'C-TO-R)
(DEFUN |DFLOAT;checkComplex| (|x| $) (C-TO-R |x|))
-(PUT '|DFLOAT;base;Pi;7| '|SPADreplace| '(XLAM NIL (FLOAT-RADIX 0.0)))
+(PUT '|DFLOAT;base;Pi;6| '|SPADreplace| '(XLAM NIL (FLOAT-RADIX 0.0)))
-(DEFUN |DFLOAT;base;Pi;7| ($) (FLOAT-RADIX 0.0))
+(DEFUN |DFLOAT;base;Pi;6| ($) (FLOAT-RADIX 0.0))
-(DEFUN |DFLOAT;mantissa;$I;8| (|x| $) (QCAR (|DFLOAT;manexp| |x| $)))
+(DEFUN |DFLOAT;mantissa;$I;7| (|x| $) (QCAR (|DFLOAT;manexp| |x| $)))
-(DEFUN |DFLOAT;exponent;$I;9| (|x| $) (QCDR (|DFLOAT;manexp| |x| $)))
+(DEFUN |DFLOAT;exponent;$I;8| (|x| $) (QCDR (|DFLOAT;manexp| |x| $)))
-(PUT '|DFLOAT;precision;Pi;10| '|SPADreplace|
+(PUT '|DFLOAT;precision;Pi;9| '|SPADreplace|
'(XLAM NIL (FLOAT-DIGITS 0.0)))
-(DEFUN |DFLOAT;precision;Pi;10| ($) (FLOAT-DIGITS 0.0))
+(DEFUN |DFLOAT;precision;Pi;9| ($) (FLOAT-DIGITS 0.0))
-(DEFUN |DFLOAT;bits;Pi;11| ($)
- (PROG (#0=#:G1421)
+(DEFUN |DFLOAT;bits;Pi;10| ($)
+ (PROG (#0=#:G1422)
(RETURN
(COND
((EQL (FLOAT-RADIX 0.0) 2) (FLOAT-DIGITS 0.0))
@@ -82,252 +75,251 @@
(SPADCALL
(FLOAT (FLOAT-RADIX 0.0)
|$DoubleFloatMaximum|)
- (|getShellEntry| $ 30))
- (|getShellEntry| $ 31)))
- |DFLOAT;bits;Pi;11|)
+ (|getShellEntry| $ 28))
+ (|getShellEntry| $ 29)))
+ |DFLOAT;bits;Pi;10|)
(|check-subtype| (> #0# 0) '(|PositiveInteger|) #0#)))))))
-(PUT '|DFLOAT;max;$;12| '|SPADreplace|
+(PUT '|DFLOAT;max;$;11| '|SPADreplace|
'(XLAM NIL |$DoubleFloatMaximum|))
-(DEFUN |DFLOAT;max;$;12| ($) |$DoubleFloatMaximum|)
+(DEFUN |DFLOAT;max;$;11| ($) |$DoubleFloatMaximum|)
-(PUT '|DFLOAT;min;$;13| '|SPADreplace|
+(PUT '|DFLOAT;min;$;12| '|SPADreplace|
'(XLAM NIL |$DoubleFloatMinimum|))
-(DEFUN |DFLOAT;min;$;13| ($) |$DoubleFloatMinimum|)
+(DEFUN |DFLOAT;min;$;12| ($) |$DoubleFloatMinimum|)
-(DEFUN |DFLOAT;order;$I;14| (|a| $)
- (- (+ (FLOAT-DIGITS 0.0) (SPADCALL |a| (|getShellEntry| $ 28))) 1))
+(DEFUN |DFLOAT;order;$I;13| (|a| $)
+ (- (+ (FLOAT-DIGITS 0.0) (SPADCALL |a| (|getShellEntry| $ 26))) 1))
-(PUT '|DFLOAT;Zero;$;15| '|SPADreplace|
+(PUT '|DFLOAT;Zero;$;14| '|SPADreplace|
'(XLAM NIL (FLOAT 0 |$DoubleFloatMaximum|)))
-(DEFUN |DFLOAT;Zero;$;15| ($) (FLOAT 0 |$DoubleFloatMaximum|))
+(DEFUN |DFLOAT;Zero;$;14| ($) (FLOAT 0 |$DoubleFloatMaximum|))
-(PUT '|DFLOAT;One;$;16| '|SPADreplace|
+(PUT '|DFLOAT;One;$;15| '|SPADreplace|
'(XLAM NIL (FLOAT 1 |$DoubleFloatMaximum|)))
-(DEFUN |DFLOAT;One;$;16| ($) (FLOAT 1 |$DoubleFloatMaximum|))
+(DEFUN |DFLOAT;One;$;15| ($) (FLOAT 1 |$DoubleFloatMaximum|))
-(DEFUN |DFLOAT;exp1;$;17| ($)
+(DEFUN |DFLOAT;exp1;$;16| ($)
(/ (FLOAT 534625820200 |$DoubleFloatMaximum|)
(FLOAT 196677847971 |$DoubleFloatMaximum|)))
-(PUT '|DFLOAT;pi;$;18| '|SPADreplace| '(XLAM NIL PI))
+(PUT '|DFLOAT;pi;$;17| '|SPADreplace| '(XLAM NIL PI))
-(DEFUN |DFLOAT;pi;$;18| ($) PI)
+(DEFUN |DFLOAT;pi;$;17| ($) PI)
-(DEFUN |DFLOAT;coerce;$Of;19| (|x| $)
- (SPADCALL (FORMAT NIL (|getShellEntry| $ 6) |x|)
- (|getShellEntry| $ 41)))
+(DEFUN |DFLOAT;coerce;$Of;18| (|x| $)
+ (SPADCALL |x| (|getShellEntry| $ 39)))
-(DEFUN |DFLOAT;convert;$If;20| (|x| $)
- (SPADCALL |x| (|getShellEntry| $ 44)))
+(DEFUN |DFLOAT;convert;$If;19| (|x| $)
+ (SPADCALL |x| (|getShellEntry| $ 42)))
-(PUT '|DFLOAT;<;2$B;21| '|SPADreplace| '<)
+(PUT '|DFLOAT;<;2$B;20| '|SPADreplace| '<)
-(DEFUN |DFLOAT;<;2$B;21| (|x| |y| $) (< |x| |y|))
+(DEFUN |DFLOAT;<;2$B;20| (|x| |y| $) (< |x| |y|))
-(PUT '|DFLOAT;-;2$;22| '|SPADreplace| '-)
+(PUT '|DFLOAT;-;2$;21| '|SPADreplace| '-)
-(DEFUN |DFLOAT;-;2$;22| (|x| $) (- |x|))
+(DEFUN |DFLOAT;-;2$;21| (|x| $) (- |x|))
-(PUT '|DFLOAT;+;3$;23| '|SPADreplace| '+)
+(PUT '|DFLOAT;+;3$;22| '|SPADreplace| '+)
-(DEFUN |DFLOAT;+;3$;23| (|x| |y| $) (+ |x| |y|))
+(DEFUN |DFLOAT;+;3$;22| (|x| |y| $) (+ |x| |y|))
-(PUT '|DFLOAT;-;3$;24| '|SPADreplace| '-)
+(PUT '|DFLOAT;-;3$;23| '|SPADreplace| '-)
-(DEFUN |DFLOAT;-;3$;24| (|x| |y| $) (- |x| |y|))
+(DEFUN |DFLOAT;-;3$;23| (|x| |y| $) (- |x| |y|))
-(PUT '|DFLOAT;*;3$;25| '|SPADreplace| '*)
+(PUT '|DFLOAT;*;3$;24| '|SPADreplace| '*)
-(DEFUN |DFLOAT;*;3$;25| (|x| |y| $) (* |x| |y|))
+(DEFUN |DFLOAT;*;3$;24| (|x| |y| $) (* |x| |y|))
-(PUT '|DFLOAT;*;I2$;26| '|SPADreplace| '*)
+(PUT '|DFLOAT;*;I2$;25| '|SPADreplace| '*)
-(DEFUN |DFLOAT;*;I2$;26| (|i| |x| $) (* |i| |x|))
+(DEFUN |DFLOAT;*;I2$;25| (|i| |x| $) (* |i| |x|))
-(PUT '|DFLOAT;max;3$;27| '|SPADreplace| 'MAX)
+(PUT '|DFLOAT;max;3$;26| '|SPADreplace| 'MAX)
-(DEFUN |DFLOAT;max;3$;27| (|x| |y| $) (MAX |x| |y|))
+(DEFUN |DFLOAT;max;3$;26| (|x| |y| $) (MAX |x| |y|))
-(PUT '|DFLOAT;min;3$;28| '|SPADreplace| 'MIN)
+(PUT '|DFLOAT;min;3$;27| '|SPADreplace| 'MIN)
-(DEFUN |DFLOAT;min;3$;28| (|x| |y| $) (MIN |x| |y|))
+(DEFUN |DFLOAT;min;3$;27| (|x| |y| $) (MIN |x| |y|))
-(PUT '|DFLOAT;=;2$B;29| '|SPADreplace| '=)
+(PUT '|DFLOAT;=;2$B;28| '|SPADreplace| '=)
-(DEFUN |DFLOAT;=;2$B;29| (|x| |y| $) (= |x| |y|))
+(DEFUN |DFLOAT;=;2$B;28| (|x| |y| $) (= |x| |y|))
-(PUT '|DFLOAT;/;$I$;30| '|SPADreplace| '/)
+(PUT '|DFLOAT;/;$I$;29| '|SPADreplace| '/)
-(DEFUN |DFLOAT;/;$I$;30| (|x| |i| $) (/ |x| |i|))
+(DEFUN |DFLOAT;/;$I$;29| (|x| |i| $) (/ |x| |i|))
-(DEFUN |DFLOAT;sqrt;2$;31| (|x| $)
+(DEFUN |DFLOAT;sqrt;2$;30| (|x| $)
(|DFLOAT;checkComplex| (SQRT |x|) $))
-(DEFUN |DFLOAT;log10;2$;32| (|x| $)
+(DEFUN |DFLOAT;log10;2$;31| (|x| $)
(|DFLOAT;checkComplex| (|log| |x|) $))
-(PUT '|DFLOAT;**;$I$;33| '|SPADreplace| 'EXPT)
+(PUT '|DFLOAT;**;$I$;32| '|SPADreplace| 'EXPT)
-(DEFUN |DFLOAT;**;$I$;33| (|x| |i| $) (EXPT |x| |i|))
+(DEFUN |DFLOAT;**;$I$;32| (|x| |i| $) (EXPT |x| |i|))
-(DEFUN |DFLOAT;**;3$;34| (|x| |y| $)
+(DEFUN |DFLOAT;**;3$;33| (|x| |y| $)
(|DFLOAT;checkComplex| (EXPT |x| |y|) $))
-(PUT '|DFLOAT;coerce;I$;35| '|SPADreplace|
+(PUT '|DFLOAT;coerce;I$;34| '|SPADreplace|
'(XLAM (|i|) (FLOAT |i| |$DoubleFloatMaximum|)))
-(DEFUN |DFLOAT;coerce;I$;35| (|i| $)
+(DEFUN |DFLOAT;coerce;I$;34| (|i| $)
(FLOAT |i| |$DoubleFloatMaximum|))
-(PUT '|DFLOAT;exp;2$;36| '|SPADreplace| 'EXP)
+(PUT '|DFLOAT;exp;2$;35| '|SPADreplace| 'EXP)
-(DEFUN |DFLOAT;exp;2$;36| (|x| $) (EXP |x|))
+(DEFUN |DFLOAT;exp;2$;35| (|x| $) (EXP |x|))
-(DEFUN |DFLOAT;log;2$;37| (|x| $) (|DFLOAT;checkComplex| (LN |x|) $))
+(DEFUN |DFLOAT;log;2$;36| (|x| $) (|DFLOAT;checkComplex| (LN |x|) $))
-(DEFUN |DFLOAT;log2;2$;38| (|x| $)
+(DEFUN |DFLOAT;log2;2$;37| (|x| $)
(|DFLOAT;checkComplex| (LOG2 |x|) $))
-(PUT '|DFLOAT;sin;2$;39| '|SPADreplace| 'SIN)
+(PUT '|DFLOAT;sin;2$;38| '|SPADreplace| 'SIN)
-(DEFUN |DFLOAT;sin;2$;39| (|x| $) (SIN |x|))
+(DEFUN |DFLOAT;sin;2$;38| (|x| $) (SIN |x|))
-(PUT '|DFLOAT;cos;2$;40| '|SPADreplace| 'COS)
+(PUT '|DFLOAT;cos;2$;39| '|SPADreplace| 'COS)
-(DEFUN |DFLOAT;cos;2$;40| (|x| $) (COS |x|))
+(DEFUN |DFLOAT;cos;2$;39| (|x| $) (COS |x|))
-(PUT '|DFLOAT;tan;2$;41| '|SPADreplace| 'TAN)
+(PUT '|DFLOAT;tan;2$;40| '|SPADreplace| 'TAN)
-(DEFUN |DFLOAT;tan;2$;41| (|x| $) (TAN |x|))
+(DEFUN |DFLOAT;tan;2$;40| (|x| $) (TAN |x|))
-(PUT '|DFLOAT;cot;2$;42| '|SPADreplace| 'COT)
+(PUT '|DFLOAT;cot;2$;41| '|SPADreplace| 'COT)
-(DEFUN |DFLOAT;cot;2$;42| (|x| $) (COT |x|))
+(DEFUN |DFLOAT;cot;2$;41| (|x| $) (COT |x|))
-(PUT '|DFLOAT;sec;2$;43| '|SPADreplace| 'SEC)
+(PUT '|DFLOAT;sec;2$;42| '|SPADreplace| 'SEC)
-(DEFUN |DFLOAT;sec;2$;43| (|x| $) (SEC |x|))
+(DEFUN |DFLOAT;sec;2$;42| (|x| $) (SEC |x|))
-(PUT '|DFLOAT;csc;2$;44| '|SPADreplace| 'CSC)
+(PUT '|DFLOAT;csc;2$;43| '|SPADreplace| 'CSC)
-(DEFUN |DFLOAT;csc;2$;44| (|x| $) (CSC |x|))
+(DEFUN |DFLOAT;csc;2$;43| (|x| $) (CSC |x|))
-(DEFUN |DFLOAT;asin;2$;45| (|x| $)
+(DEFUN |DFLOAT;asin;2$;44| (|x| $)
(|DFLOAT;checkComplex| (ASIN |x|) $))
-(DEFUN |DFLOAT;acos;2$;46| (|x| $)
+(DEFUN |DFLOAT;acos;2$;45| (|x| $)
(|DFLOAT;checkComplex| (ACOS |x|) $))
-(PUT '|DFLOAT;atan;2$;47| '|SPADreplace| 'ATAN)
+(PUT '|DFLOAT;atan;2$;46| '|SPADreplace| 'ATAN)
-(DEFUN |DFLOAT;atan;2$;47| (|x| $) (ATAN |x|))
+(DEFUN |DFLOAT;atan;2$;46| (|x| $) (ATAN |x|))
-(DEFUN |DFLOAT;acsc;2$;48| (|x| $)
+(DEFUN |DFLOAT;acsc;2$;47| (|x| $)
(|DFLOAT;checkComplex| (ACSC |x|) $))
-(PUT '|DFLOAT;acot;2$;49| '|SPADreplace| 'ACOT)
+(PUT '|DFLOAT;acot;2$;48| '|SPADreplace| 'ACOT)
-(DEFUN |DFLOAT;acot;2$;49| (|x| $) (ACOT |x|))
+(DEFUN |DFLOAT;acot;2$;48| (|x| $) (ACOT |x|))
-(DEFUN |DFLOAT;asec;2$;50| (|x| $)
+(DEFUN |DFLOAT;asec;2$;49| (|x| $)
(|DFLOAT;checkComplex| (ASEC |x|) $))
-(PUT '|DFLOAT;sinh;2$;51| '|SPADreplace| 'SINH)
+(PUT '|DFLOAT;sinh;2$;50| '|SPADreplace| 'SINH)
-(DEFUN |DFLOAT;sinh;2$;51| (|x| $) (SINH |x|))
+(DEFUN |DFLOAT;sinh;2$;50| (|x| $) (SINH |x|))
-(PUT '|DFLOAT;cosh;2$;52| '|SPADreplace| 'COSH)
+(PUT '|DFLOAT;cosh;2$;51| '|SPADreplace| 'COSH)
-(DEFUN |DFLOAT;cosh;2$;52| (|x| $) (COSH |x|))
+(DEFUN |DFLOAT;cosh;2$;51| (|x| $) (COSH |x|))
-(PUT '|DFLOAT;tanh;2$;53| '|SPADreplace| 'TANH)
+(PUT '|DFLOAT;tanh;2$;52| '|SPADreplace| 'TANH)
-(DEFUN |DFLOAT;tanh;2$;53| (|x| $) (TANH |x|))
+(DEFUN |DFLOAT;tanh;2$;52| (|x| $) (TANH |x|))
-(PUT '|DFLOAT;csch;2$;54| '|SPADreplace| 'CSCH)
+(PUT '|DFLOAT;csch;2$;53| '|SPADreplace| 'CSCH)
-(DEFUN |DFLOAT;csch;2$;54| (|x| $) (CSCH |x|))
+(DEFUN |DFLOAT;csch;2$;53| (|x| $) (CSCH |x|))
-(PUT '|DFLOAT;coth;2$;55| '|SPADreplace| 'COTH)
+(PUT '|DFLOAT;coth;2$;54| '|SPADreplace| 'COTH)
-(DEFUN |DFLOAT;coth;2$;55| (|x| $) (COTH |x|))
+(DEFUN |DFLOAT;coth;2$;54| (|x| $) (COTH |x|))
-(PUT '|DFLOAT;sech;2$;56| '|SPADreplace| 'SECH)
+(PUT '|DFLOAT;sech;2$;55| '|SPADreplace| 'SECH)
-(DEFUN |DFLOAT;sech;2$;56| (|x| $) (SECH |x|))
+(DEFUN |DFLOAT;sech;2$;55| (|x| $) (SECH |x|))
-(PUT '|DFLOAT;asinh;2$;57| '|SPADreplace| 'ASINH)
+(PUT '|DFLOAT;asinh;2$;56| '|SPADreplace| 'ASINH)
-(DEFUN |DFLOAT;asinh;2$;57| (|x| $) (ASINH |x|))
+(DEFUN |DFLOAT;asinh;2$;56| (|x| $) (ASINH |x|))
-(DEFUN |DFLOAT;acosh;2$;58| (|x| $)
+(DEFUN |DFLOAT;acosh;2$;57| (|x| $)
(|DFLOAT;checkComplex| (ACOSH |x|) $))
-(DEFUN |DFLOAT;atanh;2$;59| (|x| $)
+(DEFUN |DFLOAT;atanh;2$;58| (|x| $)
(|DFLOAT;checkComplex| (ATANH |x|) $))
-(PUT '|DFLOAT;acsch;2$;60| '|SPADreplace| 'ACSCH)
+(PUT '|DFLOAT;acsch;2$;59| '|SPADreplace| 'ACSCH)
-(DEFUN |DFLOAT;acsch;2$;60| (|x| $) (ACSCH |x|))
+(DEFUN |DFLOAT;acsch;2$;59| (|x| $) (ACSCH |x|))
-(DEFUN |DFLOAT;acoth;2$;61| (|x| $)
+(DEFUN |DFLOAT;acoth;2$;60| (|x| $)
(|DFLOAT;checkComplex| (ACOTH |x|) $))
-(DEFUN |DFLOAT;asech;2$;62| (|x| $)
+(DEFUN |DFLOAT;asech;2$;61| (|x| $)
(|DFLOAT;checkComplex| (ASECH |x|) $))
-(PUT '|DFLOAT;/;3$;63| '|SPADreplace| '/)
+(PUT '|DFLOAT;/;3$;62| '|SPADreplace| '/)
-(DEFUN |DFLOAT;/;3$;63| (|x| |y| $) (/ |x| |y|))
+(DEFUN |DFLOAT;/;3$;62| (|x| |y| $) (/ |x| |y|))
-(PUT '|DFLOAT;negative?;$B;64| '|SPADreplace| 'MINUSP)
+(PUT '|DFLOAT;negative?;$B;63| '|SPADreplace| 'MINUSP)
-(DEFUN |DFLOAT;negative?;$B;64| (|x| $) (MINUSP |x|))
+(DEFUN |DFLOAT;negative?;$B;63| (|x| $) (MINUSP |x|))
-(PUT '|DFLOAT;zero?;$B;65| '|SPADreplace| 'ZEROP)
+(PUT '|DFLOAT;zero?;$B;64| '|SPADreplace| 'ZEROP)
-(DEFUN |DFLOAT;zero?;$B;65| (|x| $) (ZEROP |x|))
+(DEFUN |DFLOAT;zero?;$B;64| (|x| $) (ZEROP |x|))
-(PUT '|DFLOAT;hash;$Si;66| '|SPADreplace| 'HASHEQ)
+(PUT '|DFLOAT;hash;$Si;65| '|SPADreplace| 'HASHEQ)
-(DEFUN |DFLOAT;hash;$Si;66| (|x| $) (HASHEQ |x|))
+(DEFUN |DFLOAT;hash;$Si;65| (|x| $) (HASHEQ |x|))
-(DEFUN |DFLOAT;recip;$U;67| (|x| $)
+(DEFUN |DFLOAT;recip;$U;66| (|x| $)
(COND ((ZEROP |x|) (CONS 1 "failed")) ('T (CONS 0 (/ 1.0 |x|)))))
-(PUT '|DFLOAT;differentiate;2$;68| '|SPADreplace| '(XLAM (|x|) 0.0))
+(PUT '|DFLOAT;differentiate;2$;67| '|SPADreplace| '(XLAM (|x|) 0.0))
-(DEFUN |DFLOAT;differentiate;2$;68| (|x| $) 0.0)
+(DEFUN |DFLOAT;differentiate;2$;67| (|x| $) 0.0)
-(DEFUN |DFLOAT;Gamma;2$;69| (|x| $)
- (SPADCALL |x| (|getShellEntry| $ 96)))
+(DEFUN |DFLOAT;Gamma;2$;68| (|x| $)
+ (SPADCALL |x| (|getShellEntry| $ 94)))
-(DEFUN |DFLOAT;Beta;3$;70| (|x| |y| $)
- (SPADCALL |x| |y| (|getShellEntry| $ 98)))
+(DEFUN |DFLOAT;Beta;3$;69| (|x| |y| $)
+ (SPADCALL |x| |y| (|getShellEntry| $ 96)))
-(PUT '|DFLOAT;wholePart;$I;71| '|SPADreplace| 'FIX)
+(PUT '|DFLOAT;wholePart;$I;70| '|SPADreplace| 'FIX)
-(DEFUN |DFLOAT;wholePart;$I;71| (|x| $) (FIX |x|))
+(DEFUN |DFLOAT;wholePart;$I;70| (|x| $) (FIX |x|))
-(DEFUN |DFLOAT;float;2IPi$;72| (|ma| |ex| |b| $)
+(DEFUN |DFLOAT;float;2IPi$;71| (|ma| |ex| |b| $)
(* |ma| (EXPT (FLOAT |b| |$DoubleFloatMaximum|) |ex|)))
-(PUT '|DFLOAT;convert;2$;73| '|SPADreplace| '(XLAM (|x|) |x|))
+(PUT '|DFLOAT;convert;2$;72| '|SPADreplace| '(XLAM (|x|) |x|))
-(DEFUN |DFLOAT;convert;2$;73| (|x| $) |x|)
+(DEFUN |DFLOAT;convert;2$;72| (|x| $) |x|)
-(DEFUN |DFLOAT;convert;$F;74| (|x| $)
- (SPADCALL |x| (|getShellEntry| $ 104)))
+(DEFUN |DFLOAT;convert;$F;73| (|x| $)
+ (SPADCALL |x| (|getShellEntry| $ 102)))
-(DEFUN |DFLOAT;rationalApproximation;$NniF;75| (|x| |d| $)
- (SPADCALL |x| |d| 10 (|getShellEntry| $ 108)))
+(DEFUN |DFLOAT;rationalApproximation;$NniF;74| (|x| |d| $)
+ (SPADCALL |x| |d| 10 (|getShellEntry| $ 106)))
-(DEFUN |DFLOAT;atan;3$;76| (|x| |y| $)
+(DEFUN |DFLOAT;atan;3$;75| (|x| |y| $)
(PROG (|theta|)
(RETURN
(SEQ (COND
@@ -338,68 +330,68 @@
('T 0.0)))
('T
(SEQ (LETT |theta| (ATAN (FLOAT-SIGN 1.0 (/ |y| |x|)))
- |DFLOAT;atan;3$;76|)
+ |DFLOAT;atan;3$;75|)
(COND
((< |x| 0.0)
- (LETT |theta| (- PI |theta|) |DFLOAT;atan;3$;76|)))
+ (LETT |theta| (- PI |theta|) |DFLOAT;atan;3$;75|)))
(COND
((< |y| 0.0)
- (LETT |theta| (- |theta|) |DFLOAT;atan;3$;76|)))
+ (LETT |theta| (- |theta|) |DFLOAT;atan;3$;75|)))
(EXIT |theta|))))))))
-(DEFUN |DFLOAT;retract;$F;77| (|x| $)
- (PROG (#0=#:G1496)
+(DEFUN |DFLOAT;retract;$F;76| (|x| $)
+ (PROG (#0=#:G1497)
(RETURN
(SPADCALL |x|
(PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1)
- |DFLOAT;retract;$F;77|)
+ |DFLOAT;retract;$F;76|)
(|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#))
- (FLOAT-RADIX 0.0) (|getShellEntry| $ 108)))))
+ (FLOAT-RADIX 0.0) (|getShellEntry| $ 106)))))
-(DEFUN |DFLOAT;retractIfCan;$U;78| (|x| $)
- (PROG (#0=#:G1501)
+(DEFUN |DFLOAT;retractIfCan;$U;77| (|x| $)
+ (PROG (#0=#:G1502)
(RETURN
(CONS 0
(SPADCALL |x|
(PROG1 (LETT #0# (- (FLOAT-DIGITS 0.0) 1)
- |DFLOAT;retractIfCan;$U;78|)
+ |DFLOAT;retractIfCan;$U;77|)
(|check-subtype| (>= #0# 0) '(|NonNegativeInteger|)
#0#))
- (FLOAT-RADIX 0.0) (|getShellEntry| $ 108))))))
+ (FLOAT-RADIX 0.0) (|getShellEntry| $ 106))))))
-(DEFUN |DFLOAT;retract;$I;79| (|x| $)
+(DEFUN |DFLOAT;retract;$I;78| (|x| $)
(PROG (|n|)
(RETURN
- (SEQ (LETT |n| (FIX |x|) |DFLOAT;retract;$I;79|)
+ (SEQ (LETT |n| (FIX |x|) |DFLOAT;retract;$I;78|)
(EXIT (COND
((= |x| (FLOAT |n| |$DoubleFloatMaximum|)) |n|)
('T (|error| "Not an integer"))))))))
-(DEFUN |DFLOAT;retractIfCan;$U;80| (|x| $)
+(DEFUN |DFLOAT;retractIfCan;$U;79| (|x| $)
(PROG (|n|)
(RETURN
- (SEQ (LETT |n| (FIX |x|) |DFLOAT;retractIfCan;$U;80|)
+ (SEQ (LETT |n| (FIX |x|) |DFLOAT;retractIfCan;$U;79|)
(EXIT (COND
((= |x| (FLOAT |n| |$DoubleFloatMaximum|))
(CONS 0 |n|))
('T (CONS 1 "failed"))))))))
-(DEFUN |DFLOAT;sign;$I;81| (|x| $)
- (SPADCALL (FLOAT-SIGN |x| 1.0) (|getShellEntry| $ 114)))
+(DEFUN |DFLOAT;sign;$I;80| (|x| $)
+ (SPADCALL (FLOAT-SIGN |x| 1.0) (|getShellEntry| $ 112)))
-(PUT '|DFLOAT;abs;2$;82| '|SPADreplace|
+(PUT '|DFLOAT;abs;2$;81| '|SPADreplace|
'(XLAM (|x|) (FLOAT-SIGN 1.0 |x|)))
-(DEFUN |DFLOAT;abs;2$;82| (|x| $) (FLOAT-SIGN 1.0 |x|))
+(DEFUN |DFLOAT;abs;2$;81| (|x| $) (FLOAT-SIGN 1.0 |x|))
(DEFUN |DFLOAT;manexp| (|x| $)
- (PROG (|s| #0=#:G1522 |me| |two53|)
+ (PROG (|s| #0=#:G1523 |me| |two53|)
(RETURN
(SEQ (EXIT (COND
((ZEROP |x|) (CONS 0 0))
('T
(SEQ (LETT |s|
- (SPADCALL |x| (|getShellEntry| $ 117))
+ (SPADCALL |x| (|getShellEntry| $ 115))
|DFLOAT;manexp|)
(LETT |x| (FLOAT-SIGN 1.0 |x|)
|DFLOAT;manexp|)
@@ -411,48 +403,48 @@
(+
(* |s|
(SPADCALL |$DoubleFloatMaximum|
- (|getShellEntry| $ 27)))
+ (|getShellEntry| $ 25)))
1)
(SPADCALL |$DoubleFloatMaximum|
- (|getShellEntry| $ 28)))
+ (|getShellEntry| $ 26)))
|DFLOAT;manexp|)
(GO #0#))))
(LETT |me| (MANEXP |x|) |DFLOAT;manexp|)
(LETT |two53|
(SPADCALL (FLOAT-RADIX 0.0)
(FLOAT-DIGITS 0.0)
- (|getShellEntry| $ 119))
+ (|getShellEntry| $ 117))
|DFLOAT;manexp|)
(EXIT (CONS (* |s|
(FIX (* |two53| (QCAR |me|))))
(- (QCDR |me|) (FLOAT-DIGITS 0.0))))))))
#0# (EXIT #0#)))))
-(DEFUN |DFLOAT;rationalApproximation;$2NniF;84| (|f| |d| |b| $)
- (PROG (|#G103| |nu| |ex| BASE #0=#:G1524 |de| |tol| |#G104| |q| |r|
- |p2| |q2| #1=#:G1540 |#G105| |#G106| |p0| |p1| |#G107|
- |#G108| |q0| |q1| |#G109| |#G110| |s| |t| #2=#:G1538)
+(DEFUN |DFLOAT;rationalApproximation;$2NniF;83| (|f| |d| |b| $)
+ (PROG (|#G102| |nu| |ex| BASE #0=#:G1525 |de| |tol| |#G103| |q| |r|
+ |p2| |q2| #1=#:G1541 |#G104| |#G105| |p0| |p1| |#G106|
+ |#G107| |q0| |q1| |#G108| |#G109| |s| |t| #2=#:G1539)
(RETURN
(SEQ (EXIT (SEQ (PROGN
- (LETT |#G103| (|DFLOAT;manexp| |f| $)
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |nu| (QCAR |#G103|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |ex| (QCDR |#G103|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
- |#G103|)
+ (LETT |#G102| (|DFLOAT;manexp| |f| $)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |nu| (QCAR |#G102|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |ex| (QCDR |#G102|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ |#G102|)
(LETT BASE (FLOAT-RADIX 0.0)
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(EXIT (COND
((< |ex| 0)
(SEQ (LETT |de|
(EXPT BASE
(PROG1
(LETT #0# (- |ex|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(|check-subtype| (>= #0# 0)
'(|NonNegativeInteger|) #0#)))
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(EXIT
(COND
((< |b| 2)
@@ -460,37 +452,37 @@
('T
(SEQ
(LETT |tol| (EXPT |b| |d|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |s| |nu|
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |t| |de|
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |p0| 0
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |p1| 1
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |q0| 1
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |q1| 0
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(EXIT
(SEQ G190 NIL
(SEQ
(PROGN
- (LETT |#G104|
+ (LETT |#G103|
(DIVIDE2 |s| |t|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |q| (QCAR |#G104|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |r| (QCDR |#G104|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
- |#G104|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |q| (QCAR |#G103|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |r| (QCDR |#G103|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ |#G103|)
(LETT |p2|
(+ (* |q| |p1|) |p0|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(LETT |q2|
(+ (* |q| |q1|) |q0|)
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(COND
((OR (EQL |r| 0)
(<
@@ -499,44 +491,44 @@
(- (* |nu| |q2|)
(* |de| |p2|)))
(|getShellEntry| $
- 122))
+ 120))
(* |de| (ABS |p2|))))
(EXIT
(PROGN
(LETT #1#
(SPADCALL |p2| |q2|
(|getShellEntry| $
- 121))
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ 119))
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(GO #1#)))))
(PROGN
- (LETT |#G105| |p1|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |#G106| |p2|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |p0| |#G105|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |p1| |#G106|
- |DFLOAT;rationalApproximation;$2NniF;84|))
+ (LETT |#G104| |p1|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |#G105| |p2|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |p0| |#G104|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |p1| |#G105|
+ |DFLOAT;rationalApproximation;$2NniF;83|))
(PROGN
- (LETT |#G107| |q1|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |#G108| |q2|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |q0| |#G107|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |q1| |#G108|
- |DFLOAT;rationalApproximation;$2NniF;84|))
+ (LETT |#G106| |q1|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |#G107| |q2|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |q0| |#G106|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |q1| |#G107|
+ |DFLOAT;rationalApproximation;$2NniF;83|))
(EXIT
(PROGN
- (LETT |#G109| |t|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |#G110| |r|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |s| |#G109|
- |DFLOAT;rationalApproximation;$2NniF;84|)
- (LETT |t| |#G110|
- |DFLOAT;rationalApproximation;$2NniF;84|))))
+ (LETT |#G108| |t|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |#G109| |r|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |s| |#G108|
+ |DFLOAT;rationalApproximation;$2NniF;83|)
+ (LETT |t| |#G109|
+ |DFLOAT;rationalApproximation;$2NniF;83|))))
NIL (GO G190) G191
(EXIT NIL)))))))))
('T
@@ -545,40 +537,40 @@
(EXPT BASE
(PROG1
(LETT #2# |ex|
- |DFLOAT;rationalApproximation;$2NniF;84|)
+ |DFLOAT;rationalApproximation;$2NniF;83|)
(|check-subtype| (>= #2# 0)
'(|NonNegativeInteger|) #2#))))
- (|getShellEntry| $ 123)))))))
+ (|getShellEntry| $ 121)))))))
#1# (EXIT #1#)))))
-(DEFUN |DFLOAT;**;$F$;85| (|x| |r| $)
- (PROG (|n| |d| #0=#:G1549)
+(DEFUN |DFLOAT;**;$F$;84| (|x| |r| $)
+ (PROG (|n| |d| #0=#:G1550)
(RETURN
(SEQ (EXIT (COND
((ZEROP |x|)
(COND
- ((SPADCALL |r| (|getShellEntry| $ 124))
+ ((SPADCALL |r| (|getShellEntry| $ 122))
(|error| "0**0 is undefined"))
- ((SPADCALL |r| (|getShellEntry| $ 125))
+ ((SPADCALL |r| (|getShellEntry| $ 123))
(|error| "division by 0"))
('T 0.0)))
- ((OR (SPADCALL |r| (|getShellEntry| $ 124))
+ ((OR (SPADCALL |r| (|getShellEntry| $ 122))
(= |x| 1.0))
1.0)
('T
(COND
- ((SPADCALL |r| (|spadConstant| $ 126)
- (|getShellEntry| $ 127))
+ ((SPADCALL |r| (|spadConstant| $ 124)
+ (|getShellEntry| $ 125))
|x|)
('T
(SEQ (LETT |n|
(SPADCALL |r|
- (|getShellEntry| $ 128))
- |DFLOAT;**;$F$;85|)
+ (|getShellEntry| $ 126))
+ |DFLOAT;**;$F$;84|)
(LETT |d|
(SPADCALL |r|
- (|getShellEntry| $ 129))
- |DFLOAT;**;$F$;85|)
+ (|getShellEntry| $ 127))
+ |DFLOAT;**;$F$;84|)
(EXIT (COND
((MINUSP |x|)
(COND
@@ -589,21 +581,21 @@
(LETT #0#
(-
(SPADCALL (- |x|) |r|
- (|getShellEntry| $ 130)))
- |DFLOAT;**;$F$;85|)
+ (|getShellEntry| $ 128)))
+ |DFLOAT;**;$F$;84|)
(GO #0#)))
('T
(PROGN
(LETT #0#
(SPADCALL (- |x|) |r|
- (|getShellEntry| $ 130))
- |DFLOAT;**;$F$;85|)
+ (|getShellEntry| $ 128))
+ |DFLOAT;**;$F$;84|)
(GO #0#)))))
('T (|error| "negative root"))))
((EQL |d| 2)
(EXPT
(SPADCALL |x|
- (|getShellEntry| $ 56))
+ (|getShellEntry| $ 54))
|n|))
('T
(SPADCALL |x|
@@ -612,13 +604,13 @@
|$DoubleFloatMaximum|)
(FLOAT |d|
|$DoubleFloatMaximum|))
- (|getShellEntry| $ 59)))))))))))
+ (|getShellEntry| $ 57)))))))))))
#0# (EXIT #0#)))))
(DEFUN |DoubleFloat| ()
(PROG ()
(RETURN
- (PROG (#0=#:G1562)
+ (PROG (#0=#:G1563)
(RETURN
(COND
((LETT #0# (HGET |$ConstructorCache| '|DoubleFloat|)
@@ -639,81 +631,79 @@
(RETURN
(PROGN
(LETT |dv$| '(|DoubleFloat|) . #0=(|DoubleFloat|))
- (LETT $ (|newShell| 143) . #0#)
+ (LETT $ (|newShell| 141) . #0#)
(|setShellEntry| $ 0 |dv$|)
(|setShellEntry| $ 3
(LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
(|haddProp| |$ConstructorCache| '|DoubleFloat| NIL (CONS 1 $))
(|stuffDomainSlots| $)
- (|setShellEntry| $ 6 "~G")
$))))
(MAKEPROP '|DoubleFloat| '|infovec|
- (LIST '#(NIL NIL NIL NIL NIL NIL '|format| (|String|)
- |DFLOAT;doubleFloatFormat;2S;1| (|OpenMathEncoding|)
- (0 . |OMencodingXML|) (|OpenMathDevice|)
+ (LIST '#(NIL NIL NIL NIL NIL NIL (|OpenMathEncoding|)
+ (0 . |OMencodingXML|) (|String|) (|OpenMathDevice|)
(4 . |OMopenString|) (|Void|) (10 . |OMputObject|)
(|DoubleFloat|) (15 . |OMputFloat|)
(21 . |OMputEndObject|) (26 . |OMclose|)
- |DFLOAT;OMwrite;$S;2| (|Boolean|) |DFLOAT;OMwrite;$BS;3|
- |DFLOAT;OMwrite;Omd$V;4| |DFLOAT;OMwrite;Omd$BV;5|
- (|PositiveInteger|) |DFLOAT;base;Pi;7| (|Integer|)
- |DFLOAT;mantissa;$I;8| |DFLOAT;exponent;$I;9|
- |DFLOAT;precision;Pi;10| |DFLOAT;log2;2$;38| (31 . *)
- |DFLOAT;bits;Pi;11| |DFLOAT;max;$;12| |DFLOAT;min;$;13|
- |DFLOAT;order;$I;14|
+ |DFLOAT;OMwrite;$S;1| (|Boolean|) |DFLOAT;OMwrite;$BS;2|
+ |DFLOAT;OMwrite;Omd$V;3| |DFLOAT;OMwrite;Omd$BV;4|
+ (|PositiveInteger|) |DFLOAT;base;Pi;6| (|Integer|)
+ |DFLOAT;mantissa;$I;7| |DFLOAT;exponent;$I;8|
+ |DFLOAT;precision;Pi;9| |DFLOAT;log2;2$;37| (31 . *)
+ |DFLOAT;bits;Pi;10| |DFLOAT;max;$;11| |DFLOAT;min;$;12|
+ |DFLOAT;order;$I;13|
(CONS IDENTITY
- (FUNCALL (|dispatchFunction| |DFLOAT;Zero;$;15|) $))
+ (FUNCALL (|dispatchFunction| |DFLOAT;Zero;$;14|) $))
(CONS IDENTITY
- (FUNCALL (|dispatchFunction| |DFLOAT;One;$;16|) $))
- |DFLOAT;exp1;$;17| |DFLOAT;pi;$;18| (|OutputForm|)
- (37 . |outputForm|) |DFLOAT;coerce;$Of;19| (|InputForm|)
- (42 . |convert|) |DFLOAT;convert;$If;20| |DFLOAT;<;2$B;21|
- |DFLOAT;-;2$;22| |DFLOAT;+;3$;23| |DFLOAT;-;3$;24|
- |DFLOAT;*;3$;25| |DFLOAT;*;I2$;26| |DFLOAT;max;3$;27|
- |DFLOAT;min;3$;28| |DFLOAT;=;2$B;29| |DFLOAT;/;$I$;30|
- |DFLOAT;sqrt;2$;31| |DFLOAT;log10;2$;32|
- |DFLOAT;**;$I$;33| |DFLOAT;**;3$;34| |DFLOAT;coerce;I$;35|
- |DFLOAT;exp;2$;36| |DFLOAT;log;2$;37| |DFLOAT;sin;2$;39|
- |DFLOAT;cos;2$;40| |DFLOAT;tan;2$;41| |DFLOAT;cot;2$;42|
- |DFLOAT;sec;2$;43| |DFLOAT;csc;2$;44| |DFLOAT;asin;2$;45|
- |DFLOAT;acos;2$;46| |DFLOAT;atan;2$;47|
- |DFLOAT;acsc;2$;48| |DFLOAT;acot;2$;49|
- |DFLOAT;asec;2$;50| |DFLOAT;sinh;2$;51|
- |DFLOAT;cosh;2$;52| |DFLOAT;tanh;2$;53|
- |DFLOAT;csch;2$;54| |DFLOAT;coth;2$;55|
- |DFLOAT;sech;2$;56| |DFLOAT;asinh;2$;57|
- |DFLOAT;acosh;2$;58| |DFLOAT;atanh;2$;59|
- |DFLOAT;acsch;2$;60| |DFLOAT;acoth;2$;61|
- |DFLOAT;asech;2$;62| |DFLOAT;/;3$;63|
- |DFLOAT;negative?;$B;64| |DFLOAT;zero?;$B;65|
- (|SingleInteger|) |DFLOAT;hash;$Si;66|
- (|Union| $ '"failed") |DFLOAT;recip;$U;67|
- |DFLOAT;differentiate;2$;68|
+ (FUNCALL (|dispatchFunction| |DFLOAT;One;$;15|) $))
+ |DFLOAT;exp1;$;16| |DFLOAT;pi;$;17| (|OutputForm|)
+ (37 . |outputForm|) |DFLOAT;coerce;$Of;18| (|InputForm|)
+ (42 . |convert|) |DFLOAT;convert;$If;19| |DFLOAT;<;2$B;20|
+ |DFLOAT;-;2$;21| |DFLOAT;+;3$;22| |DFLOAT;-;3$;23|
+ |DFLOAT;*;3$;24| |DFLOAT;*;I2$;25| |DFLOAT;max;3$;26|
+ |DFLOAT;min;3$;27| |DFLOAT;=;2$B;28| |DFLOAT;/;$I$;29|
+ |DFLOAT;sqrt;2$;30| |DFLOAT;log10;2$;31|
+ |DFLOAT;**;$I$;32| |DFLOAT;**;3$;33| |DFLOAT;coerce;I$;34|
+ |DFLOAT;exp;2$;35| |DFLOAT;log;2$;36| |DFLOAT;sin;2$;38|
+ |DFLOAT;cos;2$;39| |DFLOAT;tan;2$;40| |DFLOAT;cot;2$;41|
+ |DFLOAT;sec;2$;42| |DFLOAT;csc;2$;43| |DFLOAT;asin;2$;44|
+ |DFLOAT;acos;2$;45| |DFLOAT;atan;2$;46|
+ |DFLOAT;acsc;2$;47| |DFLOAT;acot;2$;48|
+ |DFLOAT;asec;2$;49| |DFLOAT;sinh;2$;50|
+ |DFLOAT;cosh;2$;51| |DFLOAT;tanh;2$;52|
+ |DFLOAT;csch;2$;53| |DFLOAT;coth;2$;54|
+ |DFLOAT;sech;2$;55| |DFLOAT;asinh;2$;56|
+ |DFLOAT;acosh;2$;57| |DFLOAT;atanh;2$;58|
+ |DFLOAT;acsch;2$;59| |DFLOAT;acoth;2$;60|
+ |DFLOAT;asech;2$;61| |DFLOAT;/;3$;62|
+ |DFLOAT;negative?;$B;63| |DFLOAT;zero?;$B;64|
+ (|SingleInteger|) |DFLOAT;hash;$Si;65|
+ (|Union| $ '"failed") |DFLOAT;recip;$U;66|
+ |DFLOAT;differentiate;2$;67|
(|DoubleFloatSpecialFunctions|) (47 . |Gamma|)
- |DFLOAT;Gamma;2$;69| (52 . |Beta|) |DFLOAT;Beta;3$;70|
- |DFLOAT;wholePart;$I;71| |DFLOAT;float;2IPi$;72|
- |DFLOAT;convert;2$;73| (|Float|) (58 . |convert|)
- |DFLOAT;convert;$F;74| (|Fraction| 26)
+ |DFLOAT;Gamma;2$;68| (52 . |Beta|) |DFLOAT;Beta;3$;69|
+ |DFLOAT;wholePart;$I;70| |DFLOAT;float;2IPi$;71|
+ |DFLOAT;convert;2$;72| (|Float|) (58 . |convert|)
+ |DFLOAT;convert;$F;73| (|Fraction| 24)
(|NonNegativeInteger|)
- |DFLOAT;rationalApproximation;$2NniF;84|
- |DFLOAT;rationalApproximation;$NniF;75|
- |DFLOAT;atan;3$;76| |DFLOAT;retract;$F;77|
- (|Union| 106 '"failed") |DFLOAT;retractIfCan;$U;78|
- |DFLOAT;retract;$I;79| (|Union| 26 '"failed")
- |DFLOAT;retractIfCan;$U;80| |DFLOAT;sign;$I;81|
- |DFLOAT;abs;2$;82| (63 . **) (69 . |Zero|) (73 . /)
+ |DFLOAT;rationalApproximation;$2NniF;83|
+ |DFLOAT;rationalApproximation;$NniF;74|
+ |DFLOAT;atan;3$;75| |DFLOAT;retract;$F;76|
+ (|Union| 104 '"failed") |DFLOAT;retractIfCan;$U;77|
+ |DFLOAT;retract;$I;78| (|Union| 24 '"failed")
+ |DFLOAT;retractIfCan;$U;79| |DFLOAT;sign;$I;80|
+ |DFLOAT;abs;2$;81| (63 . **) (69 . |Zero|) (73 . /)
(79 . *) (85 . |coerce|) (90 . |zero?|) (95 . |negative?|)
(100 . |One|) (104 . =) (110 . |numer|) (115 . |denom|)
- |DFLOAT;**;$F$;85| (|PatternMatchResult| 103 $)
- (|Pattern| 103) (|Factored| $)
+ |DFLOAT;**;$F$;84| (|PatternMatchResult| 101 $)
+ (|Pattern| 101) (|Factored| $)
(|Record| (|:| |coef1| $) (|:| |coef2| $))
- (|Union| 134 '"failed") (|List| $) (|Union| 136 '"failed")
+ (|Union| 132 '"failed") (|List| $) (|Union| 134 '"failed")
(|Record| (|:| |coef1| $) (|:| |coef2| $)
(|:| |generator| $))
(|Record| (|:| |quotient| $) (|:| |remainder| $))
(|SparseUnivariatePolynomial| $)
- (|Record| (|:| |coef| 136) (|:| |generator| $))
+ (|Record| (|:| |coef| 134) (|:| |generator| $))
(|Record| (|:| |unit| $) (|:| |canonical| $)
(|:| |associate| $)))
'#(~= 120 |zero?| 126 |wholePart| 131 |unitNormal| 136
@@ -732,16 +722,15 @@
|fractionPart| 422 |floor| 427 |float| 432 |factor| 445
|extendedEuclidean| 450 |exquo| 463 |expressIdealMember|
469 |exponent| 475 |exp1| 480 |exp| 484 |euclideanSize|
- 489 |doubleFloatFormat| 494 |divide| 499 |digits| 505
- |differentiate| 509 |csch| 520 |csc| 525 |coth| 530 |cot|
- 535 |cosh| 540 |cos| 545 |convert| 550 |coerce| 570
- |characteristic| 600 |ceiling| 604 |bits| 609 |base| 613
- |atanh| 617 |atan| 622 |associates?| 633 |asinh| 639
- |asin| 644 |asech| 649 |asec| 654 |acsch| 659 |acsc| 664
- |acoth| 669 |acot| 674 |acosh| 679 |acos| 684 |abs| 689
- |Zero| 694 |One| 698 |OMwrite| 702 |Gamma| 726 D 731
- |Beta| 742 >= 748 > 754 = 760 <= 766 < 772 / 778 - 790 +
- 801 ** 807 * 837)
+ 489 |divide| 494 |digits| 500 |differentiate| 504 |csch|
+ 515 |csc| 520 |coth| 525 |cot| 530 |cosh| 535 |cos| 540
+ |convert| 545 |coerce| 565 |characteristic| 595 |ceiling|
+ 599 |bits| 604 |base| 608 |atanh| 612 |atan| 617
+ |associates?| 628 |asinh| 634 |asin| 639 |asech| 644
+ |asec| 649 |acsch| 654 |acsc| 659 |acoth| 664 |acot| 669
+ |acosh| 674 |acos| 679 |abs| 684 |Zero| 689 |One| 693
+ |OMwrite| 697 |Gamma| 721 D 726 |Beta| 737 >= 743 > 749 =
+ 755 <= 761 < 767 / 773 - 785 + 796 ** 802 * 832)
'((|approximate| . 0) (|canonicalsClosed| . 0)
(|canonicalUnitNormal| . 0) (|noZeroDivisors| . 0)
((|commutative| "*") . 0) (|rightUnitary| . 0)
@@ -774,14 +763,14 @@
(|PrincipalIdealDomain|)
(|UniqueFactorizationDomain|)
(|GcdDomain|) (|DivisionRing|)
- (|IntegralDomain|) (|Algebra| 106)
+ (|IntegralDomain|) (|Algebra| 104)
(|Algebra| $$) (|DifferentialRing|)
(|CharacteristicZero|) (|OrderedRing|)
- (|Module| 106) (|EntireRing|)
+ (|Module| 104) (|EntireRing|)
(|CommutativeRing|) (|Module| $$)
- (|BiModule| 106 106) (|BiModule| $$ $$)
+ (|BiModule| 104 104) (|BiModule| $$ $$)
(|Ring|) (|OrderedAbelianGroup|)
- (|RightModule| 106) (|LeftModule| 106)
+ (|RightModule| 104) (|LeftModule| 104)
(|LeftModule| $$) (|Rng|)
(|RightModule| $$)
(|OrderedCancellationAbelianMonoid|)
@@ -790,80 +779,79 @@
(|CancellationAbelianMonoid|)
(|OrderedAbelianSemiGroup|)
(|AbelianMonoid|) (|Monoid|)
- (|PatternMatchable| 103) (|OrderedSet|)
+ (|PatternMatchable| 101) (|OrderedSet|)
(|AbelianSemiGroup|) (|SemiGroup|)
(|TranscendentalFunctionCategory|)
(|RealConstant|) (|SetCategory|)
- (|ConvertibleTo| 43)
+ (|ConvertibleTo| 41)
(|ElementaryFunctionCategory|)
(|ArcHyperbolicFunctionCategory|)
(|HyperbolicFunctionCategory|)
(|ArcTrigonometricFunctionCategory|)
(|TrigonometricFunctionCategory|)
- (|OpenMath|) (|ConvertibleTo| 132)
+ (|OpenMath|) (|ConvertibleTo| 130)
(|RadicalCategory|)
- (|RetractableTo| 106)
- (|RetractableTo| 26)
- (|ConvertibleTo| 103)
- (|ConvertibleTo| 15) (|BasicType|)
- (|CoercibleTo| 40))
- (|makeByteWordVec2| 142
- '(0 9 0 10 2 11 0 7 9 12 1 11 13 0 14 2
- 11 13 0 15 16 1 11 13 0 17 1 11 13 0
- 18 2 0 0 24 0 31 1 40 0 15 41 1 43 0
- 15 44 1 95 15 15 96 2 95 15 15 15 98
- 1 103 0 15 104 2 26 0 0 24 119 0 106
- 0 120 2 106 0 26 26 121 2 26 0 107 0
- 122 1 106 0 26 123 1 106 20 0 124 1
- 106 20 0 125 0 106 0 126 2 106 20 0 0
- 127 1 106 26 0 128 1 106 26 0 129 2 0
- 20 0 0 1 1 0 20 0 89 1 0 26 0 100 1 0
- 142 0 1 1 0 0 0 1 1 0 20 0 1 1 0 0 0
- 1 1 0 0 0 77 1 0 0 0 65 2 0 92 0 0 1
- 1 0 0 0 1 1 0 133 0 1 1 0 0 0 56 2 0
- 20 0 0 1 1 0 0 0 75 1 0 0 0 63 1 0 26
- 0 117 1 0 0 0 80 1 0 0 0 67 0 0 0 1 1
- 0 0 0 1 1 0 112 0 113 1 0 115 0 116 1
- 0 106 0 111 1 0 26 0 114 2 0 0 0 0 1
- 1 0 92 0 93 2 0 106 0 107 109 3 0 106
- 0 107 107 108 2 0 0 0 0 1 1 0 141 136
- 1 1 0 20 0 1 0 0 24 29 1 0 20 0 1 0 0
- 0 39 3 0 131 0 132 131 1 1 0 26 0 35
- 1 0 20 0 1 2 0 0 0 26 1 1 0 0 0 1 1 0
- 20 0 88 2 0 137 136 0 1 0 0 0 34 2 0
- 0 0 0 53 0 0 0 33 2 0 0 0 0 52 1 0 26
- 0 27 1 0 0 0 30 1 0 0 0 57 1 0 0 0 62
- 2 0 0 0 0 1 1 0 0 136 1 1 0 7 0 1 1 0
- 0 0 1 1 0 90 0 91 2 0 140 140 140 1 1
- 0 0 136 1 2 0 0 0 0 1 1 0 0 0 1 1 0 0
- 0 1 2 0 0 26 26 1 3 0 0 26 26 24 101
- 1 0 133 0 1 3 0 135 0 0 0 1 2 0 138 0
- 0 1 2 0 92 0 0 1 2 0 137 136 0 1 1 0
- 26 0 28 0 0 0 38 1 0 0 0 61 1 0 107 0
- 1 1 0 7 7 8 2 0 139 0 0 1 0 0 24 1 1
- 0 0 0 94 2 0 0 0 107 1 1 0 0 0 78 1 0
- 0 0 68 1 0 0 0 79 1 0 0 0 66 1 0 0 0
- 76 1 0 0 0 64 1 0 43 0 45 1 0 132 0 1
- 1 0 15 0 102 1 0 103 0 105 1 0 0 106
- 1 1 0 0 26 60 1 0 0 106 1 1 0 0 26 60
- 1 0 0 0 1 1 0 40 0 42 0 0 107 1 1 0 0
- 0 1 0 0 24 32 0 0 24 25 1 0 0 0 83 2
- 0 0 0 0 110 1 0 0 0 71 2 0 20 0 0 1 1
- 0 0 0 81 1 0 0 0 69 1 0 0 0 86 1 0 0
- 0 74 1 0 0 0 84 1 0 0 0 72 1 0 0 0 85
- 1 0 0 0 73 1 0 0 0 82 1 0 0 0 70 1 0
- 0 0 118 0 0 0 36 0 0 0 37 3 0 13 11 0
- 20 23 2 0 7 0 20 21 2 0 13 11 0 22 1
- 0 7 0 19 1 0 0 0 97 1 0 0 0 1 2 0 0 0
- 107 1 2 0 0 0 0 99 2 0 20 0 0 1 2 0
- 20 0 0 1 2 0 20 0 0 54 2 0 20 0 0 1 2
- 0 20 0 0 46 2 0 0 0 26 55 2 0 0 0 0
- 87 2 0 0 0 0 49 1 0 0 0 47 2 0 0 0 0
- 48 2 0 0 0 0 59 2 0 0 0 106 130 2 0 0
- 0 26 58 2 0 0 0 107 1 2 0 0 0 24 1 2
- 0 0 0 106 1 2 0 0 106 0 1 2 0 0 0 0
- 50 2 0 0 26 0 51 2 0 0 107 0 1 2 0 0
- 24 0 31)))))
+ (|RetractableTo| 104)
+ (|RetractableTo| 24)
+ (|ConvertibleTo| 101)
+ (|ConvertibleTo| 13) (|BasicType|)
+ (|CoercibleTo| 38))
+ (|makeByteWordVec2| 140
+ '(0 6 0 7 2 9 0 8 6 10 1 9 11 0 12 2 9
+ 11 0 13 14 1 9 11 0 15 1 9 11 0 16 2
+ 0 0 22 0 29 1 38 0 13 39 1 41 0 13 42
+ 1 93 13 13 94 2 93 13 13 13 96 1 101
+ 0 13 102 2 24 0 0 22 117 0 104 0 118
+ 2 104 0 24 24 119 2 24 0 105 0 120 1
+ 104 0 24 121 1 104 18 0 122 1 104 18
+ 0 123 0 104 0 124 2 104 18 0 0 125 1
+ 104 24 0 126 1 104 24 0 127 2 0 18 0
+ 0 1 1 0 18 0 87 1 0 24 0 98 1 0 140 0
+ 1 1 0 0 0 1 1 0 18 0 1 1 0 0 0 1 1 0
+ 0 0 75 1 0 0 0 63 2 0 90 0 0 1 1 0 0
+ 0 1 1 0 131 0 1 1 0 0 0 54 2 0 18 0 0
+ 1 1 0 0 0 73 1 0 0 0 61 1 0 24 0 115
+ 1 0 0 0 78 1 0 0 0 65 0 0 0 1 1 0 0 0
+ 1 1 0 110 0 111 1 0 113 0 114 1 0 104
+ 0 109 1 0 24 0 112 2 0 0 0 0 1 1 0 90
+ 0 91 2 0 104 0 105 107 3 0 104 0 105
+ 105 106 2 0 0 0 0 1 1 0 139 134 1 1 0
+ 18 0 1 0 0 22 27 1 0 18 0 1 0 0 0 37
+ 3 0 129 0 130 129 1 1 0 24 0 33 1 0
+ 18 0 1 2 0 0 0 24 1 1 0 0 0 1 1 0 18
+ 0 86 2 0 135 134 0 1 0 0 0 32 2 0 0 0
+ 0 51 0 0 0 31 2 0 0 0 0 50 1 0 24 0
+ 25 1 0 0 0 28 1 0 0 0 55 1 0 0 0 60 2
+ 0 0 0 0 1 1 0 0 134 1 1 0 8 0 1 1 0 0
+ 0 1 1 0 88 0 89 2 0 138 138 138 1 1 0
+ 0 134 1 2 0 0 0 0 1 1 0 0 0 1 1 0 0 0
+ 1 3 0 0 24 24 22 99 2 0 0 24 24 1 1 0
+ 131 0 1 3 0 133 0 0 0 1 2 0 136 0 0 1
+ 2 0 90 0 0 1 2 0 135 134 0 1 1 0 24 0
+ 26 0 0 0 36 1 0 0 0 59 1 0 105 0 1 2
+ 0 137 0 0 1 0 0 22 1 1 0 0 0 92 2 0 0
+ 0 105 1 1 0 0 0 76 1 0 0 0 66 1 0 0 0
+ 77 1 0 0 0 64 1 0 0 0 74 1 0 0 0 62 1
+ 0 41 0 43 1 0 130 0 1 1 0 101 0 103 1
+ 0 13 0 100 1 0 0 104 1 1 0 0 24 58 1
+ 0 0 104 1 1 0 0 24 58 1 0 0 0 1 1 0
+ 38 0 40 0 0 105 1 1 0 0 0 1 0 0 22 30
+ 0 0 22 23 1 0 0 0 81 2 0 0 0 0 108 1
+ 0 0 0 69 2 0 18 0 0 1 1 0 0 0 79 1 0
+ 0 0 67 1 0 0 0 84 1 0 0 0 72 1 0 0 0
+ 82 1 0 0 0 70 1 0 0 0 83 1 0 0 0 71 1
+ 0 0 0 80 1 0 0 0 68 1 0 0 0 116 0 0 0
+ 34 0 0 0 35 2 0 11 9 0 20 3 0 11 9 0
+ 18 21 1 0 8 0 17 2 0 8 0 18 19 1 0 0
+ 0 95 1 0 0 0 1 2 0 0 0 105 1 2 0 0 0
+ 0 97 2 0 18 0 0 1 2 0 18 0 0 1 2 0 18
+ 0 0 52 2 0 18 0 0 1 2 0 18 0 0 44 2 0
+ 0 0 24 53 2 0 0 0 0 85 2 0 0 0 0 47 1
+ 0 0 0 45 2 0 0 0 0 46 2 0 0 0 0 57 2
+ 0 0 0 104 128 2 0 0 0 24 56 2 0 0 0
+ 105 1 2 0 0 0 22 1 2 0 0 104 0 1 2 0
+ 0 0 104 1 2 0 0 0 0 48 2 0 0 24 0 49
+ 2 0 0 105 0 1 2 0 0 22 0 29)))))
'|lookupComplete|))
(SETQ |$CategoryFrame|
@@ -871,54 +859,52 @@
'(((|rationalApproximation|
((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)
(|NonNegativeInteger|)))
- T (ELT $ 108))
+ T (ELT $ 106))
((|rationalApproximation|
((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)))
- T (ELT $ 109))
- ((|doubleFloatFormat| ((|String|) (|String|))) T
- (ELT $ 8))
- ((|Beta| ($ $ $)) T (ELT $ 99))
- ((|Gamma| ($ $)) T (ELT $ 97))
- ((|atan| ($ $ $)) T (ELT $ 110))
- ((|log10| ($ $)) T (ELT $ 57))
- ((|log2| ($ $)) T (ELT $ 30))
- ((|exp1| ($)) T (ELT $ 38))
- ((/ ($ $ (|Integer|))) T (ELT $ 55))
- ((|convert| ((|InputForm|) $)) T (ELT $ 45))
- ((|tan| ($ $)) T (ELT $ 65))
- ((|sin| ($ $)) T (ELT $ 63))
- ((|sec| ($ $)) T (ELT $ 67))
- ((|csc| ($ $)) T (ELT $ 68))
- ((|cot| ($ $)) T (ELT $ 66))
- ((|cos| ($ $)) T (ELT $ 64))
- ((|acos| ($ $)) T (ELT $ 70))
- ((|acot| ($ $)) T (ELT $ 73))
- ((|acsc| ($ $)) T (ELT $ 72))
- ((|asec| ($ $)) T (ELT $ 74))
- ((|asin| ($ $)) T (ELT $ 69))
- ((|atan| ($ $)) T (ELT $ 71))
- ((|cosh| ($ $)) T (ELT $ 76))
- ((|coth| ($ $)) T (ELT $ 79))
- ((|csch| ($ $)) T (ELT $ 78))
- ((|sech| ($ $)) T (ELT $ 80))
- ((|sinh| ($ $)) T (ELT $ 75))
- ((|tanh| ($ $)) T (ELT $ 77))
- ((|acosh| ($ $)) T (ELT $ 82))
- ((|acoth| ($ $)) T (ELT $ 85))
- ((|acsch| ($ $)) T (ELT $ 84))
- ((|asech| ($ $)) T (ELT $ 86))
- ((|asinh| ($ $)) T (ELT $ 81))
- ((|atanh| ($ $)) T (ELT $ 83))
- ((|log| ($ $)) T (ELT $ 62))
- ((|exp| ($ $)) T (ELT $ 61)) ((** ($ $ $)) T (ELT $ 59))
- ((|pi| ($)) T (ELT $ 39))
+ T (ELT $ 107))
+ ((|Beta| ($ $ $)) T (ELT $ 97))
+ ((|Gamma| ($ $)) T (ELT $ 95))
+ ((|atan| ($ $ $)) T (ELT $ 108))
+ ((|log10| ($ $)) T (ELT $ 55))
+ ((|log2| ($ $)) T (ELT $ 28))
+ ((|exp1| ($)) T (ELT $ 36))
+ ((/ ($ $ (|Integer|))) T (ELT $ 53))
+ ((|convert| ((|InputForm|) $)) T (ELT $ 43))
+ ((|tan| ($ $)) T (ELT $ 63))
+ ((|sin| ($ $)) T (ELT $ 61))
+ ((|sec| ($ $)) T (ELT $ 65))
+ ((|csc| ($ $)) T (ELT $ 66))
+ ((|cot| ($ $)) T (ELT $ 64))
+ ((|cos| ($ $)) T (ELT $ 62))
+ ((|acos| ($ $)) T (ELT $ 68))
+ ((|acot| ($ $)) T (ELT $ 71))
+ ((|acsc| ($ $)) T (ELT $ 70))
+ ((|asec| ($ $)) T (ELT $ 72))
+ ((|asin| ($ $)) T (ELT $ 67))
+ ((|atan| ($ $)) T (ELT $ 69))
+ ((|cosh| ($ $)) T (ELT $ 74))
+ ((|coth| ($ $)) T (ELT $ 77))
+ ((|csch| ($ $)) T (ELT $ 76))
+ ((|sech| ($ $)) T (ELT $ 78))
+ ((|sinh| ($ $)) T (ELT $ 73))
+ ((|tanh| ($ $)) T (ELT $ 75))
+ ((|acosh| ($ $)) T (ELT $ 80))
+ ((|acoth| ($ $)) T (ELT $ 83))
+ ((|acsch| ($ $)) T (ELT $ 82))
+ ((|asech| ($ $)) T (ELT $ 84))
+ ((|asinh| ($ $)) T (ELT $ 79))
+ ((|atanh| ($ $)) T (ELT $ 81))
+ ((|log| ($ $)) T (ELT $ 60))
+ ((|exp| ($ $)) T (ELT $ 59)) ((** ($ $ $)) T (ELT $ 57))
+ ((|pi| ($)) T (ELT $ 37))
((|OMwrite| ((|Void|) (|OpenMathDevice|) $ (|Boolean|)))
- T (ELT $ 23))
+ T (ELT $ 21))
((|OMwrite| ((|Void|) (|OpenMathDevice|) $)) T
- (ELT $ 22))
- ((|OMwrite| ((|String|) $ (|Boolean|))) T (ELT $ 21))
- ((|OMwrite| ((|String|) $)) T (ELT $ 19))
- ((|differentiate| ($ $)) T (ELT $ 94))
+ (ELT $ 20))
+ ((|OMwrite| ((|String|) $ (|Boolean|))) T (ELT $ 19))
+ ((|OMwrite| ((|String|) $)) T (ELT $ 17))
+ ((|differentiate| ($ $)) T (ELT $ 92))
((D ($ $)) T (ELT $ NIL))
((|differentiate| ($ $ (|NonNegativeInteger|))) T
(ELT $ NIL))
@@ -926,11 +912,11 @@
((|max| ($))
(AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))
(|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))))
- (ELT $ 33))
+ (ELT $ 31))
((|min| ($))
(AND (|not| (|has| $ (ATTRIBUTE |arbitraryExponent|)))
(|not| (|has| $ (ATTRIBUTE |arbitraryPrecision|))))
- (ELT $ 34))
+ (ELT $ 32))
((|decreasePrecision| ((|PositiveInteger|) (|Integer|)))
(|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL))
((|increasePrecision| ((|PositiveInteger|) (|Integer|)))
@@ -941,21 +927,21 @@
(|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL))
((|bits| ((|PositiveInteger|) (|PositiveInteger|)))
(|has| $ (ATTRIBUTE |arbitraryPrecision|)) (ELT $ NIL))
- ((|precision| ((|PositiveInteger|))) T (ELT $ 29))
+ ((|precision| ((|PositiveInteger|))) T (ELT $ 27))
((|digits| ((|PositiveInteger|))) T (ELT $ NIL))
- ((|bits| ((|PositiveInteger|))) T (ELT $ 32))
- ((|mantissa| ((|Integer|) $)) T (ELT $ 27))
- ((|exponent| ((|Integer|) $)) T (ELT $ 28))
- ((|base| ((|PositiveInteger|))) T (ELT $ 25))
- ((|order| ((|Integer|) $)) T (ELT $ 35))
+ ((|bits| ((|PositiveInteger|))) T (ELT $ 30))
+ ((|mantissa| ((|Integer|) $)) T (ELT $ 25))
+ ((|exponent| ((|Integer|) $)) T (ELT $ 26))
+ ((|base| ((|PositiveInteger|))) T (ELT $ 23))
+ ((|order| ((|Integer|) $)) T (ELT $ 33))
((|float| ($ (|Integer|) (|Integer|)
(|PositiveInteger|)))
- T (ELT $ 101))
+ T (ELT $ 99))
((|float| ($ (|Integer|) (|Integer|))) T (ELT $ NIL))
((|round| ($ $)) T (ELT $ NIL))
((|truncate| ($ $)) T (ELT $ NIL))
((|fractionPart| ($ $)) T (ELT $ NIL))
- ((|wholePart| ((|Integer|) $)) T (ELT $ 100))
+ ((|wholePart| ((|Integer|) $)) T (ELT $ 98))
((|floor| ($ $)) T (ELT $ NIL))
((|ceiling| ($ $)) T (ELT $ NIL))
((|norm| ($ $)) T (ELT $ NIL))
@@ -965,34 +951,34 @@
(|PatternMatchResult| (|Float|) $)))
T (ELT $ NIL))
((|convert| ((|Pattern| (|Float|)) $)) T (ELT $ NIL))
- ((** ($ $ (|Fraction| (|Integer|)))) T (ELT $ 130))
+ ((** ($ $ (|Fraction| (|Integer|)))) T (ELT $ 128))
((|nthRoot| ($ $ (|Integer|))) T (ELT $ NIL))
- ((|sqrt| ($ $)) T (ELT $ 56))
- ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ 111))
+ ((|sqrt| ($ $)) T (ELT $ 54))
+ ((|retract| ((|Fraction| (|Integer|)) $)) T (ELT $ 109))
((|retractIfCan|
((|Union| (|Fraction| (|Integer|)) "failed") $))
- T (ELT $ 113))
+ T (ELT $ 111))
((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ NIL))
- ((|retract| ((|Integer|) $)) T (ELT $ 114))
+ ((|retract| ((|Integer|) $)) T (ELT $ 112))
((|retractIfCan| ((|Union| (|Integer|) "failed") $)) T
- (ELT $ 116))
- ((|coerce| ($ (|Integer|))) T (ELT $ 60))
- ((|convert| ((|DoubleFloat|) $)) T (ELT $ 102))
- ((|convert| ((|Float|) $)) T (ELT $ 105))
- ((< ((|Boolean|) $ $)) T (ELT $ 46))
+ (ELT $ 114))
+ ((|coerce| ($ (|Integer|))) T (ELT $ 58))
+ ((|convert| ((|DoubleFloat|) $)) T (ELT $ 100))
+ ((|convert| ((|Float|) $)) T (ELT $ 103))
+ ((< ((|Boolean|) $ $)) T (ELT $ 44))
((> ((|Boolean|) $ $)) T (ELT $ NIL))
((>= ((|Boolean|) $ $)) T (ELT $ NIL))
((<= ((|Boolean|) $ $)) T (ELT $ NIL))
- ((|max| ($ $ $)) T (ELT $ 52))
- ((|min| ($ $ $)) T (ELT $ 53))
+ ((|max| ($ $ $)) T (ELT $ 50))
+ ((|min| ($ $ $)) T (ELT $ 51))
((|positive?| ((|Boolean|) $)) T (ELT $ NIL))
- ((|negative?| ((|Boolean|) $)) T (ELT $ 88))
- ((|sign| ((|Integer|) $)) T (ELT $ 117))
- ((|abs| ($ $)) T (ELT $ 118)) ((/ ($ $ $)) T (ELT $ 87))
+ ((|negative?| ((|Boolean|) $)) T (ELT $ 86))
+ ((|sign| ((|Integer|) $)) T (ELT $ 115))
+ ((|abs| ($ $)) T (ELT $ 116)) ((/ ($ $ $)) T (ELT $ 85))
((|coerce| ($ (|Fraction| (|Integer|)))) T (ELT $ NIL))
((* ($ (|Fraction| (|Integer|)) $)) T (ELT $ NIL))
((* ($ $ (|Fraction| (|Integer|)))) T (ELT $ NIL))
- ((** ($ $ (|Integer|))) T (ELT $ 58))
+ ((** ($ $ (|Integer|))) T (ELT $ 56))
((|inv| ($ $)) T (ELT $ NIL))
((|prime?| ((|Boolean|) $)) T (ELT $ NIL))
((|squareFree| ((|Factored| $) $)) T (ELT $ NIL))
@@ -1048,29 +1034,29 @@
T (ELT $ NIL))
((|exquo| ((|Union| $ "failed") $ $)) T (ELT $ NIL))
((|coerce| ($ $)) T (ELT $ NIL))
- ((|coerce| ($ (|Integer|))) T (ELT $ 60))
+ ((|coerce| ($ (|Integer|))) T (ELT $ 58))
((|characteristic| ((|NonNegativeInteger|))) T
(ELT $ NIL))
- ((|One| ($)) T (CONST $ 37))
+ ((|One| ($)) T (CONST $ 35))
((|one?| ((|Boolean|) $)) T (ELT $ NIL))
((** ($ $ (|NonNegativeInteger|))) T (ELT $ NIL))
- ((|recip| ((|Union| $ "failed") $)) T (ELT $ 93))
- ((* ($ $ $)) T (ELT $ 50))
+ ((|recip| ((|Union| $ "failed") $)) T (ELT $ 91))
+ ((* ($ $ $)) T (ELT $ 48))
((** ($ $ (|PositiveInteger|))) T (ELT $ NIL))
- ((* ($ (|Integer|) $)) T (ELT $ 51))
- ((- ($ $ $)) T (ELT $ 49)) ((- ($ $)) T (ELT $ 47))
+ ((* ($ (|Integer|) $)) T (ELT $ 49))
+ ((- ($ $ $)) T (ELT $ 47)) ((- ($ $)) T (ELT $ 45))
((|subtractIfCan| ((|Union| $ "failed") $ $)) T
(ELT $ NIL))
((* ($ (|NonNegativeInteger|) $)) T (ELT $ NIL))
- ((|zero?| ((|Boolean|) $)) T (ELT $ 89))
+ ((|zero?| ((|Boolean|) $)) T (ELT $ 87))
((|sample| ($)) T (CONST $ NIL))
- ((|Zero| ($)) T (CONST $ 36))
- ((* ($ (|PositiveInteger|) $)) T (ELT $ 31))
- ((+ ($ $ $)) T (ELT $ 48))
+ ((|Zero| ($)) T (CONST $ 34))
+ ((* ($ (|PositiveInteger|) $)) T (ELT $ 29))
+ ((+ ($ $ $)) T (ELT $ 46))
((|latex| ((|String|) $)) T (ELT $ NIL))
- ((|hash| ((|SingleInteger|) $)) T (ELT $ 91))
- ((|coerce| ((|OutputForm|) $)) T (ELT $ 42))
- ((= ((|Boolean|) $ $)) T (ELT $ 54))
+ ((|hash| ((|SingleInteger|) $)) T (ELT $ 89))
+ ((|coerce| ((|OutputForm|) $)) T (ELT $ 40))
+ ((= ((|Boolean|) $ $)) T (ELT $ 52))
((~= ((|Boolean|) $ $)) T (ELT $ NIL)))
(|addModemap| '|DoubleFloat| '(|DoubleFloat|)
'((|Join| (|FloatingPointSystem|) (|DifferentialRing|)
@@ -1086,8 +1072,6 @@
(SIGNATURE |atan| ($ $ $))
(SIGNATURE |Gamma| ($ $))
(SIGNATURE |Beta| ($ $ $))
- (SIGNATURE |doubleFloatFormat|
- ((|String|) (|String|)))
(SIGNATURE |rationalApproximation|
((|Fraction| (|Integer|)) $
(|NonNegativeInteger|)))
@@ -1111,8 +1095,6 @@
(SIGNATURE |atan| ($ $ $))
(SIGNATURE |Gamma| ($ $))
(SIGNATURE |Beta| ($ $ $))
- (SIGNATURE |doubleFloatFormat|
- ((|String|) (|String|)))
(SIGNATURE
|rationalApproximation|
((|Fraction| (|Integer|)) $
diff --git a/src/algebra/strap/OUTFORM.lsp b/src/algebra/strap/OUTFORM.lsp
index 6605cbf3..3986749a 100644
--- a/src/algebra/strap/OUTFORM.lsp
+++ b/src/algebra/strap/OUTFORM.lsp
@@ -1,6 +1,13 @@
(/VERSIONCHECK 2)
+(DEFUN |OUTFORM;doubleFloatFormat;2S;1| (|s| $)
+ (PROG (|ss|)
+ (RETURN
+ (SEQ (LETT |ss| (|getShellEntry| $ 6)
+ |OUTFORM;doubleFloatFormat;2S;1|)
+ (SETELT $ 6 |s|) (EXIT |ss|)))))
+
(PUT '|OUTFORM;sform| '|SPADreplace| '(XLAM (|s|) |s|))
(DEFUN |OUTFORM;sform| (|s| $) |s|)
@@ -17,331 +24,330 @@
(DEFUN |OUTFORM;bless| (|x| $) |x|)
-(PUT '|OUTFORM;print;$V;5| '|SPADreplace| '|mathprint|)
+(PUT '|OUTFORM;print;$V;6| '|SPADreplace| '|mathprint|)
-(DEFUN |OUTFORM;print;$V;5| (|x| $) (|mathprint| |x|))
+(DEFUN |OUTFORM;print;$V;6| (|x| $) (|mathprint| |x|))
-(DEFUN |OUTFORM;message;S$;6| (|s| $)
+(DEFUN |OUTFORM;message;S$;7| (|s| $)
(COND
- ((SPADCALL |s| (|getShellEntry| $ 10))
- (SPADCALL (|getShellEntry| $ 11)))
+ ((SPADCALL |s| (|getShellEntry| $ 12))
+ (SPADCALL (|getShellEntry| $ 13)))
('T |s|)))
-(DEFUN |OUTFORM;messagePrint;SV;7| (|s| $)
- (SPADCALL (SPADCALL |s| (|getShellEntry| $ 12))
- (|getShellEntry| $ 7)))
+(DEFUN |OUTFORM;messagePrint;SV;8| (|s| $)
+ (SPADCALL (SPADCALL |s| (|getShellEntry| $ 14))
+ (|getShellEntry| $ 10)))
-(PUT '|OUTFORM;=;2$B;8| '|SPADreplace| 'EQUAL)
+(PUT '|OUTFORM;=;2$B;9| '|SPADreplace| 'EQUAL)
-(DEFUN |OUTFORM;=;2$B;8| (|a| |b| $) (EQUAL |a| |b|))
+(DEFUN |OUTFORM;=;2$B;9| (|a| |b| $) (EQUAL |a| |b|))
-(DEFUN |OUTFORM;=;3$;9| (|a| |b| $)
+(DEFUN |OUTFORM;=;3$;10| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "=" $) |a| |b|) $))
-(PUT '|OUTFORM;coerce;2$;10| '|SPADreplace| '(XLAM (|a|) |a|))
-
-(DEFUN |OUTFORM;coerce;2$;10| (|a| $) |a|)
+(PUT '|OUTFORM;coerce;2$;11| '|SPADreplace| '(XLAM (|a|) |a|))
-(PUT '|OUTFORM;outputForm;I$;11| '|SPADreplace| '(XLAM (|n|) |n|))
+(DEFUN |OUTFORM;coerce;2$;11| (|a| $) |a|)
-(DEFUN |OUTFORM;outputForm;I$;11| (|n| $) |n|)
+(PUT '|OUTFORM;outputForm;I$;12| '|SPADreplace| '(XLAM (|n|) |n|))
-(PUT '|OUTFORM;outputForm;S$;12| '|SPADreplace| '(XLAM (|e|) |e|))
+(DEFUN |OUTFORM;outputForm;I$;12| (|n| $) |n|)
-(DEFUN |OUTFORM;outputForm;S$;12| (|e| $) |e|)
+(PUT '|OUTFORM;outputForm;S$;13| '|SPADreplace| '(XLAM (|e|) |e|))
-(PUT '|OUTFORM;outputForm;Df$;13| '|SPADreplace| '(XLAM (|f|) |f|))
+(DEFUN |OUTFORM;outputForm;S$;13| (|e| $) |e|)
-(DEFUN |OUTFORM;outputForm;Df$;13| (|f| $) |f|)
+(DEFUN |OUTFORM;outputForm;Df$;14| (|f| $)
+ (FORMAT NIL (|getShellEntry| $ 6) |f|))
-(DEFUN |OUTFORM;outputForm;S$;14| (|s| $)
+(DEFUN |OUTFORM;outputForm;S$;15| (|s| $)
(|OUTFORM;sform|
- (SPADCALL (SPADCALL (|getShellEntry| $ 25))
- (SPADCALL |s| (SPADCALL (|getShellEntry| $ 25))
- (|getShellEntry| $ 26))
- (|getShellEntry| $ 27))
+ (SPADCALL (SPADCALL (|getShellEntry| $ 27))
+ (SPADCALL |s| (SPADCALL (|getShellEntry| $ 27))
+ (|getShellEntry| $ 28))
+ (|getShellEntry| $ 29))
$))
-(PUT '|OUTFORM;width;$I;15| '|SPADreplace| '|outformWidth|)
+(PUT '|OUTFORM;width;$I;16| '|SPADreplace| '|outformWidth|)
-(DEFUN |OUTFORM;width;$I;15| (|a| $) (|outformWidth| |a|))
+(DEFUN |OUTFORM;width;$I;16| (|a| $) (|outformWidth| |a|))
-(PUT '|OUTFORM;height;$I;16| '|SPADreplace| '|height|)
+(PUT '|OUTFORM;height;$I;17| '|SPADreplace| '|height|)
-(DEFUN |OUTFORM;height;$I;16| (|a| $) (|height| |a|))
+(DEFUN |OUTFORM;height;$I;17| (|a| $) (|height| |a|))
-(PUT '|OUTFORM;subHeight;$I;17| '|SPADreplace| '|subspan|)
+(PUT '|OUTFORM;subHeight;$I;18| '|SPADreplace| '|subspan|)
-(DEFUN |OUTFORM;subHeight;$I;17| (|a| $) (|subspan| |a|))
+(DEFUN |OUTFORM;subHeight;$I;18| (|a| $) (|subspan| |a|))
-(PUT '|OUTFORM;superHeight;$I;18| '|SPADreplace| '|superspan|)
+(PUT '|OUTFORM;superHeight;$I;19| '|SPADreplace| '|superspan|)
-(DEFUN |OUTFORM;superHeight;$I;18| (|a| $) (|superspan| |a|))
+(DEFUN |OUTFORM;superHeight;$I;19| (|a| $) (|superspan| |a|))
-(PUT '|OUTFORM;height;I;19| '|SPADreplace| '(XLAM NIL 20))
+(PUT '|OUTFORM;height;I;20| '|SPADreplace| '(XLAM NIL 20))
-(DEFUN |OUTFORM;height;I;19| ($) 20)
+(DEFUN |OUTFORM;height;I;20| ($) 20)
-(PUT '|OUTFORM;width;I;20| '|SPADreplace| '(XLAM NIL 66))
+(PUT '|OUTFORM;width;I;21| '|SPADreplace| '(XLAM NIL 66))
-(DEFUN |OUTFORM;width;I;20| ($) 66)
+(DEFUN |OUTFORM;width;I;21| ($) 66)
-(DEFUN |OUTFORM;center;$I$;21| (|a| |w| $)
+(DEFUN |OUTFORM;center;$I$;22| (|a| |w| $)
(SPADCALL
(SPADCALL
- (QUOTIENT2 (- |w| (SPADCALL |a| (|getShellEntry| $ 29))) 2)
- (|getShellEntry| $ 35))
- |a| (|getShellEntry| $ 36)))
+ (QUOTIENT2 (- |w| (SPADCALL |a| (|getShellEntry| $ 31))) 2)
+ (|getShellEntry| $ 37))
+ |a| (|getShellEntry| $ 38)))
-(DEFUN |OUTFORM;left;$I$;22| (|a| |w| $)
+(DEFUN |OUTFORM;left;$I$;23| (|a| |w| $)
(SPADCALL |a|
- (SPADCALL (- |w| (SPADCALL |a| (|getShellEntry| $ 29)))
- (|getShellEntry| $ 35))
- (|getShellEntry| $ 36)))
+ (SPADCALL (- |w| (SPADCALL |a| (|getShellEntry| $ 31)))
+ (|getShellEntry| $ 37))
+ (|getShellEntry| $ 38)))
-(DEFUN |OUTFORM;right;$I$;23| (|a| |w| $)
+(DEFUN |OUTFORM;right;$I$;24| (|a| |w| $)
(SPADCALL
- (SPADCALL (- |w| (SPADCALL |a| (|getShellEntry| $ 29)))
- (|getShellEntry| $ 35))
- |a| (|getShellEntry| $ 36)))
+ (SPADCALL (- |w| (SPADCALL |a| (|getShellEntry| $ 31)))
+ (|getShellEntry| $ 37))
+ |a| (|getShellEntry| $ 38)))
-(DEFUN |OUTFORM;center;2$;24| (|a| $)
- (SPADCALL |a| (SPADCALL (|getShellEntry| $ 34))
- (|getShellEntry| $ 37)))
+(DEFUN |OUTFORM;center;2$;25| (|a| $)
+ (SPADCALL |a| (SPADCALL (|getShellEntry| $ 36))
+ (|getShellEntry| $ 39)))
-(DEFUN |OUTFORM;left;2$;25| (|a| $)
- (SPADCALL |a| (SPADCALL (|getShellEntry| $ 34))
- (|getShellEntry| $ 38)))
+(DEFUN |OUTFORM;left;2$;26| (|a| $)
+ (SPADCALL |a| (SPADCALL (|getShellEntry| $ 36))
+ (|getShellEntry| $ 40)))
-(DEFUN |OUTFORM;right;2$;26| (|a| $)
- (SPADCALL |a| (SPADCALL (|getShellEntry| $ 34))
- (|getShellEntry| $ 39)))
+(DEFUN |OUTFORM;right;2$;27| (|a| $)
+ (SPADCALL |a| (SPADCALL (|getShellEntry| $ 36))
+ (|getShellEntry| $ 41)))
-(DEFUN |OUTFORM;vspace;I$;27| (|n| $)
+(DEFUN |OUTFORM;vspace;I$;28| (|n| $)
(COND
- ((EQL |n| 0) (SPADCALL (|getShellEntry| $ 11)))
+ ((EQL |n| 0) (SPADCALL (|getShellEntry| $ 13)))
('T
(SPADCALL (|OUTFORM;sform| " " $)
- (SPADCALL (- |n| 1) (|getShellEntry| $ 43))
- (|getShellEntry| $ 44)))))
+ (SPADCALL (- |n| 1) (|getShellEntry| $ 45))
+ (|getShellEntry| $ 46)))))
-(DEFUN |OUTFORM;hspace;I$;28| (|n| $)
+(DEFUN |OUTFORM;hspace;I$;29| (|n| $)
(COND
- ((EQL |n| 0) (SPADCALL (|getShellEntry| $ 11)))
+ ((EQL |n| 0) (SPADCALL (|getShellEntry| $ 13)))
('T (|OUTFORM;sform| (|fillerSpaces| |n|) $))))
-(DEFUN |OUTFORM;rspace;2I$;29| (|n| |m| $)
+(DEFUN |OUTFORM;rspace;2I$;30| (|n| |m| $)
(COND
- ((OR (EQL |n| 0) (EQL |m| 0)) (SPADCALL (|getShellEntry| $ 11)))
+ ((OR (EQL |n| 0) (EQL |m| 0)) (SPADCALL (|getShellEntry| $ 13)))
('T
- (SPADCALL (SPADCALL |n| (|getShellEntry| $ 35))
- (SPADCALL |n| (- |m| 1) (|getShellEntry| $ 45))
- (|getShellEntry| $ 44)))))
+ (SPADCALL (SPADCALL |n| (|getShellEntry| $ 37))
+ (SPADCALL |n| (- |m| 1) (|getShellEntry| $ 47))
+ (|getShellEntry| $ 46)))))
-(DEFUN |OUTFORM;matrix;L$;30| (|ll| $)
- (PROG (#0=#:G1440 |l| #1=#:G1441 |lv|)
+(DEFUN |OUTFORM;matrix;L$;31| (|ll| $)
+ (PROG (#0=#:G1445 |l| #1=#:G1446 |lv|)
(RETURN
(SEQ (LETT |lv|
(|OUTFORM;bless|
(PROGN
- (LETT #0# NIL |OUTFORM;matrix;L$;30|)
- (SEQ (LETT |l| NIL |OUTFORM;matrix;L$;30|)
- (LETT #1# |ll| |OUTFORM;matrix;L$;30|) G190
+ (LETT #0# NIL |OUTFORM;matrix;L$;31|)
+ (SEQ (LETT |l| NIL |OUTFORM;matrix;L$;31|)
+ (LETT #1# |ll| |OUTFORM;matrix;L$;31|) G190
(COND
((OR (ATOM #1#)
(PROGN
(LETT |l| (CAR #1#)
- |OUTFORM;matrix;L$;30|)
+ |OUTFORM;matrix;L$;31|)
NIL))
(GO G191)))
(SEQ (EXIT (LETT #0#
(CONS (LIST2VEC |l|) #0#)
- |OUTFORM;matrix;L$;30|)))
- (LETT #1# (CDR #1#) |OUTFORM;matrix;L$;30|)
+ |OUTFORM;matrix;L$;31|)))
+ (LETT #1# (CDR #1#) |OUTFORM;matrix;L$;31|)
(GO G190) G191 (EXIT (NREVERSE0 #0#))))
$)
- |OUTFORM;matrix;L$;30|)
+ |OUTFORM;matrix;L$;31|)
(EXIT (CONS (|OUTFORM;eform| 'MATRIX $) (LIST2VEC |lv|)))))))
-(DEFUN |OUTFORM;pile;L$;31| (|l| $)
+(DEFUN |OUTFORM;pile;L$;32| (|l| $)
(CONS (|OUTFORM;eform| 'SC $) |l|))
-(DEFUN |OUTFORM;commaSeparate;L$;32| (|l| $)
+(DEFUN |OUTFORM;commaSeparate;L$;33| (|l| $)
(CONS (|OUTFORM;eform| 'AGGLST $) |l|))
-(DEFUN |OUTFORM;semicolonSeparate;L$;33| (|l| $)
+(DEFUN |OUTFORM;semicolonSeparate;L$;34| (|l| $)
(CONS (|OUTFORM;eform| 'AGGSET $) |l|))
-(DEFUN |OUTFORM;blankSeparate;L$;34| (|l| $)
- (PROG (|c| |u| #0=#:G1449 |l1|)
+(DEFUN |OUTFORM;blankSeparate;L$;35| (|l| $)
+ (PROG (|c| |u| #0=#:G1454 |l1|)
(RETURN
(SEQ (LETT |c| (|OUTFORM;eform| 'CONCATB $)
- |OUTFORM;blankSeparate;L$;34|)
- (LETT |l1| NIL |OUTFORM;blankSeparate;L$;34|)
- (SEQ (LETT |u| NIL |OUTFORM;blankSeparate;L$;34|)
- (LETT #0# (SPADCALL |l| (|getShellEntry| $ 53))
- |OUTFORM;blankSeparate;L$;34|)
+ |OUTFORM;blankSeparate;L$;35|)
+ (LETT |l1| NIL |OUTFORM;blankSeparate;L$;35|)
+ (SEQ (LETT |u| NIL |OUTFORM;blankSeparate;L$;35|)
+ (LETT #0# (SPADCALL |l| (|getShellEntry| $ 55))
+ |OUTFORM;blankSeparate;L$;35|)
G190
(COND
((OR (ATOM #0#)
(PROGN
(LETT |u| (CAR #0#)
- |OUTFORM;blankSeparate;L$;34|)
+ |OUTFORM;blankSeparate;L$;35|)
NIL))
(GO G191)))
(SEQ (EXIT (COND
((EQCAR |u| |c|)
(LETT |l1|
(SPADCALL (CDR |u|) |l1|
- (|getShellEntry| $ 54))
- |OUTFORM;blankSeparate;L$;34|))
+ (|getShellEntry| $ 56))
+ |OUTFORM;blankSeparate;L$;35|))
('T
(LETT |l1| (CONS |u| |l1|)
- |OUTFORM;blankSeparate;L$;34|)))))
- (LETT #0# (CDR #0#) |OUTFORM;blankSeparate;L$;34|)
+ |OUTFORM;blankSeparate;L$;35|)))))
+ (LETT #0# (CDR #0#) |OUTFORM;blankSeparate;L$;35|)
(GO G190) G191 (EXIT NIL))
(EXIT (CONS |c| |l1|))))))
-(DEFUN |OUTFORM;brace;2$;35| (|a| $)
+(DEFUN |OUTFORM;brace;2$;36| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'BRACE $) |a|) $))
-(DEFUN |OUTFORM;brace;L$;36| (|l| $)
- (SPADCALL (SPADCALL |l| (|getShellEntry| $ 50))
- (|getShellEntry| $ 56)))
+(DEFUN |OUTFORM;brace;L$;37| (|l| $)
+ (SPADCALL (SPADCALL |l| (|getShellEntry| $ 52))
+ (|getShellEntry| $ 58)))
-(DEFUN |OUTFORM;bracket;2$;37| (|a| $)
+(DEFUN |OUTFORM;bracket;2$;38| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'BRACKET $) |a|) $))
-(DEFUN |OUTFORM;bracket;L$;38| (|l| $)
- (SPADCALL (SPADCALL |l| (|getShellEntry| $ 50))
- (|getShellEntry| $ 58)))
+(DEFUN |OUTFORM;bracket;L$;39| (|l| $)
+ (SPADCALL (SPADCALL |l| (|getShellEntry| $ 52))
+ (|getShellEntry| $ 60)))
-(DEFUN |OUTFORM;paren;2$;39| (|a| $)
+(DEFUN |OUTFORM;paren;2$;40| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'PAREN $) |a|) $))
-(DEFUN |OUTFORM;paren;L$;40| (|l| $)
- (SPADCALL (SPADCALL |l| (|getShellEntry| $ 50))
- (|getShellEntry| $ 60)))
+(DEFUN |OUTFORM;paren;L$;41| (|l| $)
+ (SPADCALL (SPADCALL |l| (|getShellEntry| $ 52))
+ (|getShellEntry| $ 62)))
-(DEFUN |OUTFORM;sub;3$;41| (|a| |b| $)
+(DEFUN |OUTFORM;sub;3$;42| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'SUB $) |a| |b|) $))
-(DEFUN |OUTFORM;super;3$;42| (|a| |b| $)
+(DEFUN |OUTFORM;super;3$;43| (|a| |b| $)
(|OUTFORM;bless|
(LIST (|OUTFORM;eform| 'SUPERSUB $) |a| (|OUTFORM;sform| " " $)
|b|)
$))
-(DEFUN |OUTFORM;presub;3$;43| (|a| |b| $)
+(DEFUN |OUTFORM;presub;3$;44| (|a| |b| $)
(|OUTFORM;bless|
(LIST (|OUTFORM;eform| 'SUPERSUB $) |a| (|OUTFORM;sform| " " $)
(|OUTFORM;sform| " " $) (|OUTFORM;sform| " " $) |b|)
$))
-(DEFUN |OUTFORM;presuper;3$;44| (|a| |b| $)
+(DEFUN |OUTFORM;presuper;3$;45| (|a| |b| $)
(|OUTFORM;bless|
(LIST (|OUTFORM;eform| 'SUPERSUB $) |a| (|OUTFORM;sform| " " $)
(|OUTFORM;sform| " " $) |b|)
$))
-(DEFUN |OUTFORM;scripts;$L$;45| (|a| |l| $)
+(DEFUN |OUTFORM;scripts;$L$;46| (|a| |l| $)
(COND
- ((SPADCALL |l| (|getShellEntry| $ 66)) |a|)
- ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 67))
- (|getShellEntry| $ 66))
- (SPADCALL |a| (SPADCALL |l| (|getShellEntry| $ 68))
- (|getShellEntry| $ 62)))
+ ((SPADCALL |l| (|getShellEntry| $ 68)) |a|)
+ ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 69))
+ (|getShellEntry| $ 68))
+ (SPADCALL |a| (SPADCALL |l| (|getShellEntry| $ 70))
+ (|getShellEntry| $ 64)))
('T (CONS (|OUTFORM;eform| 'SUPERSUB $) (CONS |a| |l|)))))
-(DEFUN |OUTFORM;supersub;$L$;46| (|a| |l| $)
+(DEFUN |OUTFORM;supersub;$L$;47| (|a| |l| $)
(SEQ (COND
- ((ODDP (SPADCALL |l| (|getShellEntry| $ 71)))
+ ((ODDP (SPADCALL |l| (|getShellEntry| $ 73)))
(LETT |l|
- (SPADCALL |l| (LIST (SPADCALL (|getShellEntry| $ 11)))
- (|getShellEntry| $ 54))
- |OUTFORM;supersub;$L$;46|)))
+ (SPADCALL |l| (LIST (SPADCALL (|getShellEntry| $ 13)))
+ (|getShellEntry| $ 56))
+ |OUTFORM;supersub;$L$;47|)))
(EXIT (CONS (|OUTFORM;eform| 'ALTSUPERSUB $) (CONS |a| |l|)))))
-(DEFUN |OUTFORM;hconcat;3$;47| (|a| |b| $)
+(DEFUN |OUTFORM;hconcat;3$;48| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'CONCAT $) |a| |b|) $))
-(DEFUN |OUTFORM;hconcat;L$;48| (|l| $)
+(DEFUN |OUTFORM;hconcat;L$;49| (|l| $)
(CONS (|OUTFORM;eform| 'CONCAT $) |l|))
-(DEFUN |OUTFORM;vconcat;3$;49| (|a| |b| $)
+(DEFUN |OUTFORM;vconcat;3$;50| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'VCONCAT $) |a| |b|) $))
-(DEFUN |OUTFORM;vconcat;L$;50| (|l| $)
+(DEFUN |OUTFORM;vconcat;L$;51| (|l| $)
(CONS (|OUTFORM;eform| 'VCONCAT $) |l|))
-(DEFUN |OUTFORM;~=;3$;51| (|a| |b| $)
+(DEFUN |OUTFORM;~=;3$;52| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "~=" $) |a| |b|) $))
-(DEFUN |OUTFORM;<;3$;52| (|a| |b| $)
+(DEFUN |OUTFORM;<;3$;53| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "<" $) |a| |b|) $))
-(DEFUN |OUTFORM;>;3$;53| (|a| |b| $)
+(DEFUN |OUTFORM;>;3$;54| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| ">" $) |a| |b|) $))
-(DEFUN |OUTFORM;<=;3$;54| (|a| |b| $)
+(DEFUN |OUTFORM;<=;3$;55| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "<=" $) |a| |b|) $))
-(DEFUN |OUTFORM;>=;3$;55| (|a| |b| $)
+(DEFUN |OUTFORM;>=;3$;56| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| ">=" $) |a| |b|) $))
-(DEFUN |OUTFORM;+;3$;56| (|a| |b| $)
+(DEFUN |OUTFORM;+;3$;57| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "+" $) |a| |b|) $))
-(DEFUN |OUTFORM;-;3$;57| (|a| |b| $)
+(DEFUN |OUTFORM;-;3$;58| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "-" $) |a| |b|) $))
-(DEFUN |OUTFORM;-;2$;58| (|a| $)
+(DEFUN |OUTFORM;-;2$;59| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "-" $) |a|) $))
-(DEFUN |OUTFORM;*;3$;59| (|a| |b| $)
+(DEFUN |OUTFORM;*;3$;60| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "*" $) |a| |b|) $))
-(DEFUN |OUTFORM;/;3$;60| (|a| |b| $)
+(DEFUN |OUTFORM;/;3$;61| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "/" $) |a| |b|) $))
-(DEFUN |OUTFORM;**;3$;61| (|a| |b| $)
+(DEFUN |OUTFORM;**;3$;62| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "**" $) |a| |b|) $))
-(DEFUN |OUTFORM;div;3$;62| (|a| |b| $)
+(DEFUN |OUTFORM;div;3$;63| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "div" $) |a| |b|) $))
-(DEFUN |OUTFORM;rem;3$;63| (|a| |b| $)
+(DEFUN |OUTFORM;rem;3$;64| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "rem" $) |a| |b|) $))
-(DEFUN |OUTFORM;quo;3$;64| (|a| |b| $)
+(DEFUN |OUTFORM;quo;3$;65| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "quo" $) |a| |b|) $))
-(DEFUN |OUTFORM;exquo;3$;65| (|a| |b| $)
+(DEFUN |OUTFORM;exquo;3$;66| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "exquo" $) |a| |b|) $))
-(DEFUN |OUTFORM;and;3$;66| (|a| |b| $)
+(DEFUN |OUTFORM;and;3$;67| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "and" $) |a| |b|) $))
-(DEFUN |OUTFORM;or;3$;67| (|a| |b| $)
+(DEFUN |OUTFORM;or;3$;68| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "or" $) |a| |b|) $))
-(DEFUN |OUTFORM;not;2$;68| (|a| $)
+(DEFUN |OUTFORM;not;2$;69| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;sform| "not" $) |a|) $))
-(DEFUN |OUTFORM;SEGMENT;3$;69| (|a| |b| $)
+(DEFUN |OUTFORM;SEGMENT;3$;70| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'SEGMENT $) |a| |b|) $))
-(DEFUN |OUTFORM;SEGMENT;2$;70| (|a| $)
+(DEFUN |OUTFORM;SEGMENT;2$;71| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'SEGMENT $) |a|) $))
-(DEFUN |OUTFORM;binomial;3$;71| (|a| |b| $)
+(DEFUN |OUTFORM;binomial;3$;72| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'BINOMIAL $) |a| |b|) $))
-(DEFUN |OUTFORM;empty;$;72| ($)
+(DEFUN |OUTFORM;empty;$;73| ($)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'NOTHING $)) $))
-(DEFUN |OUTFORM;infix?;$B;73| (|a| $)
- (PROG (#0=#:G1494 |e|)
+(DEFUN |OUTFORM;infix?;$B;74| (|a| $)
+ (PROG (#0=#:G1499 |e|)
(RETURN
(SEQ (EXIT (SEQ (LETT |e|
(COND
@@ -349,180 +355,180 @@
((STRINGP |a|) (INTERN |a|))
('T
(PROGN
- (LETT #0# 'NIL |OUTFORM;infix?;$B;73|)
+ (LETT #0# 'NIL |OUTFORM;infix?;$B;74|)
(GO #0#))))
- |OUTFORM;infix?;$B;73|)
+ |OUTFORM;infix?;$B;74|)
(EXIT (COND ((GET |e| 'INFIXOP) 'T) ('T 'NIL)))))
#0# (EXIT #0#)))))
-(PUT '|OUTFORM;elt;$L$;74| '|SPADreplace| 'CONS)
+(PUT '|OUTFORM;elt;$L$;75| '|SPADreplace| 'CONS)
-(DEFUN |OUTFORM;elt;$L$;74| (|a| |l| $) (CONS |a| |l|))
+(DEFUN |OUTFORM;elt;$L$;75| (|a| |l| $) (CONS |a| |l|))
-(DEFUN |OUTFORM;prefix;$L$;75| (|a| |l| $)
+(DEFUN |OUTFORM;prefix;$L$;76| (|a| |l| $)
(COND
- ((NULL (SPADCALL |a| (|getShellEntry| $ 96))) (CONS |a| |l|))
+ ((NULL (SPADCALL |a| (|getShellEntry| $ 98))) (CONS |a| |l|))
('T
(SPADCALL |a|
- (SPADCALL (SPADCALL |l| (|getShellEntry| $ 50))
- (|getShellEntry| $ 60))
- (|getShellEntry| $ 36)))))
+ (SPADCALL (SPADCALL |l| (|getShellEntry| $ 52))
+ (|getShellEntry| $ 62))
+ (|getShellEntry| $ 38)))))
-(DEFUN |OUTFORM;infix;$L$;76| (|a| |l| $)
+(DEFUN |OUTFORM;infix;$L$;77| (|a| |l| $)
(COND
- ((SPADCALL |l| (|getShellEntry| $ 66))
- (SPADCALL (|getShellEntry| $ 11)))
- ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 67))
- (|getShellEntry| $ 66))
- (SPADCALL |l| (|getShellEntry| $ 68)))
- ((SPADCALL |a| (|getShellEntry| $ 96)) (CONS |a| |l|))
+ ((SPADCALL |l| (|getShellEntry| $ 68))
+ (SPADCALL (|getShellEntry| $ 13)))
+ ((SPADCALL (SPADCALL |l| (|getShellEntry| $ 69))
+ (|getShellEntry| $ 68))
+ (SPADCALL |l| (|getShellEntry| $ 70)))
+ ((SPADCALL |a| (|getShellEntry| $ 98)) (CONS |a| |l|))
('T
(SPADCALL
- (LIST (SPADCALL |l| (|getShellEntry| $ 68)) |a|
- (SPADCALL |a| (SPADCALL |l| (|getShellEntry| $ 67))
- (|getShellEntry| $ 99)))
- (|getShellEntry| $ 73)))))
+ (LIST (SPADCALL |l| (|getShellEntry| $ 70)) |a|
+ (SPADCALL |a| (SPADCALL |l| (|getShellEntry| $ 69))
+ (|getShellEntry| $ 101)))
+ (|getShellEntry| $ 75)))))
-(DEFUN |OUTFORM;infix;4$;77| (|a| |b| |c| $)
+(DEFUN |OUTFORM;infix;4$;78| (|a| |b| |c| $)
(COND
- ((SPADCALL |a| (|getShellEntry| $ 96))
+ ((SPADCALL |a| (|getShellEntry| $ 98))
(|OUTFORM;bless| (LIST |a| |b| |c|) $))
- ('T (SPADCALL (LIST |b| |a| |c|) (|getShellEntry| $ 73)))))
+ ('T (SPADCALL (LIST |b| |a| |c|) (|getShellEntry| $ 75)))))
-(DEFUN |OUTFORM;postfix;3$;78| (|a| |b| $)
- (SPADCALL |b| |a| (|getShellEntry| $ 36)))
+(DEFUN |OUTFORM;postfix;3$;79| (|a| |b| $)
+ (SPADCALL |b| |a| (|getShellEntry| $ 38)))
-(DEFUN |OUTFORM;string;2$;79| (|a| $)
+(DEFUN |OUTFORM;string;2$;80| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'STRING $) |a|) $))
-(DEFUN |OUTFORM;quote;2$;80| (|a| $)
+(DEFUN |OUTFORM;quote;2$;81| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'QUOTE $) |a|) $))
-(DEFUN |OUTFORM;overbar;2$;81| (|a| $)
+(DEFUN |OUTFORM;overbar;2$;82| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'OVERBAR $) |a|) $))
-(DEFUN |OUTFORM;dot;2$;82| (|a| $)
- (SPADCALL |a| (|OUTFORM;sform| "." $) (|getShellEntry| $ 63)))
+(DEFUN |OUTFORM;dot;2$;83| (|a| $)
+ (SPADCALL |a| (|OUTFORM;sform| "." $) (|getShellEntry| $ 65)))
-(DEFUN |OUTFORM;prime;2$;83| (|a| $)
- (SPADCALL |a| (|OUTFORM;sform| "," $) (|getShellEntry| $ 63)))
+(DEFUN |OUTFORM;prime;2$;84| (|a| $)
+ (SPADCALL |a| (|OUTFORM;sform| "," $) (|getShellEntry| $ 65)))
-(DEFUN |OUTFORM;dot;$Nni$;84| (|a| |nn| $)
+(DEFUN |OUTFORM;dot;$Nni$;85| (|a| |nn| $)
(PROG (|s|)
(RETURN
(SEQ (LETT |s|
(MAKE-FULL-CVEC |nn|
- (SPADCALL "." (|getShellEntry| $ 107)))
- |OUTFORM;dot;$Nni$;84|)
+ (SPADCALL "." (|getShellEntry| $ 109)))
+ |OUTFORM;dot;$Nni$;85|)
(EXIT (SPADCALL |a| (|OUTFORM;sform| |s| $)
- (|getShellEntry| $ 63)))))))
+ (|getShellEntry| $ 65)))))))
-(DEFUN |OUTFORM;prime;$Nni$;85| (|a| |nn| $)
+(DEFUN |OUTFORM;prime;$Nni$;86| (|a| |nn| $)
(PROG (|s|)
(RETURN
(SEQ (LETT |s|
(MAKE-FULL-CVEC |nn|
- (SPADCALL "," (|getShellEntry| $ 107)))
- |OUTFORM;prime;$Nni$;85|)
+ (SPADCALL "," (|getShellEntry| $ 109)))
+ |OUTFORM;prime;$Nni$;86|)
(EXIT (SPADCALL |a| (|OUTFORM;sform| |s| $)
- (|getShellEntry| $ 63)))))))
+ (|getShellEntry| $ 65)))))))
-(DEFUN |OUTFORM;overlabel;3$;86| (|a| |b| $)
+(DEFUN |OUTFORM;overlabel;3$;87| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'OVERLABEL $) |a| |b|) $))
-(DEFUN |OUTFORM;box;2$;87| (|a| $)
+(DEFUN |OUTFORM;box;2$;88| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'BOX $) |a|) $))
-(DEFUN |OUTFORM;zag;3$;88| (|a| |b| $)
+(DEFUN |OUTFORM;zag;3$;89| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'ZAG $) |a| |b|) $))
-(DEFUN |OUTFORM;root;2$;89| (|a| $)
+(DEFUN |OUTFORM;root;2$;90| (|a| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'ROOT $) |a|) $))
-(DEFUN |OUTFORM;root;3$;90| (|a| |b| $)
+(DEFUN |OUTFORM;root;3$;91| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'ROOT $) |a| |b|) $))
-(DEFUN |OUTFORM;over;3$;91| (|a| |b| $)
+(DEFUN |OUTFORM;over;3$;92| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'OVER $) |a| |b|) $))
-(DEFUN |OUTFORM;slash;3$;92| (|a| |b| $)
+(DEFUN |OUTFORM;slash;3$;93| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'SLASH $) |a| |b|) $))
-(DEFUN |OUTFORM;assign;3$;93| (|a| |b| $)
+(DEFUN |OUTFORM;assign;3$;94| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'LET $) |a| |b|) $))
-(DEFUN |OUTFORM;label;3$;94| (|a| |b| $)
+(DEFUN |OUTFORM;label;3$;95| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'EQUATNUM $) |a| |b|) $))
-(DEFUN |OUTFORM;rarrow;3$;95| (|a| |b| $)
+(DEFUN |OUTFORM;rarrow;3$;96| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'TAG $) |a| |b|) $))
-(DEFUN |OUTFORM;differentiate;$Nni$;96| (|a| |nn| $)
- (PROG (#0=#:G1524 |r| |s|)
+(DEFUN |OUTFORM;differentiate;$Nni$;97| (|a| |nn| $)
+ (PROG (#0=#:G1529 |r| |s|)
(RETURN
(SEQ (COND
((ZEROP |nn|) |a|)
- ((< |nn| 4) (SPADCALL |a| |nn| (|getShellEntry| $ 109)))
+ ((< |nn| 4) (SPADCALL |a| |nn| (|getShellEntry| $ 111)))
('T
(SEQ (LETT |r|
(SPADCALL
(PROG1 (LETT #0# |nn|
- |OUTFORM;differentiate;$Nni$;96|)
+ |OUTFORM;differentiate;$Nni$;97|)
(|check-subtype| (> #0# 0)
'(|PositiveInteger|) #0#))
- (|getShellEntry| $ 122))
- |OUTFORM;differentiate;$Nni$;96|)
- (LETT |s| (SPADCALL |r| (|getShellEntry| $ 123))
- |OUTFORM;differentiate;$Nni$;96|)
+ (|getShellEntry| $ 124))
+ |OUTFORM;differentiate;$Nni$;97|)
+ (LETT |s| (SPADCALL |r| (|getShellEntry| $ 125))
+ |OUTFORM;differentiate;$Nni$;97|)
(EXIT (SPADCALL |a|
(SPADCALL (|OUTFORM;sform| |s| $)
- (|getShellEntry| $ 60))
- (|getShellEntry| $ 63))))))))))
+ (|getShellEntry| $ 62))
+ (|getShellEntry| $ 65))))))))))
-(DEFUN |OUTFORM;sum;2$;97| (|a| $)
+(DEFUN |OUTFORM;sum;2$;98| (|a| $)
(|OUTFORM;bless|
(LIST (|OUTFORM;eform| 'SIGMA $)
- (SPADCALL (|getShellEntry| $ 11)) |a|)
+ (SPADCALL (|getShellEntry| $ 13)) |a|)
$))
-(DEFUN |OUTFORM;sum;3$;98| (|a| |b| $)
+(DEFUN |OUTFORM;sum;3$;99| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'SIGMA $) |b| |a|) $))
-(DEFUN |OUTFORM;sum;4$;99| (|a| |b| |c| $)
+(DEFUN |OUTFORM;sum;4$;100| (|a| |b| |c| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'SIGMA2 $) |b| |c| |a|) $))
-(DEFUN |OUTFORM;prod;2$;100| (|a| $)
+(DEFUN |OUTFORM;prod;2$;101| (|a| $)
(|OUTFORM;bless|
- (LIST (|OUTFORM;eform| 'PI $) (SPADCALL (|getShellEntry| $ 11))
+ (LIST (|OUTFORM;eform| 'PI $) (SPADCALL (|getShellEntry| $ 13))
|a|)
$))
-(DEFUN |OUTFORM;prod;3$;101| (|a| |b| $)
+(DEFUN |OUTFORM;prod;3$;102| (|a| |b| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'PI $) |b| |a|) $))
-(DEFUN |OUTFORM;prod;4$;102| (|a| |b| |c| $)
+(DEFUN |OUTFORM;prod;4$;103| (|a| |b| |c| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'PI2 $) |b| |c| |a|) $))
-(DEFUN |OUTFORM;int;2$;103| (|a| $)
+(DEFUN |OUTFORM;int;2$;104| (|a| $)
(|OUTFORM;bless|
(LIST (|OUTFORM;eform| 'INTSIGN $)
- (SPADCALL (|getShellEntry| $ 11))
- (SPADCALL (|getShellEntry| $ 11)) |a|)
+ (SPADCALL (|getShellEntry| $ 13))
+ (SPADCALL (|getShellEntry| $ 13)) |a|)
$))
-(DEFUN |OUTFORM;int;3$;104| (|a| |b| $)
+(DEFUN |OUTFORM;int;3$;105| (|a| |b| $)
(|OUTFORM;bless|
(LIST (|OUTFORM;eform| 'INTSIGN $) |b|
- (SPADCALL (|getShellEntry| $ 11)) |a|)
+ (SPADCALL (|getShellEntry| $ 13)) |a|)
$))
-(DEFUN |OUTFORM;int;4$;105| (|a| |b| |c| $)
+(DEFUN |OUTFORM;int;4$;106| (|a| |b| |c| $)
(|OUTFORM;bless| (LIST (|OUTFORM;eform| 'INTSIGN $) |b| |c| |a|) $))
(DEFUN |OutputForm| ()
(PROG ()
(RETURN
- (PROG (#0=#:G1538)
+ (PROG (#0=#:G1543)
(RETURN
(COND
((LETT #0# (HGET |$ConstructorCache| '|OutputForm|)
@@ -542,73 +548,75 @@
(RETURN
(PROGN
(LETT |dv$| '(|OutputForm|) . #0=(|OutputForm|))
- (LETT $ (|newShell| 135) . #0#)
+ (LETT $ (|newShell| 137) . #0#)
(|setShellEntry| $ 0 |dv$|)
(|setShellEntry| $ 3
(LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
(|haddProp| |$ConstructorCache| '|OutputForm| NIL (CONS 1 $))
(|stuffDomainSlots| $)
+ (|setShellEntry| $ 6 "~G")
$))))
(MAKEPROP '|OutputForm| '|infovec|
- (LIST '#(NIL NIL NIL NIL NIL NIL (|Void|) |OUTFORM;print;$V;5|
- (|Boolean|) (|String|) (0 . |empty?|) |OUTFORM;empty;$;72|
- |OUTFORM;message;S$;6| |OUTFORM;messagePrint;SV;7|
- |OUTFORM;=;2$B;8| |OUTFORM;=;3$;9| (|OutputForm|)
- |OUTFORM;coerce;2$;10| (|Integer|)
- |OUTFORM;outputForm;I$;11| (|Symbol|)
- |OUTFORM;outputForm;S$;12| (|DoubleFloat|)
- |OUTFORM;outputForm;Df$;13| (|Character|) (5 . |quote|)
- (9 . |concat|) (15 . |concat|) |OUTFORM;outputForm;S$;14|
- |OUTFORM;width;$I;15| |OUTFORM;height;$I;16|
- |OUTFORM;subHeight;$I;17| |OUTFORM;superHeight;$I;18|
- |OUTFORM;height;I;19| |OUTFORM;width;I;20|
- |OUTFORM;hspace;I$;28| |OUTFORM;hconcat;3$;47|
- |OUTFORM;center;$I$;21| |OUTFORM;left;$I$;22|
- |OUTFORM;right;$I$;23| |OUTFORM;center;2$;24|
- |OUTFORM;left;2$;25| |OUTFORM;right;2$;26|
- |OUTFORM;vspace;I$;27| |OUTFORM;vconcat;3$;49|
- |OUTFORM;rspace;2I$;29| (|List| $) (|List| 46)
- |OUTFORM;matrix;L$;30| |OUTFORM;pile;L$;31|
- |OUTFORM;commaSeparate;L$;32|
- |OUTFORM;semicolonSeparate;L$;33| (|List| $$)
+ (LIST '#(NIL NIL NIL NIL NIL NIL '|format| (|String|)
+ |OUTFORM;doubleFloatFormat;2S;1| (|Void|)
+ |OUTFORM;print;$V;6| (|Boolean|) (0 . |empty?|)
+ |OUTFORM;empty;$;73| |OUTFORM;message;S$;7|
+ |OUTFORM;messagePrint;SV;8| |OUTFORM;=;2$B;9|
+ |OUTFORM;=;3$;10| (|OutputForm|) |OUTFORM;coerce;2$;11|
+ (|Integer|) |OUTFORM;outputForm;I$;12| (|Symbol|)
+ |OUTFORM;outputForm;S$;13| (|DoubleFloat|)
+ |OUTFORM;outputForm;Df$;14| (|Character|) (5 . |quote|)
+ (9 . |concat|) (15 . |concat|) |OUTFORM;outputForm;S$;15|
+ |OUTFORM;width;$I;16| |OUTFORM;height;$I;17|
+ |OUTFORM;subHeight;$I;18| |OUTFORM;superHeight;$I;19|
+ |OUTFORM;height;I;20| |OUTFORM;width;I;21|
+ |OUTFORM;hspace;I$;29| |OUTFORM;hconcat;3$;48|
+ |OUTFORM;center;$I$;22| |OUTFORM;left;$I$;23|
+ |OUTFORM;right;$I$;24| |OUTFORM;center;2$;25|
+ |OUTFORM;left;2$;26| |OUTFORM;right;2$;27|
+ |OUTFORM;vspace;I$;28| |OUTFORM;vconcat;3$;50|
+ |OUTFORM;rspace;2I$;30| (|List| $) (|List| 48)
+ |OUTFORM;matrix;L$;31| |OUTFORM;pile;L$;32|
+ |OUTFORM;commaSeparate;L$;33|
+ |OUTFORM;semicolonSeparate;L$;34| (|List| $$)
(21 . |reverse|) (26 . |append|)
- |OUTFORM;blankSeparate;L$;34| |OUTFORM;brace;2$;35|
- |OUTFORM;brace;L$;36| |OUTFORM;bracket;2$;37|
- |OUTFORM;bracket;L$;38| |OUTFORM;paren;2$;39|
- |OUTFORM;paren;L$;40| |OUTFORM;sub;3$;41|
- |OUTFORM;super;3$;42| |OUTFORM;presub;3$;43|
- |OUTFORM;presuper;3$;44| (32 . |null|) (37 . |rest|)
- (42 . |first|) |OUTFORM;scripts;$L$;45|
+ |OUTFORM;blankSeparate;L$;35| |OUTFORM;brace;2$;36|
+ |OUTFORM;brace;L$;37| |OUTFORM;bracket;2$;38|
+ |OUTFORM;bracket;L$;39| |OUTFORM;paren;2$;40|
+ |OUTFORM;paren;L$;41| |OUTFORM;sub;3$;42|
+ |OUTFORM;super;3$;43| |OUTFORM;presub;3$;44|
+ |OUTFORM;presuper;3$;45| (32 . |null|) (37 . |rest|)
+ (42 . |first|) |OUTFORM;scripts;$L$;46|
(|NonNegativeInteger|) (47 . |#|)
- |OUTFORM;supersub;$L$;46| |OUTFORM;hconcat;L$;48|
- |OUTFORM;vconcat;L$;50| |OUTFORM;~=;3$;51|
- |OUTFORM;<;3$;52| |OUTFORM;>;3$;53| |OUTFORM;<=;3$;54|
- |OUTFORM;>=;3$;55| |OUTFORM;+;3$;56| |OUTFORM;-;3$;57|
- |OUTFORM;-;2$;58| |OUTFORM;*;3$;59| |OUTFORM;/;3$;60|
- |OUTFORM;**;3$;61| |OUTFORM;div;3$;62| |OUTFORM;rem;3$;63|
- |OUTFORM;quo;3$;64| |OUTFORM;exquo;3$;65|
- |OUTFORM;and;3$;66| |OUTFORM;or;3$;67| |OUTFORM;not;2$;68|
- |OUTFORM;SEGMENT;3$;69| |OUTFORM;SEGMENT;2$;70|
- |OUTFORM;binomial;3$;71| |OUTFORM;infix?;$B;73|
- |OUTFORM;elt;$L$;74| |OUTFORM;prefix;$L$;75|
- |OUTFORM;infix;$L$;76| |OUTFORM;infix;4$;77|
- |OUTFORM;postfix;3$;78| |OUTFORM;string;2$;79|
- |OUTFORM;quote;2$;80| |OUTFORM;overbar;2$;81|
- |OUTFORM;dot;2$;82| |OUTFORM;prime;2$;83| (52 . |char|)
- |OUTFORM;dot;$Nni$;84| |OUTFORM;prime;$Nni$;85|
- |OUTFORM;overlabel;3$;86| |OUTFORM;box;2$;87|
- |OUTFORM;zag;3$;88| |OUTFORM;root;2$;89|
- |OUTFORM;root;3$;90| |OUTFORM;over;3$;91|
- |OUTFORM;slash;3$;92| |OUTFORM;assign;3$;93|
- |OUTFORM;label;3$;94| |OUTFORM;rarrow;3$;95|
+ |OUTFORM;supersub;$L$;47| |OUTFORM;hconcat;L$;49|
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+ |OUTFORM;dot;2$;83| |OUTFORM;prime;2$;84| (52 . |char|)
+ |OUTFORM;dot;$Nni$;85| |OUTFORM;prime;$Nni$;86|
+ |OUTFORM;overlabel;3$;87| |OUTFORM;box;2$;88|
+ |OUTFORM;zag;3$;89| |OUTFORM;root;2$;90|
+ |OUTFORM;root;3$;91| |OUTFORM;over;3$;92|
+ |OUTFORM;slash;3$;93| |OUTFORM;assign;3$;94|
+ |OUTFORM;label;3$;95| |OUTFORM;rarrow;3$;96|
(|PositiveInteger|) (|NumberFormats|) (57 . |FormatRoman|)
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- |OUTFORM;int;2$;103| |OUTFORM;int;3$;104|
- |OUTFORM;int;4$;105| (|SingleInteger|))
+ (62 . |lowerCase|) |OUTFORM;differentiate;$Nni$;97|
+ |OUTFORM;sum;2$;98| |OUTFORM;sum;3$;99|
+ |OUTFORM;sum;4$;100| |OUTFORM;prod;2$;101|
+ |OUTFORM;prod;3$;102| |OUTFORM;prod;4$;103|
+ |OUTFORM;int;2$;104| |OUTFORM;int;3$;105|
+ |OUTFORM;int;4$;106| (|SingleInteger|))
'#(~= 67 |zag| 79 |width| 85 |vspace| 94 |vconcat| 99
|supersub| 110 |superHeight| 116 |super| 121 |sum| 127
|subHeight| 145 |sub| 150 |string| 156 |slash| 161
@@ -621,159 +629,163 @@
|matrix| 360 |left| 365 |latex| 376 |label| 381 |int| 387
|infix?| 405 |infix| 410 |hspace| 423 |height| 428
|hconcat| 437 |hash| 448 |exquo| 453 |empty| 459 |elt| 463
- |dot| 469 |div| 480 |differentiate| 486 |commaSeparate|
- 492 |coerce| 497 |center| 502 |bracket| 513 |brace| 523
- |box| 533 |blankSeparate| 538 |binomial| 543 |assign| 549
- |and| 555 SEGMENT 561 >= 572 > 578 = 584 <= 596 < 602 /
- 608 - 614 + 625 ** 631 * 637)
+ |doubleFloatFormat| 469 |dot| 474 |div| 485
+ |differentiate| 491 |commaSeparate| 497 |coerce| 502
+ |center| 507 |bracket| 518 |brace| 528 |box| 538
+ |blankSeparate| 543 |binomial| 548 |assign| 554 |and| 560
+ SEGMENT 566 >= 577 > 583 = 589 <= 601 < 607 / 613 - 619 +
+ 630 ** 636 * 642)
'NIL
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+ '(((SEGMENT ($ $)) T (ELT $ 96))
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+ ((|width| ((|Integer|))) T (ELT $ 36))
+ ((|height| ((|Integer|) $)) T (ELT $ 32))
+ ((|width| ((|Integer|) $)) T (ELT $ 31))
+ ((|doubleFloatFormat| ((|String|) (|String|))) T
+ (ELT $ 8))
+ ((|empty| ($)) T (ELT $ 13))
+ ((|outputForm| ($ (|DoubleFloat|))) T (ELT $ 25))
+ ((|outputForm| ($ (|String|))) T (ELT $ 30))
+ ((|outputForm| ($ (|Symbol|))) T (ELT $ 23))
+ ((|outputForm| ($ (|Integer|))) T (ELT $ 21))
+ ((|messagePrint| ((|Void|) (|String|))) T (ELT $ 15))
+ ((|message| ($ (|String|))) T (ELT $ 14))
+ ((|print| ((|Void|) $)) T (ELT $ 10))
((|latex| ((|String|) $)) T (ELT $ NIL))
((|hash| ((|SingleInteger|) $)) T (ELT $ NIL))
- ((|coerce| ((|OutputForm|) $)) T (ELT $ 17))
- ((= ((|Boolean|) $ $)) T (ELT $ 14))
+ ((|coerce| ((|OutputForm|) $)) T (ELT $ 19))
+ ((= ((|Boolean|) $ $)) T (ELT $ 16))
((~= ((|Boolean|) $ $)) T (ELT $ NIL)))
(|addModemap| '|OutputForm| '(|OutputForm|)
'((|Join| (|SetCategory|)
@@ -788,6 +800,8 @@
(SIGNATURE |outputForm|
($ (|DoubleFloat|)))
(SIGNATURE |empty| ($))
+ (SIGNATURE |doubleFloatFormat|
+ ((|String|) (|String|)))
(SIGNATURE |width| ((|Integer|) $))
(SIGNATURE |height| ((|Integer|) $))
(SIGNATURE |width| ((|Integer|)))
@@ -907,6 +921,8 @@
(SIGNATURE |outputForm|
($ (|DoubleFloat|)))
(SIGNATURE |empty| ($))
+ (SIGNATURE |doubleFloatFormat|
+ ((|String|) (|String|)))
(SIGNATURE |width|
((|Integer|) $))
(SIGNATURE |height|
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 0ffdb818..c292e4ed 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(2267193 . 3431822560)
+(2267755 . 3431897906)
(-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.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
(-20 S)
((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\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(\\spad{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(\\spad{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| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(\\spad{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(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . 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(\\spad{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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{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| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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(\\spad{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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(\\spad{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| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-4339 . T) (-4337 . T) (-4336 . T) ((-4344 "*") . T) (-4335 . T) (-4340 . T) (-4334 . T) (-1964 . T))
+((-4341 . T) (-4339 . T) (-4338 . T) ((-4346 "*") . T) (-4337 . T) (-4342 . T) (-4336 . T) (-2836 . T))
NIL
(-30)
((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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.")))
@@ -56,17 +56,17 @@ 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 -3260)
+(-32 R -3327)
((|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 -1011) (QUOTE (-550)))))
+((|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))))
(-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 -4342)))
+((|HasAttribute| |#1| (QUOTE -4344)))
(-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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-35)
((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}.")))
@@ -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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}.")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
(-37 S R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra.")))
@@ -82,20 +82,20 @@ NIL
NIL
(-38 R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . 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 -3260 UP UPUP -4189)
+(-40 -3327 UP UPUP -2351)
((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}")))
-((-4335 |has| (-400 |#2|) (-356)) (-4340 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1561 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1561 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1561 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1561 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))))
-(-41 R -3260)
+((-4337 |has| (-400 |#2|) (-356)) (-4342 |has| (-400 |#2|) (-356)) (-4336 |has| (-400 |#2|) (-356)) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1489 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1489 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1489 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1489 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))))
+(-41 R -3327)
((|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| $)) $) "\\spad{numer(x)} \\undocumented")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))))
+((-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -423) (|devaluate| |#1|)))))
(-42 OV E P)
((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}.")))
NIL
@@ -106,31 +106,31 @@ NIL
((|HasCategory| |#1| (QUOTE (-300))))
(-44 R |n| |ls| |gamma|)
((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra.")))
-((-4339 |has| |#1| (-542)) (-4337 . T) (-4336 . T))
+((-4341 |has| |#1| (-542)) (-4339 . T) (-4338 . T))
((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542))))
(-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.")))
-((-4342 . T) (-4343 . T))
-((-1561 (-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|))))))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-1489 (-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|))))))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-825))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
(-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356))))
(-47 R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-48)
((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| $ (QUOTE (-1020))) (|HasCategory| $ (LIST (QUOTE -1011) (QUOTE (-550)))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| $ (QUOTE (-1021))) (|HasCategory| $ (LIST (QUOTE -1012) (QUOTE (-550)))))
(-49)
((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}.")))
NIL
NIL
(-50 R |lVar|)
((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}.")))
-((-4339 . T))
+((-4341 . 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 -3260)
+(-54 |Base| R -3327)
((|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
@@ -154,7 +154,7 @@ NIL
NIL
(-56 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")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
(-57 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),{}...]}.")))
@@ -162,65 +162,65 @@ NIL
NIL
(-58 S)
((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-59 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-60 -1916)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-60 -1856)
((|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
-(-61 -1916)
+(-61 -1856)
((|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
-(-62 -1916)
+(-62 -1856)
((|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
-(-63 -1916)
+(-63 -1856)
((|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
-(-64 -1916)
+(-64 -1856)
((|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}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-65 -1916)
+(-65 -1856)
((|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
-(-66 -1916)
+(-66 -1856)
((|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
-(-67 -1916)
+(-67 -1856)
((|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
-(-68 -1916)
+(-68 -1856)
((|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
-(-69 -1916)
+(-69 -1856)
((|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
-(-70 -1916)
+(-70 -1856)
((|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
-(-71 -1916)
+(-71 -1856)
((|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
-(-72 -1916)
+(-72 -1856)
((|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
-(-73 -1916)
+(-73 -1856)
((|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
@@ -232,55 +232,55 @@ 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
-(-76 -1916)
+(-76 -1856)
((|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
-(-77 -1916)
+(-77 -1856)
((|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
-(-78 -1916)
+(-78 -1856)
((|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
-(-79 -1916)
+(-79 -1856)
((|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
-(-80 -1916)
+(-80 -1856)
((|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}")) (|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 -1916)
+(-81 -1856)
((|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
-(-82 -1916)
+(-82 -1856)
((|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
-(-83 -1916)
+(-83 -1856)
((|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
-(-84 -1916)
+(-84 -1856)
((|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
-(-85 -1916)
+(-85 -1856)
((|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
-(-86 -1916)
+(-86 -1856)
((|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
-(-87 -1916)
+(-87 -1856)
((|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
-(-88 -1916)
+(-88 -1856)
((|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
@@ -290,8 +290,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-356))))
(-90 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-91 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
NIL
@@ -314,15 +314,15 @@ NIL
NIL
(-96)
((|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\".")))
-((-4342 . T))
+((-4344 . T))
NIL
(-97)
((|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.")))
-((-4342 . T) ((-4344 "*") . T) (-4343 . T) (-4339 . T) (-4337 . T) (-4336 . T) (-4335 . T) (-4340 . T) (-4334 . T) (-4333 . T) (-4332 . T) (-4331 . T) (-4330 . T) (-4338 . T) (-4341 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4329 . T))
+((-4344 . T) ((-4346 "*") . T) (-4345 . T) (-4341 . T) (-4339 . T) (-4338 . T) (-4337 . T) (-4342 . T) (-4336 . T) (-4335 . T) (-4334 . T) (-4333 . T) (-4332 . T) (-4340 . T) (-4343 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4331 . T))
NIL
(-98 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}.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-99 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{\\spad{pi}} is balanced with respect to \\spad{b}.")))
@@ -338,15 +338,15 @@ NIL
NIL
(-102 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-103 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 (-4344 "*"))))
+((|HasAttribute| |#1| (QUOTE (-4346 "*"))))
(-104)
((|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")))
-((-4342 . T))
+((-4344 . T))
NIL
(-105 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.")))
@@ -354,12 +354,12 @@ NIL
NIL
(-106 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.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
(-107)
((|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.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-550) (QUOTE (-882))) (|HasCategory| (-550) (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-995))) (|HasCategory| (-550) (QUOTE (-798))) (-1561 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1119))) (|HasCategory| (-550) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1144)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-882)))) (|HasCategory| (-550) (QUOTE (-143)))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-550) (QUOTE (-883))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-996))) (|HasCategory| (-550) (QUOTE (-798))) (-1489 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1120))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1145)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (|HasCategory| (-550) (QUOTE (-143)))))
(-108)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}")))
NIL
@@ -370,11 +370,11 @@ NIL
NIL
(-110)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| (-112) (QUOTE (-1068))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-112) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-112) (QUOTE (-1068))) (|HasCategory| (-112) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| (-112) (QUOTE (-1069))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-112) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-112) (QUOTE (-1069))) (|HasCategory| (-112) (LIST (QUOTE -595) (QUOTE (-837)))))
(-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}")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
(-112)
((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant.")))
@@ -388,25 +388,25 @@ NIL
((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}.")))
NIL
NIL
-(-115 -3260 UP)
+(-115 -3327 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
(-116 |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}.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-117 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-116 |#1|) (QUOTE (-882))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-116 |#1|) (QUOTE (-995))) (|HasCategory| (-116 |#1|) (QUOTE (-798))) (-1561 (|HasCategory| (-116 |#1|) (QUOTE (-798))) (|HasCategory| (-116 |#1|) (QUOTE (-825)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-116 |#1|) (QUOTE (-1119))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-116 |#1|) (QUOTE (-227))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -505) (QUOTE (-1144)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-300))) (|HasCategory| (-116 |#1|) (QUOTE (-535))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-882)))) (|HasCategory| (-116 |#1|) (QUOTE (-143)))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-116 |#1|) (QUOTE (-883))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-116 |#1|) (QUOTE (-996))) (|HasCategory| (-116 |#1|) (QUOTE (-798))) (-1489 (|HasCategory| (-116 |#1|) (QUOTE (-798))) (|HasCategory| (-116 |#1|) (QUOTE (-825)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-116 |#1|) (QUOTE (-1120))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-116 |#1|) (QUOTE (-227))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -505) (QUOTE (-1145)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-300))) (|HasCategory| (-116 |#1|) (QUOTE (-535))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-883)))) (|HasCategory| (-116 |#1|) (QUOTE (-143)))))
(-118 A S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4343)))
+((|HasAttribute| |#1| (QUOTE -4345)))
(-119 S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-120 UP)
((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive.")))
@@ -414,15 +414,15 @@ NIL
NIL
(-121 S)
((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-122 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")))
NIL
NIL
(-123)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
(-124 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
@@ -430,20 +430,20 @@ NIL
NIL
(-125 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
(-126 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-127 S)
((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-128)
((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes.")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| (-129) (QUOTE (-825))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1068))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129)))))) (-1561 (-12 (|HasCategory| (-129) (QUOTE (-1068))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-129) (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| (-129) (QUOTE (-825))) (|HasCategory| (-129) (QUOTE (-1068)))) (|HasCategory| (-129) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-129) (QUOTE (-1068))) (-12 (|HasCategory| (-129) (QUOTE (-1068))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| (-129) (QUOTE (-825))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1069))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129)))))) (-1489 (-12 (|HasCategory| (-129) (QUOTE (-1069))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-129) (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| (-129) (QUOTE (-825))) (|HasCategory| (-129) (QUOTE (-1069)))) (|HasCategory| (-129) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-129) (QUOTE (-1069))) (-12 (|HasCategory| (-129) (QUOTE (-1069))) (|HasCategory| (-129) (LIST (QUOTE -302) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -595) (QUOTE (-837)))))
(-129)
((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|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
@@ -462,13 +462,13 @@ NIL
NIL
(-133)
((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")))
-(((-4344 "*") . T))
+(((-4346 "*") . T))
NIL
-(-134 |minix| -3873 S T$)
+(-134 |minix| -2281 S T$)
((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}.")))
NIL
NIL
-(-135 |minix| -3873 R)
+(-135 |minix| -2281 R)
((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor.")))
NIL
NIL
@@ -486,8 +486,8 @@ NIL
NIL
(-139)
((|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}.")))
-((-4342 . T) (-4332 . T) (-4343 . T))
-((-1561 (-12 (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1068))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4334 . T) (-4345 . T))
+((-1489 (-12 (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-142) (QUOTE (-361))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1069))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-837)))))
(-140 R Q A)
((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}.")))
NIL
@@ -502,7 +502,7 @@ NIL
NIL
(-143)
((|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.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-144 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}.")))
@@ -510,9 +510,9 @@ NIL
NIL
(-145)
((|constructor| (NIL "Rings of Characteristic Zero.")))
-((-4339 . T))
+((-4341 . T))
NIL
-(-146 -3260 UP UPUP)
+(-146 -3327 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
@@ -523,14 +523,14 @@ NIL
(-148 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 -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasAttribute| |#1| (QUOTE -4342)))
+((|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasAttribute| |#1| (QUOTE -4344)))
(-149 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.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-150 |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.")))
-((-4337 . T) (-4336 . T) (-4339 . T))
+((-4339 . T) (-4338 . T) (-4341 . T))
NIL
(-151)
((|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.")))
@@ -552,7 +552,7 @@ 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
-(-156 R -3260)
+(-156 R -3327)
((|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
@@ -583,10 +583,10 @@ NIL
(-163 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 (-882))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-1166))) (|HasCategory| |#2| (QUOTE (-1029))) (|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasAttribute| |#2| (QUOTE -4338)) (|HasAttribute| |#2| (QUOTE -4341)) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-825))))
+((|HasCategory| |#2| (QUOTE (-883))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-976))) (|HasCategory| |#2| (QUOTE (-1167))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasAttribute| |#2| (QUOTE -4340)) (|HasAttribute| |#2| (QUOTE -4343)) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-825))))
(-164 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})")))
-((-4335 -1561 (|has| |#1| (-542)) (-12 (|has| |#1| (-300)) (|has| |#1| (-882)))) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4338 |has| |#1| (-6 -4338)) (-4341 |has| |#1| (-6 -4341)) (-2738 . T) (-1964 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 -1489 (|has| |#1| (-542)) (-12 (|has| |#1| (-300)) (|has| |#1| (-883)))) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4340 |has| |#1| (-6 -4340)) (-4343 |has| |#1| (-6 -4343)) (-2167 . T) (-2836 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-165 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.")))
@@ -598,8 +598,8 @@ NIL
NIL
(-167 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}.")))
-((-4335 -1561 (|has| |#1| (-542)) (-12 (|has| |#1| (-300)) (|has| |#1| (-882)))) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4338 |has| |#1| (-6 -4338)) (-4341 |has| |#1| (-6 -4341)) (-2738 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-342))) (-1561 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1561 (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1144)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-227))) (-12 (|HasCategory| |#1| 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(-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144))))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-143)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-342)))))
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(QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-806)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-825)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-996)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-1167)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-883))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) 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(QUOTE -505) (QUOTE (-1145)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| |#1| (QUOTE (-1030))) (-12 (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-1167)))) (|HasCategory| |#1| (QUOTE (-535))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-356)))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-227))) (-12 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasAttribute| |#1| (QUOTE -4340)) (|HasAttribute| |#1| (QUOTE -4343)) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145))))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-143)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-342)))))
(-168 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
@@ -610,7 +610,7 @@ NIL
NIL
(-170)
((|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.")))
-(((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-171)
((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations.")))
@@ -618,7 +618,7 @@ NIL
NIL
(-172 R)
((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}.")))
-(((-4344 "*") . T) (-4335 . T) (-4340 . T) (-4334 . T) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") . T) (-4337 . T) (-4342 . T) (-4336 . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-173)
((|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| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|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}.")))
@@ -635,7 +635,7 @@ NIL
(-176 R S CS)
((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
-((|HasCategory| (-925 |#2|) (LIST (QUOTE -859) (|devaluate| |#1|))))
+((|HasCategory| (-926 |#2|) (LIST (QUOTE -860) (|devaluate| |#1|))))
(-177 R)
((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}")))
NIL
@@ -656,7 +656,7 @@ NIL
((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor")))
NIL
NIL
-(-182 R -3260)
+(-182 R -3327)
((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels.")))
NIL
NIL
@@ -764,23 +764,23 @@ NIL
((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}")))
NIL
NIL
-(-209 -3260 UP UPUP R)
+(-209 -3327 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
-(-210 -3260 FP)
+(-210 -3327 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
(-211)
((|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.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
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+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-550) (QUOTE (-883))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-996))) (|HasCategory| (-550) (QUOTE (-798))) (-1489 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1120))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1145)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (|HasCategory| (-550) (QUOTE (-143)))))
(-212)
((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-213 R -3260)
+(-213 R -3327)
((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
@@ -794,19 +794,19 @@ NIL
NIL
(-216 S)
((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-217 |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}.")))
-((-4339 . T))
+((-4341 . T))
NIL
-(-218 R -3260)
+(-218 R -3327)
((|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
(-219)
-((|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)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|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}.")))
-((-2001 . T) (-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((|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}.")))
+((-2154 . T) (-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-220)
((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}")))
@@ -814,23 +814,23 @@ NIL
NIL
(-221 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}")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4344 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4346 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-222 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
(-223 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.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
(-224 S R)
((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-227))))
+((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-227))))
(-225 R)
((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-226 S)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")))
@@ -838,36 +838,36 @@ NIL
NIL
(-227)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-228 A S)
((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4342)))
+((|HasAttribute| |#1| (QUOTE -4344)))
(-229 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}.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
(-230)
((|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
-(-231 S -3873 R)
+(-231 S -2281 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size")))
NIL
-((|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (QUOTE (-823))) (|HasAttribute| |#3| (QUOTE -4339)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (QUOTE (-1068))))
-(-232 -3873 R)
+((|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (QUOTE (-823))) (|HasAttribute| |#3| (QUOTE -4341)) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (QUOTE (-1069))))
+(-232 -2281 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size")))
-((-4336 |has| |#2| (-1020)) (-4337 |has| |#2| (-1020)) (-4339 |has| |#2| (-6 -4339)) ((-4344 "*") |has| |#2| (-170)) (-4342 . T) (-1964 . T))
+((-4338 |has| |#2| (-1021)) (-4339 |has| |#2| (-1021)) (-4341 |has| |#2| (-6 -4341)) ((-4346 "*") |has| |#2| (-170)) (-4344 . T) (-2836 . T))
NIL
-(-233 -3873 A B)
+(-233 -2281 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
-(-234 -3873 R)
+(-234 -2281 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.")))
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(-235)
((|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
@@ -878,47 +878,47 @@ NIL
NIL
(-237)
((|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}.")))
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NIL
(-238 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.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-239 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}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}")))
-((-4343 . T) (-4342 . T))
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+((-4345 . T) (-4344 . T))
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(-240 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
(-241 |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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(-242)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: January 19,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall")) (|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")))
NIL
NIL
(-243 |n| R M S)
((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view.")))
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(-244 |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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(-550))))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-823))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550)))))) (|HasCategory| (-550) (QUOTE (-825))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -874) (QUOTE (-1145))))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1021)))) (-1489 (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1021)))) (|HasCategory| |#3| (QUOTE (-705))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -874) (QUOTE (-1145)))))) (-1489 (|HasCategory| |#3| (QUOTE (-1021))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550)))))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#3| (QUOTE (-1069)))) (-1489 (|HasAttribute| |#3| (QUOTE -4341)) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (QUOTE (-1021)))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#3| (QUOTE (-1021))) (|HasCategory| |#3| (LIST (QUOTE -874) (QUOTE (-1145)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -595) (QUOTE (-837)))))
(-245 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 (-227))))
(-246 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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
(-247 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}.")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
(-248)
((|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.")))
@@ -958,8 +958,8 @@ NIL
NIL
(-257 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")))
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(-258 A S)
((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate.")))
NIL
@@ -1004,11 +1004,11 @@ 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
-(-269 R -3260)
+(-269 R -3327)
((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}")))
NIL
NIL
-(-270 R -3260)
+(-270 R -3327)
((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels.")))
NIL
NIL
@@ -1027,10 +1027,10 @@ NIL
(-274 A S)
((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1068))))
+((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1069))))
(-275 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}.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
(-276 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}.")))
@@ -1051,18 +1051,18 @@ NIL
(-280 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 -4343)))
+((|HasAttribute| |#1| (QUOTE -4345)))
(-281 |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
-(-282 S R |Mod| -2824 -1832 |exactQuo|)
+(-282 S R |Mod| -1591 -2441 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-283)
((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
-((-4335 . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-284)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment")))
@@ -1078,21 +1078,21 @@ NIL
NIL
(-287 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.")))
-((-4339 -1561 (|has| |#1| (-1020)) (|has| |#1| (-465))) (-4336 |has| |#1| (-1020)) (-4337 |has| |#1| (-1020)))
-((|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705)))) (|HasCategory| |#1| (QUOTE (-465))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1068)))) (-1561 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1144)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-295))) (-1561 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465)))) (-1561 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705)))) (-1561 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))))
+((-4341 -1489 (|has| |#1| (-1021)) (|has| |#1| (-465))) (-4338 |has| |#1| (-1021)) (-4339 |has| |#1| (-1021)))
+((|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1021)))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-1021)))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1021)))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1021)))) (-1489 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705)))) (|HasCategory| |#1| (QUOTE (-465))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1069)))) (-1489 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1081)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1145)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-295))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-465)))) (-1489 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705)))) (-1489 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1021)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))))
(-288 |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.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|)))))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
(-289)
((|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
-(-290 -3260 S)
+(-290 -3327 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
-(-291 E -3260)
+(-291 E -3327)
((|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
@@ -1107,7 +1107,7 @@ NIL
(-294 S)
((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}.")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1020))))
+((|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1021))))
(-295)
((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}.")))
NIL
@@ -1130,7 +1130,7 @@ NIL
NIL
(-300)
((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-301 S R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}.")))
@@ -1140,7 +1140,7 @@ 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
-(-303 -3260)
+(-303 -3327)
((|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
@@ -1154,8 +1154,8 @@ NIL
NIL
(-306 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))}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-882))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-995))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-798))) (-1561 (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-798))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-825)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-1119))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-227))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -505) (QUOTE (-1144)) (LIST (QUOTE -1213) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -302) (LIST (QUOTE -1213) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (LIST (QUOTE -279) (LIST (QUOTE -1213) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1213) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-300))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-535))) (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-12 (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-882))) (|HasCategory| $ (QUOTE (-143)))) (-1561 (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1213 |#1| |#2| |#3| |#4|) (QUOTE (-882))) (|HasCategory| $ (QUOTE (-143))))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-883))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-996))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-798))) (-1489 (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-798))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-825)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-1120))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-227))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -505) (QUOTE (-1145)) (LIST (QUOTE -1214) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -302) (LIST (QUOTE -1214) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (LIST (QUOTE -279) (LIST (QUOTE -1214) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1214) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-300))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-535))) (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-12 (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-883))) (|HasCategory| $ (QUOTE (-143)))) (-1489 (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1214 |#1| |#2| |#3| |#4|) (QUOTE (-883))) (|HasCategory| $ (QUOTE (-143))))))
(-307 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
@@ -1166,9 +1166,9 @@ NIL
NIL
(-309 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.")))
-((-4339 -1561 (-1262 (|has| |#1| (-1020)) (|has| |#1| (-619 (-550)))) (-12 (|has| |#1| (-542)) (-1561 (-1262 (|has| |#1| (-1020)) (|has| |#1| (-619 (-550)))) (|has| |#1| (-1020)) (|has| |#1| (-465)))) (|has| |#1| (-1020)) (|has| |#1| (-465))) (-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) ((-4344 "*") |has| |#1| (-542)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-542)) (-4334 |has| |#1| (-542)))
-((-1561 (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))))) (|HasCategory| |#1| (QUOTE (-542))) (-1561 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1020)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (-1561 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550))))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542)))) (-1561 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-542)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550))))) (-1561 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-1080)))) (-1561 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))))) (-1561 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-1080)))) (-1561 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))))) (-1561 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1020)))) (-1561 (-12 (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| $ (QUOTE (-1020))) (|HasCategory| $ (LIST (QUOTE -1011) (QUOTE (-550)))))
-(-310 R -3260)
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+(-310 R -3327)
((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}.")))
NIL
NIL
@@ -1178,8 +1178,8 @@ NIL
NIL
(-312 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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
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(-313 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
@@ -1190,7 +1190,7 @@ NIL
NIL
(-315 S)
((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative.")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
((|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-770))))
(-316 S E)
((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}.")))
@@ -1206,19 +1206,19 @@ NIL
((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))))
(-319 R E)
((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-320 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.")))
-((-4343 . T) (-4342 . T))
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-(-321 S -3260)
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-321 S -3327)
((|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 (-361))))
-(-322 -3260)
+(-322 -3327)
((|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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-323)
((|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.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm.")))
@@ -1236,54 +1236,54 @@ 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
-(-327 S -3260 UP UPUP R)
+(-327 S -3327 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
-(-328 -3260 UP UPUP R)
+(-328 -3327 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
-(-329 -3260 UP UPUP R)
+(-329 -3327 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}.")))
NIL
NIL
(-330 S R)
((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1144)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))))
+((|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1145)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))))
(-331 R)
((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
NIL
(-332 |basicSymbols| |subscriptedSymbols| R)
((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#3| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#3| (LIST (QUOTE -1011) (QUOTE (-372)))) (|HasCategory| $ (QUOTE (-1020))) (|HasCategory| $ (LIST (QUOTE -1011) (QUOTE (-550)))))
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#3| (LIST (QUOTE -1012) (QUOTE (-372)))) (|HasCategory| $ (QUOTE (-1021))) (|HasCategory| $ (LIST (QUOTE -1012) (QUOTE (-550)))))
(-333 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
-(-334 S -3260 UP UPUP)
+(-334 S -3327 UP UPUP)
((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components.")))
NIL
((|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-356))))
-(-335 -3260 UP UPUP)
+(-335 -3327 UP UPUP)
((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components.")))
-((-4335 |has| (-400 |#2|) (-356)) (-4340 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 |has| (-400 |#2|) (-356)) (-4342 |has| (-400 |#2|) (-356)) (-4336 |has| (-400 |#2|) (-356)) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-336 |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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| (-883 |#1|) (QUOTE (-143))) (|HasCategory| (-883 |#1|) (QUOTE (-361)))) (|HasCategory| (-883 |#1|) (QUOTE (-145))) (|HasCategory| (-883 |#1|) (QUOTE (-361))) (|HasCategory| (-883 |#1|) (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| (-884 |#1|) (QUOTE (-143))) (|HasCategory| (-884 |#1|) (QUOTE (-361)))) (|HasCategory| (-884 |#1|) (QUOTE (-145))) (|HasCategory| (-884 |#1|) (QUOTE (-361))) (|HasCategory| (-884 |#1|) (QUOTE (-143))))
(-337 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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
(-338 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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
(-339 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
@@ -1298,33 +1298,33 @@ NIL
NIL
(-342)
((|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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-343 R UP -3260)
+(-343 R UP -3327)
((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
(-344 |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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| (-883 |#1|) (QUOTE (-143))) (|HasCategory| (-883 |#1|) (QUOTE (-361)))) (|HasCategory| (-883 |#1|) (QUOTE (-145))) (|HasCategory| (-883 |#1|) (QUOTE (-361))) (|HasCategory| (-883 |#1|) (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| (-884 |#1|) (QUOTE (-143))) (|HasCategory| (-884 |#1|) (QUOTE (-361)))) (|HasCategory| (-884 |#1|) (QUOTE (-145))) (|HasCategory| (-884 |#1|) (QUOTE (-361))) (|HasCategory| (-884 |#1|) (QUOTE (-143))))
(-345 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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
(-346 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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
(-347 |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}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| (-883 |#1|) (QUOTE (-143))) (|HasCategory| (-883 |#1|) (QUOTE (-361)))) (|HasCategory| (-883 |#1|) (QUOTE (-145))) (|HasCategory| (-883 |#1|) (QUOTE (-361))) (|HasCategory| (-883 |#1|) (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| (-884 |#1|) (QUOTE (-143))) (|HasCategory| (-884 |#1|) (QUOTE (-361)))) (|HasCategory| (-884 |#1|) (QUOTE (-145))) (|HasCategory| (-884 |#1|) (QUOTE (-361))) (|HasCategory| (-884 |#1|) (QUOTE (-143))))
(-348 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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
-(-349 -3260 GF)
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
+(-349 -3327 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
@@ -1332,21 +1332,21 @@ 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
-(-351 -3260 FP FPP)
+(-351 -3327 FP FPP)
((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")))
NIL
NIL
(-352 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}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-143))))
(-353 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
(-354 S)
((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-355 S)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
@@ -1354,7 +1354,7 @@ NIL
NIL
(-356)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-357 |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.")))
@@ -1370,7 +1370,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-542))))
(-360 R)
((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
-((-4339 |has| |#1| (-542)) (-4337 . T) (-4336 . T))
+((-4341 |has| |#1| (-542)) (-4339 . T) (-4338 . T))
NIL
(-361)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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.")))
@@ -1382,7 +1382,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-356))))
(-363 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-364 S A R B)
((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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.")))
@@ -1391,14 +1391,14 @@ NIL
(-365 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4343)) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1068))))
+((|HasAttribute| |#1| (QUOTE -4345)) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1069))))
(-366 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-4342 . T) (-1964 . T))
+((-4344 . T) (-2836 . T))
NIL
(-367 |VarSet| R)
((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4337 . T) (-4336 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4339 . T) (-4338 . T))
NIL
(-368 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.")))
@@ -1410,7 +1410,7 @@ NIL
((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))))
(-370 R)
((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}")))
-((-4339 . T))
+((-4341 . T))
NIL
(-371 |Par|)
((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}.")))
@@ -1418,7 +1418,7 @@ NIL
NIL
(-372)
((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|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}.")))
-((-4325 . T) (-4333 . T) (-2001 . T) (-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4327 . T) (-4335 . T) (-2154 . T) (-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-373 |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}.")))
@@ -1426,23 +1426,23 @@ NIL
NIL
(-374 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}")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
((|HasCategory| |#1| (QUOTE (-170))))
(-375 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}.")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
(-376)
((|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}.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-377)
((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
-((-1964 . T))
+((-2836 . T))
NIL
(-378 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.")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
((|HasCategory| |#1| (QUOTE (-170))))
(-379 S)
((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
@@ -1450,7 +1450,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-825))))
(-380)
((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-381)
((|constructor| (NIL "This domain provides an interface to names in the file system.")))
@@ -1462,13 +1462,13 @@ NIL
NIL
(-383 |n| |class| R)
((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
(-384)
((|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
-(-385 -3260 UP UPUP R)
+(-385 -3327 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
@@ -1482,27 +1482,27 @@ NIL
NIL
(-388)
((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-389)
((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
-((-1964 . T))
+((-2836 . T))
NIL
(-390)
((|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
-(-391 -1916 |returnType| -2899 |symbols|)
+(-391 -1856 |returnType| -2642 |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
-(-392 -3260 UP)
+(-392 -3327 UP)
((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}")))
NIL
NIL
(-393 R)
((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers).")))
-((-1964 . T))
+((-2836 . T))
NIL
(-394 S)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
@@ -1510,15 +1510,15 @@ NIL
NIL
(-395)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-396 S)
((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4325)) (|HasAttribute| |#1| (QUOTE -4333)))
+((|HasAttribute| |#1| (QUOTE -4327)) (|HasAttribute| |#1| (QUOTE -4335)))
(-397)
((|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\".")))
-((-2001 . T) (-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-2154 . T) (-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-398 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.")))
@@ -1530,20 +1530,20 @@ NIL
NIL
(-400 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.")))
-((-4329 -12 (|has| |#1| (-6 -4340)) (|has| |#1| (-444)) (|has| |#1| (-6 -4329))) (-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
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(-401 S R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
NIL
(-402 R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-403 A S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))))
+((|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))))
(-404 S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
@@ -1552,14 +1552,14 @@ 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
-(-406 R -3260 UP A)
+(-406 R -3327 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)}.")))
-((-4339 . T))
+((-4341 . T))
NIL
-(-407 R -3260 UP A |ibasis|)
+(-407 R -3327 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")))
NIL
-((|HasCategory| |#4| (LIST (QUOTE -1011) (|devaluate| |#2|))))
+((|HasCategory| |#4| (LIST (QUOTE -1012) (|devaluate| |#2|))))
(-408 AR R AS S)
((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}.")))
NIL
@@ -1570,12 +1570,12 @@ NIL
((|HasCategory| |#2| (QUOTE (-356))))
(-410 R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4339 |has| |#1| (-542)) (-4337 . T) (-4336 . T))
+((-4341 |has| |#1| (-542)) (-4339 . T) (-4338 . T))
NIL
(-411 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.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
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+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1145)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -302) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -279) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-1186))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-1186)))) (|HasCategory| |#1| (QUOTE (-996))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1145)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-535))) (|HasCategory| |#1| (QUOTE (-444))))
(-412 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
@@ -1602,37 +1602,37 @@ NIL
((|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-361))))
(-418 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-4342 . T) (-4332 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4334 . T) (-4345 . T) (-2836 . T))
NIL
-(-419 R -3260)
+(-419 R -3327)
((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")))
NIL
NIL
(-420 R E)
((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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")))
-((-4329 -12 (|has| |#1| (-6 -4329)) (|has| |#2| (-6 -4329))) (-4336 . T) (-4337 . T) (-4339 . T))
-((-12 (|HasAttribute| |#1| (QUOTE -4329)) (|HasAttribute| |#2| (QUOTE -4329))))
-(-421 R -3260)
+((-4331 -12 (|has| |#1| (-6 -4331)) (|has| |#2| (-6 -4331))) (-4338 . T) (-4339 . T) (-4341 . T))
+((-12 (|HasAttribute| |#1| (QUOTE -4331)) (|HasAttribute| |#2| (QUOTE -4331))))
+(-421 R -3327)
((|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
(-422 S R)
((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1020))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))))
+((|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))))
(-423 R)
((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}.")))
-((-4339 -1561 (|has| |#1| (-1020)) (|has| |#1| (-465))) (-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) ((-4344 "*") |has| |#1| (-542)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-542)) (-4334 |has| |#1| (-542)) (-1964 . T))
+((-4341 -1489 (|has| |#1| (-1021)) (|has| |#1| (-465))) (-4339 |has| |#1| (-170)) (-4338 |has| |#1| (-170)) ((-4346 "*") |has| |#1| (-542)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-542)) (-4336 |has| |#1| (-542)) (-2836 . T))
NIL
-(-424 R -3260)
+(-424 R -3327)
((|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
-(-425 R -3260)
+(-425 R -3327)
((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.")))
NIL
((|HasCategory| |#2| (QUOTE (-27))))
-(-426 R -3260)
+(-426 R -3327)
((|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
@@ -1640,10 +1640,10 @@ 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
-(-428 R -3260 UP)
+(-428 R -3327 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 -1011) (QUOTE (-48)))))
+((|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-48)))))
(-429)
((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}.")))
NIL
@@ -1658,17 +1658,17 @@ NIL
NIL
(-432)
((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} 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.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-433)
((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
-((-1964 . T))
+((-2836 . T))
NIL
(-434 UP)
((|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
-(-435 R UP -3260)
+(-435 R UP -3327)
((|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
@@ -1706,16 +1706,16 @@ NIL
NIL
(-444)
((|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}.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-445 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")))
-((-4339 |has| (-400 (-925 |#1|)) (-542)) (-4337 . T) (-4336 . T))
-((|HasCategory| (-400 (-925 |#1|)) (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-400 (-925 |#1|)) (QUOTE (-542))))
+((-4341 |has| (-400 (-926 |#1|)) (-542)) (-4339 . T) (-4338 . T))
+((|HasCategory| (-400 (-926 |#1|)) (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-400 (-926 |#1|)) (QUOTE (-542))))
(-446 |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")))
-(((-4344 "*") |has| |#2| (-170)) (-4335 |has| |#2| (-542)) (-4340 |has| |#2| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-882))) (-1561 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-1561 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))) (-1561 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#2| (QUOTE -4340)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-143)))))
+(((-4346 "*") |has| |#2| (-170)) (-4337 |has| |#2| (-542)) (-4342 |has| |#2| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#2| (QUOTE (-883))) (-1489 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-883)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-1489 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372)))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550)))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))) (-1489 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#2| (QUOTE -4342)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-883)))) (|HasCategory| |#2| (QUOTE (-143)))))
(-447 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
@@ -1742,7 +1742,7 @@ NIL
NIL
(-453 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
(-454 E V R P Q)
((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}.")))
@@ -1750,8 +1750,8 @@ NIL
NIL
(-455 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-837)))))
(-456 S R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}.")))
NIL
@@ -1780,7 +1780,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-463 |lv| -3260 R)
+(-463 |lv| -3327 R)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}.")))
NIL
NIL
@@ -1790,23 +1790,23 @@ NIL
NIL
(-465)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-466 |Coef| |var| |cen|)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-550)) (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-1561 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (QUOTE (-1144)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1561 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-1166))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -1489) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1144))))) (|HasSignature| |#1| (LIST (QUOTE -3141) (LIST (LIST (QUOTE -623) (QUOTE (-1144))) (|devaluate| |#1|)))))))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-550)) (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasSignature| |#1| (LIST (QUOTE -2233) (LIST (|devaluate| |#1|) (QUOTE (-1145)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1489 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -2149) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1145))))) (|HasSignature| |#1| (LIST (QUOTE -1516) (LIST (LIST (QUOTE -623) (QUOTE (-1145))) (|devaluate| |#1|)))))))
(-467 |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.")))
-((-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|)))))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-825))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-825))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
(-468 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)}")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-837)))))
(-469)
((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-470)
((|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'.")))
@@ -1814,29 +1814,29 @@ NIL
NIL
(-471 |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.")))
-((-4342 . T) (-4343 . T))
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+((-4344 . T) (-4345 . T))
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(-472)
((|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
(-473 |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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((|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}.")))
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-302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))))) (-1489 (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-1069)))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1021)))) (-12 (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145))))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (|HasCategory| 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(|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-705))) (|HasCategory| |#2| (QUOTE (-771))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1021)))) (-1489 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1021)))) (-1489 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1021)))) (-1489 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1021)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-25)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-170)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-361)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-705)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-771)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-823)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-1021)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-1069))))) (-1489 (-12 (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-705))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-771))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))))) (|HasCategory| (-550) (QUOTE (-825))) (-12 (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (QUOTE (-1021)))) (-12 (|HasCategory| |#2| (QUOTE (-1021))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145))))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550))))) (-1489 (|HasCategory| |#2| (QUOTE (-1021))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-1069)))) (|HasAttribute| |#2| (QUOTE -4341)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))))
(-475)
((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header.")))
NIL
NIL
(-476 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-477 -3260 UP UPUP R)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-477 -3327 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
@@ -1846,15 +1846,15 @@ NIL
NIL
(-479)
((|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.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-550) (QUOTE (-882))) (|HasCategory| (-550) (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-995))) (|HasCategory| (-550) (QUOTE (-798))) (-1561 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1119))) (|HasCategory| (-550) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1144)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-882)))) (|HasCategory| (-550) (QUOTE (-143)))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-550) (QUOTE (-883))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-996))) (|HasCategory| (-550) (QUOTE (-798))) (-1489 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1120))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1145)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (|HasCategory| (-550) (QUOTE (-143)))))
(-480 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 -4342)) (|HasAttribute| |#1| (QUOTE -4343)) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))))
+((|HasAttribute| |#1| (QUOTE -4344)) (|HasAttribute| |#1| (QUOTE -4345)) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))))
(-481 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-482)
((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}.")))
@@ -1868,34 +1868,34 @@ NIL
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-485 -3260 UP |AlExt| |AlPol|)
+(-485 -3327 UP |AlExt| |AlPol|)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP.")))
NIL
NIL
(-486)
((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| $ (QUOTE (-1020))) (|HasCategory| $ (LIST (QUOTE -1011) (QUOTE (-550)))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| $ (QUOTE (-1021))) (|HasCategory| $ (LIST (QUOTE -1012) (QUOTE (-550)))))
(-487 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type.")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-488 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.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-489 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
-(-490 R UP -3260)
+(-490 R UP -3327)
((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
(-491 |mn|)
((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| (-112) (QUOTE (-1068))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-112) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-112) (QUOTE (-1068))) (|HasCategory| (-112) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| (-112) (QUOTE (-1069))) (|HasCategory| (-112) (LIST (QUOTE -302) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-112) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-112) (QUOTE (-1069))) (|HasCategory| (-112) (LIST (QUOTE -595) (QUOTE (-837)))))
(-492 K R UP L)
((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.")))
NIL
@@ -1908,10 +1908,10 @@ NIL
((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}.")))
NIL
NIL
-(-495 -3260 |Expon| |VarSet| |DPoly|)
+(-495 -3327 |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 -596) (QUOTE (-1144)))))
+((|HasCategory| |#3| (LIST (QUOTE -596) (QUOTE (-1145)))))
(-496 |vl| |nv|)
((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime.")))
NIL
@@ -1958,36 +1958,36 @@ NIL
((|HasCategory| |#2| (QUOTE (-770))))
(-507 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}")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-508)
((|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
(-509 |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}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((-1561 (|HasCategory| (-565 |#1|) (QUOTE (-143))) (|HasCategory| (-565 |#1|) (QUOTE (-361)))) (|HasCategory| (-565 |#1|) (QUOTE (-145))) (|HasCategory| (-565 |#1|) (QUOTE (-361))) (|HasCategory| (-565 |#1|) (QUOTE (-143))))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((-1489 (|HasCategory| (-565 |#1|) (QUOTE (-143))) (|HasCategory| (-565 |#1|) (QUOTE (-361)))) (|HasCategory| (-565 |#1|) (QUOTE (-145))) (|HasCategory| (-565 |#1|) (QUOTE (-361))) (|HasCategory| (-565 |#1|) (QUOTE (-143))))
(-510 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-511 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.")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-512 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 -4343)))
+((|HasAttribute| |#3| (QUOTE -4345)))
(-513 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 -4343)))
+((|HasAttribute| |#7| (QUOTE -4345)))
(-514 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.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4344 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4346 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-515)
((|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
@@ -2009,7 +2009,7 @@ NIL
NIL
NIL
(-520)
-((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when end-of-file has been reached for the conduit file `ifile'.")) (|openBinaryFile| (($ (|String|)) "\\spad{openBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{openBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.")))
+((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.")))
NIL
NIL
(-521 R)
@@ -2020,7 +2020,7 @@ NIL
((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables")))
NIL
NIL
-(-523 K -3260 |Par|)
+(-523 K -3327 |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
@@ -2040,7 +2040,7 @@ 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
-(-528 K -3260 |Par|)
+(-528 K -3327 |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
@@ -2070,17 +2070,17 @@ NIL
NIL
(-535)
((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\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.")))
-((-4340 . T) (-4341 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4342 . T) (-4343 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-536 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|)))))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-537 R -3260)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-537 R -3327)
((|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
-(-538 R0 -3260 UP UPUP R)
+(-538 R0 -3327 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
@@ -2090,7 +2090,7 @@ NIL
NIL
(-540 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.")))
-((-2001 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-2154 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-541 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.")))
@@ -2098,9 +2098,9 @@ NIL
NIL
(-542)
((|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.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-543 R -3260)
+(-543 R -3327)
((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise.")))
NIL
NIL
@@ -2112,7 +2112,7 @@ 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
-(-546 R -3260 L)
+(-546 R -3327 L)
((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}.")))
NIL
((|HasCategory| |#3| (LIST (QUOTE -634) (|devaluate| |#2|))))
@@ -2120,31 +2120,31 @@ 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
-(-548 -3260 UP UPUP R)
+(-548 -3327 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
-(-549 -3260 UP)
+(-549 -3327 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
(-550)
((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")))
-((-4324 . T) (-4330 . T) (-4334 . T) (-4329 . T) (-4340 . T) (-4341 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4326 . T) (-4332 . T) (-4336 . T) (-4331 . T) (-4342 . T) (-4343 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-551)
((|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
-(-552 R -3260 L)
+(-552 R -3327 L)
((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}.")))
NIL
((|HasCategory| |#3| (LIST (QUOTE -634) (|devaluate| |#2|))))
-(-553 R -3260)
+(-553 R -3327)
((|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 -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1107)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-609)))))
-(-554 -3260 UP)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1108)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-609)))))
+(-554 -3327 UP)
((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}.")))
NIL
NIL
@@ -2152,27 +2152,27 @@ 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
-(-556 -3260)
+(-556 -3327)
((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}.")))
NIL
NIL
(-557 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.")))
-((-2001 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-2154 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-558)
((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")))
NIL
NIL
-(-559 R -3260)
+(-559 R -3327)
((|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 -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-277))) (|HasCategory| |#2| (QUOTE (-609))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-1144))))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-277)))) (|HasCategory| |#1| (QUOTE (-542))))
-(-560 -3260 UP)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-277))) (|HasCategory| |#2| (QUOTE (-609))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1145))))) (-12 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-277)))) (|HasCategory| |#1| (QUOTE (-542))))
+(-560 -3327 UP)
((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}.")))
NIL
NIL
-(-561 R -3260)
+(-561 R -3327)
((|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
@@ -2186,28 +2186,28 @@ NIL
NIL
(-564 |p| |unBalanced?|)
((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-565 |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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-361))))
(-566)
((|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
-(-567 R -3260)
+(-567 R -3327)
((|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
-(-568 E -3260)
+(-568 E -3327)
((|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
-(-569 -3260)
+(-569 -3327)
((|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}.")))
-((-4337 . T) (-4336 . T))
-((|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-1144)))))
+((-4339 . T) (-4338 . T))
+((|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-1145)))))
(-570 I)
((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise")))
NIL
@@ -2234,19 +2234,19 @@ NIL
NIL
(-576 |mn|)
((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (-1561 (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-836)))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1068)))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1068))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (-1489 (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-837)))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1069)))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1069))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-837)))))
(-577 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
(-578 |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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-550)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-550)) (|devaluate| |#1|)))) (|HasCategory| (-550) (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (QUOTE (-1144)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-550))))))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-550)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-550)) (|devaluate| |#1|)))) (|HasCategory| (-550) (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -2233) (LIST (|devaluate| |#1|) (QUOTE (-1145)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-550))))))
(-579 |Coef|)
((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}")))
-((-4337 |has| |#1| (-542)) (-4336 |has| |#1| (-542)) ((-4344 "*") |has| |#1| (-542)) (-4335 |has| |#1| (-542)) (-4339 . T))
+((-4339 |has| |#1| (-542)) (-4338 |has| |#1| (-542)) ((-4346 "*") |has| |#1| (-542)) (-4337 |has| |#1| (-542)) (-4341 . T))
((|HasCategory| |#1| (QUOTE (-542))))
(-580 A B)
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}.")))
@@ -2256,7 +2256,7 @@ 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
-(-582 R -3260 FG)
+(-582 R -3327 FG)
((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain.")))
NIL
NIL
@@ -2266,15 +2266,15 @@ NIL
NIL
(-584 R |mn|)
((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index.")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1021))) (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1021)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-585 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 -4343)) (|HasCategory| |#2| (QUOTE (-825))) (|HasAttribute| |#1| (QUOTE -4342)) (|HasCategory| |#3| (QUOTE (-1068))))
+((|HasAttribute| |#1| (QUOTE -4345)) (|HasCategory| |#2| (QUOTE (-825))) (|HasAttribute| |#1| (QUOTE -4344)) (|HasCategory| |#3| (QUOTE (-1069))))
(-586 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-587)
((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode.")))
@@ -2286,19 +2286,19 @@ NIL
NIL
(-589 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).")))
-((-4339 -1561 (-1262 (|has| |#2| (-360 |#1|)) (|has| |#1| (-542))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-542)))) (-4337 . T) (-4336 . T))
-((-1561 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))))
+((-4341 -1489 (-1304 (|has| |#2| (-360 |#1|)) (|has| |#1| (-542))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-542)))) (-4339 . T) (-4338 . T))
+((-1489 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))))
(-590 |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.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (QUOTE (-1126))) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| (-1126) (QUOTE (-825))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (QUOTE (-1127))) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| (-1127) (QUOTE (-825))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -595) (QUOTE (-837)))))
(-591 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
(-592 |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}.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
(-593 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")))
@@ -2307,7 +2307,7 @@ NIL
(-594 S)
((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op.")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))))
+((|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))))
(-595 S)
((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}.")))
NIL
@@ -2316,7 +2316,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-597 -3260 UP)
+(-597 -3327 UP)
((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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
@@ -2330,20 +2330,20 @@ NIL
NIL
(-600 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.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-601 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}.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
((|HasCategory| |#1| (QUOTE (-823))))
-(-602 R -3260)
+(-602 R -3327)
((|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
(-603 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")))
-((-4337 . T) (-4336 . T) ((-4344 "*") . T) (-4335 . T) (-4339 . T))
-((|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))))
+((-4339 . T) (-4338 . T) ((-4346 "*") . T) (-4337 . T) (-4341 . T))
+((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))))
(-604 R E V P TS ST)
((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional.")))
NIL
@@ -2358,7 +2358,7 @@ NIL
NIL
(-607 |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}}.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-608 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}}.")))
@@ -2368,30 +2368,30 @@ NIL
((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}.")))
NIL
NIL
-(-610 R -3260)
+(-610 R -3327)
((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian")))
NIL
NIL
-(-611 |lv| -3260)
+(-611 |lv| -3327)
((|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
(-612)
((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file.")))
-((-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (QUOTE (-1126))) (LIST (QUOTE |:|) (QUOTE -2119) (QUOTE (-52))))))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-52) (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-1126) (QUOTE (-825))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (QUOTE (-1127))) (LIST (QUOTE |:|) (QUOTE -3859) (QUOTE (-52))))))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-52) (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-1127) (QUOTE (-825))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))))
(-613 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
NIL
((|HasCategory| |#2| (QUOTE (-356))))
(-614 R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4337 . T) (-4336 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4339 . T) (-4338 . T))
NIL
(-615 R A)
((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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).")))
-((-4339 -1561 (-1262 (|has| |#2| (-360 |#1|)) (|has| |#1| (-542))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-542)))) (-4337 . T) (-4336 . T))
-((-1561 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))))
+((-4341 -1489 (-1304 (|has| |#2| (-360 |#1|)) (|has| |#1| (-542))) (-12 (|has| |#2| (-410 |#1|)) (|has| |#1| (-542)))) (-4339 . T) (-4338 . T))
+((-1489 (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|)))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -410) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -360) (|devaluate| |#1|))))
(-616 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
@@ -2403,10 +2403,10 @@ NIL
(-618 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
-((-3462 (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-356))))
+((-3548 (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-356))))
(-619 R)
((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-620 A B)
((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}.")))
@@ -2422,16 +2422,16 @@ NIL
NIL
(-623 S)
((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list.")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-806))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-624 T$)
((|constructor| (NIL "This domain represents AST for Spad literals.")))
NIL
NIL
(-625 S)
((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-626 R)
((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}.")))
NIL
@@ -2443,39 +2443,39 @@ NIL
(-628 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#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 -4343)))
+((|HasAttribute| |#1| (QUOTE -4345)))
(-629 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-630 R -3260 L)
+(-630 R -3327 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
(-631 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}}")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
(-632 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
(-633 S A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}.")))
NIL
((|HasCategory| |#2| (QUOTE (-356))))
(-634 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}.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-635 -3260 UP)
+(-635 -3327 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))))
-(-636 A -4208)
+(-636 A -2548)
((|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}}")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
(-637 A L)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")))
NIL
@@ -2490,7 +2490,7 @@ NIL
NIL
(-640 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}.")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
((|HasCategory| |#1| (QUOTE (-769))))
(-641 R)
((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists.")))
@@ -2498,7 +2498,7 @@ NIL
NIL
(-642 |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) (-4337 . T) (-4336 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4339 . T) (-4338 . T))
((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-170))))
(-643 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}.")))
@@ -2506,13 +2506,13 @@ NIL
NIL
(-644 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}.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-645 -3260)
+(-645 -3327)
((|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
-(-646 -3260 |Row| |Col| M)
+(-646 -3327 |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
@@ -2522,8 +2522,8 @@ NIL
NIL
(-648 |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.")))
-((-4339 . T) (-4342 . T) (-4336 . T) (-4337 . T))
-((|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4344 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (-1561 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-542))) (-1561 (|HasAttribute| |#2| (QUOTE (-4344 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-170))))
+((-4341 . T) (-4344 . T) (-4338 . T) (-4339 . T))
+((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4346 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (-1489 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-542))) (-1489 (|HasAttribute| |#2| (QUOTE (-4346 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-170))))
(-649)
((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'.")))
NIL
@@ -2538,12 +2538,12 @@ NIL
NIL
(-652 S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}.")))
-((-1964 . T))
+((-2836 . T))
NIL
(-653 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
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (QUOTE (-1021))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-654)
((|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
@@ -2587,10 +2587,10 @@ NIL
(-664 S R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
NIL
-((|HasAttribute| |#2| (QUOTE (-4344 "*"))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-542))))
+((|HasAttribute| |#2| (QUOTE (-4346 "*"))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-542))))
(-665 R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
(-666 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.")))
@@ -2598,8 +2598,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))))
(-667 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.")))
-((-4342 . T) (-4343 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-542))) (|HasAttribute| |#1| (QUOTE (-4344 "*"))) (|HasCategory| |#1| (QUOTE (-356))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4345 . T))
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(-668 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
@@ -2608,7 +2608,7 @@ NIL
((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} 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}.")))
NIL
NIL
-(-670 S -3260 FLAF FLAS)
+(-670 S -3327 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
@@ -2618,11 +2618,11 @@ NIL
NIL
(-672)
((|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")))
-((-4335 . T) (-4340 |has| (-677) (-356)) (-4334 |has| (-677) (-356)) (-2738 . T) (-4341 |has| (-677) (-6 -4341)) (-4338 |has| (-677) (-6 -4338)) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
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(-673 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}.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
(-674 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}.")))
@@ -2632,13 +2632,13 @@ 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
-(-676 OV E -3260 PG)
+(-676 OV E -3327 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
(-677)
((|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}")))
-((-2001 . T) (-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-2154 . T) (-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-678 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.")))
@@ -2646,7 +2646,7 @@ NIL
NIL
(-679)
((|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}")))
-((-4341 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4343 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-680 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")))
@@ -2668,7 +2668,7 @@ 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
-(-685 S -4183 I)
+(-685 S -1901 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
@@ -2678,7 +2678,7 @@ NIL
NIL
(-687 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)}.}")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-688 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}.")))
@@ -2688,25 +2688,25 @@ 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
-(-690 R |Mod| -2824 -1832 |exactQuo|)
+(-690 R |Mod| -1591 -2441 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-691 R |Rep|)
((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(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")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4338 |has| |#1| (-356)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-882))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1119))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-342))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4340)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-883))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| (-1051) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| (-1051) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| (-1051) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372)))))) (-12 (|HasCategory| (-1051) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550)))))) (-12 (|HasCategory| (-1051) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-342))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasAttribute| |#1| (QUOTE -4342)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-143)))))
(-692 IS E |ff|)
((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented")))
NIL
NIL
(-693 R M)
((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}.")))
-((-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) (-4339 . T))
+((-4339 |has| |#1| (-170)) (-4338 |has| |#1| (-170)) (-4341 . T))
((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))))
-(-694 R |Mod| -2824 -1832 |exactQuo|)
+(-694 R |Mod| -1591 -2441 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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")))
-((-4339 . T))
+((-4341 . T))
NIL
(-695 S R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
@@ -2714,11 +2714,11 @@ NIL
NIL
(-696 R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
-(-697 -3260)
+(-697 -3327)
((|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]]}.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-698 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.")))
@@ -2742,7 +2742,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-342))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-361))))
(-703 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.")))
-((-4335 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 |has| |#1| (-356)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-704 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.")))
@@ -2752,7 +2752,7 @@ 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
-(-706 -3260 UP)
+(-706 -3327 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
@@ -2770,8 +2770,8 @@ NIL
NIL
(-710 |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.")))
-(((-4344 "*") |has| |#2| (-170)) (-4335 |has| |#2| (-542)) (-4340 |has| |#2| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-882))) (-1561 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-1561 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| (-838 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))) (-1561 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#2| (QUOTE -4340)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-143)))))
+(((-4346 "*") |has| |#2| (-170)) (-4337 |has| |#2| (-542)) (-4342 |has| |#2| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#2| (QUOTE (-883))) (-1489 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-883)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-1489 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372)))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550)))))) (-12 (|HasCategory| (-839 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))) (-1489 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#2| (QUOTE -4342)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-883)))) (|HasCategory| |#2| (QUOTE (-143)))))
(-711 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
@@ -2786,16 +2786,16 @@ NIL
NIL
(-714 R M)
((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}.")))
-((-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) (-4339 . T))
+((-4339 |has| |#1| (-170)) (-4338 |has| |#1| (-170)) (-4341 . T))
((-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-825))))
(-715 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
-((-4332 . T) (-4343 . T) (-1964 . T))
+((-4334 . T) (-4345 . T) (-2836 . T))
NIL
(-716 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}.")))
-((-4342 . T) (-4332 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4344 . T) (-4334 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
(-717)
((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned.")))
NIL
@@ -2806,7 +2806,7 @@ NIL
NIL
(-719 |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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4337 . T) (-4336 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
(-720 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")))
@@ -2822,7 +2822,7 @@ NIL
NIL
(-723 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}.")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
(-724)
((|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}.")))
@@ -2904,15 +2904,15 @@ 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
-(-744 -3260)
+(-744 -3327)
((|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
-(-745 P -3260)
+(-745 P -3327)
((|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
-(-746 UP -3260)
+(-746 UP -3327)
((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}.")))
NIL
NIL
@@ -2926,9 +2926,9 @@ NIL
NIL
(-749)
((|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.")))
-(((-4344 "*") . T))
+(((-4346 "*") . T))
NIL
-(-750 R -3260)
+(-750 R -3327)
((|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
@@ -2948,7 +2948,7 @@ 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
-(-755 -3260 |ExtF| |SUEx| |ExtP| |n|)
+(-755 -3327 |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
@@ -2962,28 +2962,28 @@ NIL
NIL
(-758 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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
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(-759 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
(-760 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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(-761 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 -400) (QUOTE (-550))))))
(-762 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.}")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
(-763 S)
((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1020))) (|HasCategory| |#1| (QUOTE (-170))))
+((-12 (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-1021))) (|HasCategory| |#1| (QUOTE (-170))))
(-764)
((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}.")))
NIL
@@ -3027,28 +3027,28 @@ NIL
(-774 S R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-1029))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-361))))
+((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-361))))
(-775 R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-776 -1561 R OS S)
+(-776 -1489 R OS S)
((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}.")))
NIL
NIL
(-777 R)
((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1144)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-1561 (|HasCategory| (-972 |#1|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1561 (|HasCategory| (-972 |#1|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-535))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-972 |#1|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))))
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1145)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (-1489 (|HasCategory| (-973 |#1|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1489 (|HasCategory| (-973 |#1|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-535))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| (-973 |#1|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-973 |#1|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))))
(-778)
((|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
-(-779 R -3260 L)
+(-779 R -3327 L)
((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}.")))
NIL
NIL
-(-780 R -3260)
+(-780 R -3327)
((|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
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@@ -3056,7 +3056,7 @@ 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
-(-782 R -3260)
+(-782 R -3327)
((|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
@@ -3064,11 +3064,11 @@ 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
-(-784 -3260 UP UPUP R)
+(-784 -3327 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
-(-785 -3260 UP L LQ)
+(-785 -3327 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
@@ -3076,41 +3076,41 @@ 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| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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
-(-787 -3260 UP L LQ)
+(-787 -3327 UP L LQ)
((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}.")))
NIL
NIL
-(-788 -3260 UP)
+(-788 -3327 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
-(-789 -3260 L UP A LO)
+(-789 -3327 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
-(-790 -3260 UP)
+(-790 -3327 UP)
((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")))
NIL
((|HasCategory| |#1| (QUOTE (-27))))
-(-791 -3260 LO)
+(-791 -3327 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
-(-792 -3260 LODO)
+(-792 -3327 LODO)
((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.")))
NIL
NIL
-(-793 -3873 S |f|)
+(-793 -2281 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}.")))
-((-4336 |has| |#2| (-1020)) (-4337 |has| |#2| (-1020)) (-4339 |has| |#2| (-6 -4339)) ((-4344 "*") |has| |#2| (-170)) (-4342 . T))
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(-794 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")))
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(-795 |Kernels| R |var|)
((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring.")))
-(((-4344 "*") |has| |#2| (-356)) (-4335 |has| |#2| (-356)) (-4340 |has| |#2| (-356)) (-4334 |has| |#2| (-356)) (-4339 . T) (-4337 . T) (-4336 . T))
+(((-4346 "*") |has| |#2| (-356)) (-4337 |has| |#2| (-356)) (-4342 |has| |#2| (-356)) (-4336 |has| |#2| (-356)) (-4341 . T) (-4339 . T) (-4338 . T))
((|HasCategory| |#2| (QUOTE (-356))))
(-796 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})).")))
@@ -3122,7 +3122,7 @@ NIL
NIL
(-798)
((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-799)
((|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}")))
@@ -3150,7 +3150,7 @@ NIL
NIL
(-805 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}.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-227))))
(-806)
((|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.")))
@@ -3162,7 +3162,7 @@ NIL
NIL
(-808 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-4342 . T) (-4332 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4334 . T) (-4345 . T) (-2836 . T))
NIL
(-809)
((|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.")))
@@ -3174,11 +3174,11 @@ NIL
NIL
(-811 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.")))
-((-4339 |has| |#1| (-823)))
-((|HasCategory| |#1| (QUOTE (-823))) (-1561 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-535))) (-1561 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-21))))
+((-4341 |has| |#1| (-823)))
+((|HasCategory| |#1| (QUOTE (-823))) (-1489 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-535))) (-1489 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-21))))
(-812 R)
((|constructor| (NIL "Algebra of ADDITIVE operators over a ring.")))
-((-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) (-4339 . T))
+((-4339 |has| |#1| (-170)) (-4338 |has| |#1| (-170)) (-4341 . T))
((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))))
(-813)
((|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).")))
@@ -3202,13 +3202,13 @@ NIL
NIL
(-818 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.")))
-((-4339 |has| |#1| (-823)))
-((|HasCategory| |#1| (QUOTE (-823))) (-1561 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-535))) (-1561 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-21))))
+((-4341 |has| |#1| (-823)))
+((|HasCategory| |#1| (QUOTE (-823))) (-1489 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-535))) (-1489 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-21))))
(-819)
((|constructor| (NIL "Ordered finite sets.")))
NIL
NIL
-(-820 -3873 S)
+(-820 -2281 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
@@ -3222,7 +3222,7 @@ NIL
NIL
(-823)
((|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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0.")))
-((-4339 . T))
+((-4341 . T))
NIL
(-824 S)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set.")))
@@ -3238,20 +3238,20 @@ NIL
((|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))))
(-827 R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
(-828 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 (-356))) (|HasCategory| |#1| (QUOTE (-542))))
-(-829 R |sigma| -3754)
+(-829 R |sigma| -1940)
((|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.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
-(-830 |x| R |sigma| -3754)
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-356))))
+(-830 |x| R |sigma| -1940)
((|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}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-356))))
+((-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-356))))
(-831 R)
((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")))
NIL
@@ -3273,1684 +3273,1688 @@ NIL
NIL
NIL
(-836)
-((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}.")))
+((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.")))
NIL
NIL
(-837)
+((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}.")))
+NIL
+NIL
+(-838)
((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.")))
NIL
NIL
-(-838 |VariableList|)
+(-839 |VariableList|)
((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed")))
NIL
NIL
-(-839 R |vl| |wl| |wtlevel|)
+(-840 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights")))
-((-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) (-4339 . T))
+((-4339 |has| |#1| (-170)) (-4338 |has| |#1| (-170)) (-4341 . T))
((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))))
-(-840 R PS UP)
+(-841 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).")))
NIL
NIL
-(-841 R |x| |pt|)
+(-842 R |x| |pt|)
((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}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.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\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).")))
NIL
NIL
-(-842 |p|)
+(-843 |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}.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-843 |p|)
+(-844 |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).")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-844 |p|)
+(-845 |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).")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-843 |#1|) (QUOTE (-882))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| (-843 |#1|) (QUOTE (-143))) (|HasCategory| (-843 |#1|) (QUOTE (-145))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-843 |#1|) (QUOTE (-995))) (|HasCategory| (-843 |#1|) (QUOTE (-798))) (-1561 (|HasCategory| (-843 |#1|) (QUOTE (-798))) (|HasCategory| (-843 |#1|) (QUOTE (-825)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-843 |#1|) (QUOTE (-1119))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-843 |#1|) (QUOTE (-227))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -505) (QUOTE (-1144)) (LIST (QUOTE -843) (|devaluate| |#1|)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -843) (|devaluate| |#1|)))) (|HasCategory| (-843 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -843) (|devaluate| |#1|)) (LIST (QUOTE -843) (|devaluate| |#1|)))) (|HasCategory| (-843 |#1|) (QUOTE (-300))) (|HasCategory| (-843 |#1|) (QUOTE (-535))) (|HasCategory| (-843 |#1|) (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-843 |#1|) (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-843 |#1|) (QUOTE (-882)))) (|HasCategory| (-843 |#1|) (QUOTE (-143)))))
-(-845 |p| PADIC)
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-844 |#1|) (QUOTE (-883))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-844 |#1|) (QUOTE (-143))) (|HasCategory| (-844 |#1|) (QUOTE (-145))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-844 |#1|) (QUOTE (-996))) (|HasCategory| (-844 |#1|) (QUOTE (-798))) (-1489 (|HasCategory| (-844 |#1|) (QUOTE (-798))) (|HasCategory| (-844 |#1|) (QUOTE (-825)))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-844 |#1|) (QUOTE (-1120))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-844 |#1|) (QUOTE (-227))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -505) (QUOTE (-1145)) (LIST (QUOTE -844) (|devaluate| |#1|)))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -302) (LIST (QUOTE -844) (|devaluate| |#1|)))) (|HasCategory| (-844 |#1|) (LIST (QUOTE -279) (LIST (QUOTE -844) (|devaluate| |#1|)) (LIST (QUOTE -844) (|devaluate| |#1|)))) (|HasCategory| (-844 |#1|) (QUOTE (-300))) (|HasCategory| (-844 |#1|) (QUOTE (-535))) (|HasCategory| (-844 |#1|) (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-844 |#1|) (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-844 |#1|) (QUOTE (-883)))) (|HasCategory| (-844 |#1|) (QUOTE (-143)))))
+(-846 |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)}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-882))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-798))) (-1561 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1144)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-143)))))
-(-846 S T$)
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#2| (QUOTE (-883))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-798))) (-1489 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-825)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (LIST (QUOTE -505) (QUOTE (-1145)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -279) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-825))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-883)))) (|HasCategory| |#2| (QUOTE (-143)))))
+(-847 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 (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))))
-(-847)
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))))
+(-848)
((|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
NIL
-(-848)
+(-849)
((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.")))
NIL
NIL
-(-849 CF1 CF2)
+(-850 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-850 |ComponentFunction|)
+(-851 |ComponentFunction|)
((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,{}c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}.")))
NIL
NIL
-(-851 CF1 CF2)
+(-852 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-852 |ComponentFunction|)
+(-853 |ComponentFunction|)
((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,{}c2,{}c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}.")))
NIL
NIL
-(-853)
+(-854)
((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result.")))
NIL
NIL
-(-854 CF1 CF2)
+(-855 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-855 |ComponentFunction|)
+(-856 |ComponentFunction|)
((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,{}i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,{}c2,{}c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}.")))
NIL
NIL
-(-856)
+(-857)
((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,{}2,{}3,{}...,{}n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,{}l1,{}l2,{}..,{}ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,{}l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,{}2,{}4],{}[2,{}3,{}5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,{}st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,{}l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}")))
NIL
NIL
-(-857 R)
+(-858 R)
((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself.")))
NIL
NIL
-(-858 R S L)
+(-859 R S L)
((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,{}r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|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
-(-859 S)
+(-860 S)
((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\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 (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches.")))
NIL
NIL
-(-860 |Base| |Subject| |Pat|)
+(-861 |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 (-3462 (|HasCategory| |#2| (QUOTE (-1020)))) (-3462 (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-1144)))))) (-12 (|HasCategory| |#2| (QUOTE (-1020))) (-3462 (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-1144)))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-1144)))))
-(-861 R A B)
+((-12 (-3548 (|HasCategory| |#2| (QUOTE (-1021)))) (-3548 (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1145)))))) (-12 (|HasCategory| |#2| (QUOTE (-1021))) (-3548 (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1145)))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1145)))))
+(-862 R A B)
((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))].")))
NIL
NIL
-(-862 R S)
+(-863 R S)
((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match.")))
NIL
NIL
-(-863 R -4183)
+(-864 R -1901)
((|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
-(-864 R S)
+(-865 R S)
((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}.")))
NIL
NIL
-(-865 R)
+(-866 R)
((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0")))
NIL
NIL
-(-866 |VarSet|)
+(-867 |VarSet|)
((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list.")))
NIL
NIL
-(-867 UP R)
+(-868 UP R)
((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented")))
NIL
NIL
-(-868)
+(-869)
((|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
-(-869 UP -3260)
+(-870 UP -3327)
((|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
-(-870)
+(-871)
((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|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 PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} 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 PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\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 PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} 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 PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\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 PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\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 PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\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 PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}")))
NIL
NIL
-(-871)
+(-872)
((|retract| (((|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{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|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{coerce(x)} \\undocumented{}")))
NIL
NIL
-(-872 A S)
+(-873 A S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|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}-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)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")))
NIL
NIL
-(-873 S)
+(-874 S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")))
-((-4339 . T))
+((-4341 . T))
NIL
-(-874 S)
+(-875 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}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-875 |n| R)
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-876 |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
-(-876 S)
+(-877 S)
((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.")))
-((-4339 . T))
+((-4341 . T))
NIL
-(-877 S)
+(-878 S)
((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}.")))
NIL
NIL
-(-878 S)
+(-879 S)
((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation.")))
-((-4339 . T))
-((-1561 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-825))))
-(-879 R E |VarSet| S)
+((-4341 . T))
+((-1489 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-825))))
+(-880 R E |VarSet| S)
((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned.")))
NIL
NIL
-(-880 R S)
+(-881 R S)
((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned.")))
NIL
NIL
-(-881 S)
+(-882 S)
((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}.")))
NIL
((|HasCategory| |#1| (QUOTE (-143))))
-(-882)
+(-883)
((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-883 |p|)
+(-884 |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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-361))))
-(-884 R0 -3260 UP UPUP R)
+(-885 R0 -3327 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
-(-885 UP UPUP R)
+(-886 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| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented")))
NIL
NIL
-(-886 UP UPUP)
+(-887 UP UPUP)
((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}")))
NIL
NIL
-(-887 R)
+(-888 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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-888 R)
+(-889 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.")))
NIL
NIL
-(-889 E OV R P)
+(-890 E OV R P)
((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-890)
+(-891)
((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}.")))
NIL
NIL
-(-891 -3260)
+(-892 -3327)
((|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
-(-892 R)
+(-893 R)
((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R}).")))
NIL
NIL
-(-893)
+(-894)
((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-894)
+(-895)
((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}.")))
-(((-4344 "*") . T))
+(((-4346 "*") . T))
NIL
-(-895 -3260 P)
+(-896 -3327 P)
((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented")))
NIL
NIL
-(-896 |xx| -3260)
+(-897 |xx| -3327)
((|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
-(-897 R |Var| |Expon| GR)
+(-898 R |Var| |Expon| GR)
((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}")))
NIL
NIL
-(-898 S)
+(-899 S)
((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval")))
NIL
NIL
-(-899)
+(-900)
((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")))
NIL
NIL
-(-900)
+(-901)
((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}.")))
NIL
NIL
-(-901)
+(-902)
((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented")))
NIL
NIL
-(-902 R -3260)
+(-903 R -3327)
((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol.")))
NIL
NIL
-(-903)
+(-904)
((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}.")))
NIL
NIL
-(-904 S A B)
+(-905 S A B)
((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B).")))
NIL
NIL
-(-905 S R -3260)
+(-906 S R -3327)
((|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
-(-906 I)
+(-907 I)
((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n,{} pat,{} res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-907 S E)
+(-908 S E)
((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,{}...,{}en),{} pat,{} res)} matches the pattern \\spad{pat} to \\spad{f(e1,{}...,{}en)}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-908 S R L)
+(-909 S R L)
((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l,{} pat,{} res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-909 S E V R P)
+(-910 S E V R P)
((|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 -859) (|devaluate| |#1|))))
-(-910 R -3260 -4183)
+((|HasCategory| |#3| (LIST (QUOTE -860) (|devaluate| |#1|))))
+(-911 R -3327 -1901)
((|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
-(-911 -4183)
+(-912 -1901)
((|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
-(-912 S R Q)
+(-913 S R Q)
((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b,{} pat,{} res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-913 S)
+(-914 S)
((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\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 (necessary for recursion).")))
NIL
NIL
-(-914 S R P)
+(-915 S R P)
((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj,{} lpat,{} res,{} match)} matches the product of patterns \\spad{reduce(*,{}lpat)} to the product of subjects \\spad{reduce(*,{}lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj,{} lpat,{} op,{} res,{} match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}.")))
NIL
NIL
-(-915)
+(-916)
((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}.")))
NIL
NIL
-(-916 R)
+(-917 R)
((|constructor| (NIL "This domain implements points in coordinate space")))
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1020))) (-12 (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-1020)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-917 |lv| R)
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1021))) (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1021)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-918 |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
NIL
-(-918 |TheField| |ThePols|)
+(-919 |TheField| |ThePols|)
((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term")))
NIL
((|HasCategory| |#1| (QUOTE (-823))))
-(-919 R S)
+(-920 R S)
((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}.")))
NIL
NIL
-(-920 |x| R)
+(-921 |x| R)
((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}.")))
NIL
NIL
-(-921 S R E |VarSet|)
+(-922 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 (-882))) (|HasAttribute| |#2| (QUOTE -4340)) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#4| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#4| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#4| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-825))))
-(-922 R E |VarSet|)
+((|HasCategory| |#2| (QUOTE (-883))) (|HasAttribute| |#2| (QUOTE -4342)) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#4| (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#4| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#4| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#4| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-825))))
+(-923 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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
-(-923 E V R P -3260)
+(-924 E V R P -3327)
((|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
-(-924 E |Vars| R P S)
+(-925 E |Vars| R P S)
((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}")))
NIL
NIL
-(-925 R)
+(-926 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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-882))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| (-1144) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| (-1144) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| (-1144) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| (-1144) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| (-1144) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4340)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-143)))))
-(-926 E V R P -3260)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-883))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| (-1145) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| (-1145) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| (-1145) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372)))))) (-12 (|HasCategory| (-1145) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550)))))) (-12 (|HasCategory| (-1145) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4342)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-927 E V R P -3327)
((|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)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented")))
NIL
((|HasCategory| |#3| (QUOTE (-444))))
-(-927)
+(-928)
((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}.")))
NIL
NIL
-(-928)
+(-929)
((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}.")))
NIL
NIL
-(-929 R L)
+(-930 R L)
((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}.")))
NIL
NIL
-(-930 A B)
+(-931 A B)
((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")))
NIL
NIL
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((|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")))
-((-4343 . T) (-4342 . T))
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-(-932)
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
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((|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
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((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}.")))
NIL
NIL
-(-934 I)
+(-935 I)
((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime")))
NIL
NIL
-(-935)
+(-936)
((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter.")))
NIL
NIL
-(-936 R E)
+(-937 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}")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4336 . T) (-4337 . T) (-4339 . T))
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-(-937 A B)
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+(-938 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")))
-((-4339 -12 (|has| |#2| (-465)) (|has| |#1| (-465))))
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((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}")))
NIL
NIL
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((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the variable name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula")))
NIL
NIL
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((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")))
NIL
NIL
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((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}.")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
-(-942 R |polR|)
+(-943 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}}")))
NIL
((|HasCategory| |#1| (QUOTE (-444))))
-(-943)
+(-944)
((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted.")))
NIL
NIL
-(-944)
+(-945)
((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|coerce| (((|List| (|Integer|)) $) "\\spad{coerce(p)} coerces a partition into a list of integers")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition")))
NIL
NIL
-(-945 S |Coef| |Expon| |Var|)
+(-946 S |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| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}.")))
NIL
NIL
-(-946 |Coef| |Expon| |Var|)
+(-947 |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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-947)
+(-948)
((|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}.")))
NIL
NIL
-(-948 S R E |VarSet| P)
+(-949 S R E |VarSet| P)
((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
NIL
((|HasCategory| |#2| (QUOTE (-542))))
-(-949 R E |VarSet| P)
+(-950 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.")))
-((-4342 . T) (-1964 . T))
+((-4344 . T) (-2836 . T))
NIL
-(-950 R E V P)
+(-951 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.")))
NIL
((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-300)))) (|HasCategory| |#1| (QUOTE (-444))))
-(-951 K)
+(-952 K)
((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m,{} v)} returns \\spad{[[C_1,{} g_1],{}...,{}[C_k,{} g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,{}...,{}C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M,{} A,{} sig,{} der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M,{} sig,{} der)} returns \\spad{[R,{} A,{} A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation.")))
NIL
NIL
-(-952 |VarSet| E RC P)
+(-953 |VarSet| E RC P)
((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")))
NIL
NIL
-(-953 R)
+(-954 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| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|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}.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-954 R1 R2)
+(-955 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented")))
NIL
NIL
-(-955 R)
+(-956 R)
((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")))
NIL
NIL
-(-956 K)
+(-957 K)
((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,{}n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise.")))
NIL
NIL
-(-957 R E OV PPR)
+(-958 R E OV PPR)
((|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
-(-958 K R UP -3260)
+(-959 K R UP -3327)
((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")))
NIL
NIL
-(-959 |vl| |nv|)
+(-960 |vl| |nv|)
((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals")))
NIL
NIL
-(-960 R |Var| |Expon| |Dpoly|)
+(-961 R |Var| |Expon| |Dpoly|)
((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set")))
NIL
((-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-300)))))
-(-961 R E V P TS)
+(-962 R E V P TS)
((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
NIL
NIL
-(-962)
+(-963)
((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation.")))
NIL
NIL
-(-963 A B R S)
+(-964 A B R S)
((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}.")))
NIL
NIL
-(-964 A S)
+(-965 A S)
((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-882))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1119))))
-(-965 S)
+((|HasCategory| |#2| (QUOTE (-883))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-996))) (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-1120))))
+(-966 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}.")))
-((-1964 . T) (-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-2836 . T) (-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-966 |n| K)
+(-967 |n| K)
((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}.")))
NIL
NIL
-(-967)
+(-968)
((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted.")))
NIL
NIL
-(-968 S)
+(-969 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.")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
-(-969 S R)
+(-970 S R)
((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-1029))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-283))))
-(-970 R)
+((|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-283))))
+(-971 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}.")))
-((-4335 |has| |#1| (-283)) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 |has| |#1| (-283)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-971 QR R QS S)
+(-972 QR R QS S)
((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}.")))
NIL
NIL
-(-972 R)
+(-973 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.}")))
-((-4335 |has| |#1| (-283)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1144)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1029))) (|HasCategory| |#1| (QUOTE (-535))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356)))))
-(-973 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
+((-4337 |has| |#1| (-283)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-283))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -505) (QUOTE (-1145)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -279) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-535))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356)))))
(-974 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}.")))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-975 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
NIL
-(-975)
+(-976)
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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
-(-976 -3260 UP UPUP |radicnd| |n|)
+(-977 -3327 UP UPUP |radicnd| |n|)
((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x}).")))
-((-4335 |has| (-400 |#2|) (-356)) (-4340 |has| (-400 |#2|) (-356)) (-4334 |has| (-400 |#2|) (-356)) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1561 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1561 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1561 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1561 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))))
-(-977 |bb|)
+((-4337 |has| (-400 |#2|) (-356)) (-4342 |has| (-400 |#2|) (-356)) (-4336 |has| (-400 |#2|) (-356)) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-400 |#2|) (QUOTE (-143))) (|HasCategory| (-400 |#2|) (QUOTE (-145))) (|HasCategory| (-400 |#2|) (QUOTE (-342))) (-1489 (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (|HasCategory| (-400 |#2|) (QUOTE (-356))) (|HasCategory| (-400 |#2|) (QUOTE (-361))) (-1489 (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (|HasCategory| (-400 |#2|) (QUOTE (-342)))) (-1489 (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-400 |#2|) (QUOTE (-342))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1489 (|HasCategory| (-400 |#2|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))) (-12 (|HasCategory| (-400 |#2|) (QUOTE (-227))) (|HasCategory| (-400 |#2|) (QUOTE (-356)))))
+(-978 |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.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-550) (QUOTE (-882))) (|HasCategory| (-550) (LIST (QUOTE -1011) (QUOTE (-1144)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-995))) (|HasCategory| (-550) (QUOTE (-798))) (-1561 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1119))) (|HasCategory| (-550) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1144)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-882)))) (|HasCategory| (-550) (QUOTE (-143)))))
-(-978)
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-550) (QUOTE (-883))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-1145)))) (|HasCategory| (-550) (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-145))) (|HasCategory| (-550) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-996))) (|HasCategory| (-550) (QUOTE (-798))) (-1489 (|HasCategory| (-550) (QUOTE (-798))) (|HasCategory| (-550) (QUOTE (-825)))) (|HasCategory| (-550) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-1120))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| (-550) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| (-550) (QUOTE (-227))) (|HasCategory| (-550) (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| (-550) (LIST (QUOTE -505) (QUOTE (-1145)) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -302) (QUOTE (-550)))) (|HasCategory| (-550) (LIST (QUOTE -279) (QUOTE (-550)) (QUOTE (-550)))) (|HasCategory| (-550) (QUOTE (-300))) (|HasCategory| (-550) (QUOTE (-535))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-550) (LIST (QUOTE -619) (QUOTE (-550)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-550) (QUOTE (-883)))) (|HasCategory| (-550) (QUOTE (-143)))))
+(-979)
((|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
NIL
-(-979)
+(-980)
((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size().")))
NIL
NIL
-(-980 RP)
+(-981 RP)
((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers.")))
NIL
NIL
-(-981 S)
+(-982 S)
((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number.")))
NIL
NIL
-(-982 A S)
+(-983 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 -4343)) (|HasCategory| |#2| (QUOTE (-1068))))
-(-983 S)
+((|HasAttribute| |#1| (QUOTE -4345)) (|HasCategory| |#2| (QUOTE (-1069))))
+(-984 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}.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-984 S)
+(-985 S)
((|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}}")))
NIL
NIL
-(-985)
+(-986)
((|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}}")))
-((-4335 . T) (-4340 . T) (-4334 . T) (-4337 . T) (-4336 . T) ((-4344 "*") . T) (-4339 . T))
+((-4337 . T) (-4342 . T) (-4336 . T) (-4339 . T) (-4338 . T) ((-4346 "*") . T) (-4341 . T))
NIL
-(-986 R -3260)
+(-987 R -3327)
((|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
-(-987 R -3260)
+(-988 R -3327)
((|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
-(-988 -3260 UP)
+(-989 -3327 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
-(-989 -3260 UP)
+(-990 -3327 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
-(-990 S)
+(-991 S)
((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,{}u,{}n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented")))
NIL
NIL
-(-991 F1 UP UPUP R F2)
+(-992 F1 UP UPUP R F2)
((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented")))
NIL
NIL
-(-992)
+(-993)
((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied.")))
NIL
NIL
-(-993 |Pol|)
+(-994 |Pol|)
((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}.")))
NIL
NIL
-(-994 |Pol|)
+(-995 |Pol|)
((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}.")))
NIL
NIL
-(-995)
+(-996)
((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats.")))
NIL
NIL
-(-996)
+(-997)
((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,{}lv,{}eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}.")))
NIL
NIL
-(-997 |TheField|)
+(-998 |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")))
-((-4335 . T) (-4340 . T) (-4334 . T) (-4337 . T) (-4336 . T) ((-4344 "*") . T) (-4339 . T))
-((-1561 (|HasCategory| (-400 (-550)) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-400 (-550)) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 (-550)) (LIST (QUOTE -1011) (QUOTE (-550)))))
-(-998 -3260 L)
+((-4337 . T) (-4342 . T) (-4336 . T) (-4339 . T) (-4338 . T) ((-4346 "*") . T) (-4341 . T))
+((-1489 (|HasCategory| (-400 (-550)) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-400 (-550)) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-400 (-550)) (LIST (QUOTE -1012) (QUOTE (-550)))))
+(-999 -3327 L)
((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}.")))
NIL
NIL
-(-999 S)
+(-1000 S)
((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-1068))))
-(-1000 R E V P)
+((|HasCategory| |#1| (QUOTE (-1069))))
+(-1001 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.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1001 R)
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1002 R)
((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.")))
NIL
-((|HasAttribute| |#1| (QUOTE (-4344 "*"))))
-(-1002 R)
+((|HasAttribute| |#1| (QUOTE (-4346 "*"))))
+(-1003 R)
((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis.")))
NIL
((-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-300))))
-(-1003 S)
+(-1004 S)
((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-1004)
+(-1005)
((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals.")))
NIL
NIL
-(-1005 S)
+(-1006 S)
((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-1006 S)
+(-1007 S)
((|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
-(-1007 -3260 |Expon| |VarSet| |FPol| |LFPol|)
+(-1008 -3327 |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")))
-(((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1008)
-((|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.}")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (QUOTE (-1144))) (LIST (QUOTE |:|) (QUOTE -2119) (QUOTE (-52))))))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-52) (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-1144) (QUOTE (-825))) (|HasCategory| (-52) (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))))
(-1009)
+((|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.}")))
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3859) (QUOTE (-52))))))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-52) (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-1145) (QUOTE (-825))) (|HasCategory| (-52) (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1010)
((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'.")))
NIL
NIL
-(-1010 A S)
+(-1011 A S)
((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%.")))
NIL
NIL
-(-1011 S)
+(-1012 S)
((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#1|) "\\spad{coerce(a)} transforms a into an element of \\%.")))
NIL
NIL
-(-1012 Q R)
+(-1013 Q R)
((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible.")))
NIL
NIL
-(-1013)
+(-1014)
((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented")))
NIL
NIL
-(-1014 UP)
+(-1015 UP)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}.")))
NIL
NIL
-(-1015 R)
+(-1016 R)
((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}.")))
NIL
NIL
-(-1016 R)
+(-1017 R)
((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}.")))
NIL
NIL
-(-1017 R |ls|)
+(-1018 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}.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| (-758 |#1| (-838 |#2|)) (QUOTE (-1068))) (|HasCategory| (-758 |#1| (-838 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -758) (|devaluate| |#1|) (LIST (QUOTE -838) (|devaluate| |#2|)))))) (|HasCategory| (-758 |#1| (-838 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-758 |#1| (-838 |#2|)) (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-838 |#2|) (QUOTE (-361))) (|HasCategory| (-758 |#1| (-838 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1018)
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| (-758 |#1| (-839 |#2|)) (QUOTE (-1069))) (|HasCategory| (-758 |#1| (-839 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -758) (|devaluate| |#1|) (LIST (QUOTE -839) (|devaluate| |#2|)))))) (|HasCategory| (-758 |#1| (-839 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-758 |#1| (-839 |#2|)) (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| (-839 |#2|) (QUOTE (-361))) (|HasCategory| (-758 |#1| (-839 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1019)
((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented")))
NIL
NIL
-(-1019 S)
+(-1020 S)
((|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\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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.")))
NIL
NIL
-(-1020)
+(-1021)
((|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\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|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.")))
-((-4339 . T))
+((-4341 . T))
NIL
-(-1021 |xx| -3260)
+(-1022 |xx| -3327)
((|constructor| (NIL "This package exports rational interpolation algorithms")))
NIL
NIL
-(-1022 S |m| |n| R |Row| |Col|)
+(-1023 S |m| |n| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite")))
NIL
((|HasCategory| |#4| (QUOTE (-300))) (|HasCategory| |#4| (QUOTE (-356))) (|HasCategory| |#4| (QUOTE (-542))) (|HasCategory| |#4| (QUOTE (-170))))
-(-1023 |m| |n| R |Row| |Col|)
+(-1024 |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")))
-((-4342 . T) (-1964 . T) (-4337 . T) (-4336 . T))
+((-4344 . T) (-2836 . T) (-4339 . T) (-4338 . T))
NIL
-(-1024 |m| |n| R)
+(-1025 |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.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}.")))
-((-4342 . T) (-4337 . T) (-4336 . T))
-((-1561 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -596) (QUOTE (-526)))) (-1561 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (QUOTE (-300))) (|HasCategory| |#3| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -595) (QUOTE (-836)))) (-12 (|HasCategory| |#3| (QUOTE (-1068))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))))
-(-1025 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+((-4344 . T) (-4339 . T) (-4338 . T))
+((-1489 (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (QUOTE (-300))) (|HasCategory| |#3| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -595) (QUOTE (-837)))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))))
+(-1026 |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
NIL
-(-1026 R)
+(-1027 R)
((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}.")))
NIL
NIL
-(-1027)
+(-1028)
((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")))
NIL
NIL
-(-1028 S)
+(-1029 S)
((|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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value.")))
NIL
NIL
-(-1029)
+(-1030)
((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1030 |TheField| |ThePolDom|)
+(-1031 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval")))
NIL
NIL
-(-1031)
+(-1032)
((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(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.")))
-((-4330 . T) (-4334 . T) (-4329 . T) (-4340 . T) (-4341 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4332 . T) (-4336 . T) (-4331 . T) (-4342 . T) (-4343 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1032)
+(-1033)
((|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}")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (QUOTE (-1144))) (LIST (QUOTE |:|) (QUOTE -2119) (QUOTE (-52))))))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-52) (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| (-52) (QUOTE (-1068))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (QUOTE (-1068))) (|HasCategory| (-1144) (QUOTE (-825))) (|HasCategory| (-52) (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 (-1144)) (|:| -2119 (-52))) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1033 S R E V)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3859) (QUOTE (-52))))))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-52) (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| (-52) (QUOTE (-1069))) (|HasCategory| (-52) (LIST (QUOTE -302) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (QUOTE (-1069))) (|HasCategory| (-1145) (QUOTE (-825))) (|HasCategory| (-52) (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-52) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 (-1145)) (|:| -3859 (-52))) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1034 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -965) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-1144)))))
-(-1034 R E V)
+((|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-535))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -966) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-1145)))))
+(-1035 R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
-(-1035)
+(-1036)
((|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'.")))
NIL
NIL
-(-1036 S |TheField| |ThePols|)
+(-1037 S |TheField| |ThePols|)
((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}")))
NIL
NIL
-(-1037 |TheField| |ThePols|)
+(-1038 |TheField| |ThePols|)
((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}")))
NIL
NIL
-(-1038 R E V P TS)
+(-1039 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 proposed: 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 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 \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} 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 \\axiom{\\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.}")))
NIL
NIL
-(-1039 S R E V P)
+(-1040 S 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,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{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| |#5|) (|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| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\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| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\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| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\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| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\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| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\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| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\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| |#5| (|List| $)) |#5| |#5| $) "\\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| $) |#5| $) "\\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|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\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| $)) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\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|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")))
NIL
NIL
-(-1040 R E V P)
+(-1041 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,{}...,{}\\spad{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,{}...,{}\\spad{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(\\spad{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}.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-1041 R E V P TS)
+(-1042 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.")))
NIL
NIL
-(-1042)
+(-1043)
((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted.")))
NIL
NIL
-(-1043 |f|)
+(-1044 |f|)
((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-1044 |Base| R -3260)
+(-1045 |Base| R -3327)
((|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
-(-1045 |Base| R -3260)
+(-1046 |Base| R -3327)
((|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
-(-1046 R |ls|)
+(-1047 R |ls|)
((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor.")))
NIL
NIL
-(-1047 UP SAE UPA)
+(-1048 UP SAE UPA)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}.")))
NIL
NIL
-(-1048 R UP M)
+(-1049 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.")))
-((-4335 |has| |#1| (-356)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
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-(-1049 UP SAE UPA)
+((-4337 |has| |#1| (-356)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-342))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-361))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-342)))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145))))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145))))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (QUOTE (-356)))))
+(-1050 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
NIL
-(-1050)
+(-1051)
((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable")))
NIL
NIL
-(-1051)
+(-1052)
((|constructor| (NIL "This is the category of Spad syntax objects.")))
NIL
NIL
-(-1052 S)
+(-1053 S)
((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache.")))
NIL
NIL
-(-1053)
+(-1054)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,{}s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(n,{}s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `failed'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope.")))
NIL
NIL
-(-1054 R)
+(-1055 R)
((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}")))
NIL
NIL
-(-1055 R)
+(-1056 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")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-882))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| (-1056 (-1144)) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| (-1056 (-1144)) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| (-1056 (-1144)) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| (-1056 (-1144)) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| (-1056 (-1144)) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4340)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-143)))))
-(-1056 S)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-883))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| (-1057 (-1145)) (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| (-1057 (-1145)) (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| (-1057 (-1145)) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372)))))) (-12 (|HasCategory| (-1057 (-1145)) (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550)))))) (-12 (|HasCategory| (-1057 (-1145)) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-227))) (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4342)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-1057 S)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u})).")))
NIL
NIL
-(-1057 R S)
+(-1058 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}.")))
NIL
((|HasCategory| |#1| (QUOTE (-823))))
-(-1058)
+(-1059)
((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list.")))
NIL
NIL
-(-1059 R S)
+(-1060 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}.")))
NIL
NIL
-(-1060 S)
+(-1061 S)
((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form.")))
NIL
-((|HasCategory| |#1| (QUOTE (-1068))))
-(-1061 S)
+((|HasCategory| |#1| (QUOTE (-1069))))
+(-1062 S)
((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-1062 S)
+(-1063 S)
((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1068))))
-(-1063 S L)
+((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1069))))
+(-1064 S L)
((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-1064)
+(-1065)
((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'.")))
NIL
NIL
-(-1065 A S)
+(-1066 A S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
NIL
NIL
-(-1066 S)
+(-1067 S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}.")))
-((-4332 . T) (-1964 . T))
+((-4334 . T) (-2836 . T))
NIL
-(-1067 S)
+(-1068 S)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1068)
+(-1069)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1069 |m| |n|)
+(-1070 |m| |n|)
((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")))
NIL
NIL
-(-1070 S)
+(-1071 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)}}")))
-((-4342 . T) (-4332 . T) (-4343 . T))
-((-1561 (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-825))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1071 |Str| |Sym| |Int| |Flt| |Expr|)
+((-4344 . T) (-4334 . T) (-4345 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-825))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1072 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp.")))
NIL
NIL
-(-1072)
+(-1073)
((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values.")))
NIL
NIL
-(-1073 |Str| |Sym| |Int| |Flt| |Expr|)
+(-1074 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types.")))
NIL
NIL
-(-1074 R FS)
+(-1075 R FS)
((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,{}ftype,{}body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program.")))
NIL
NIL
-(-1075 R E V P TS)
+(-1076 R E V P TS)
((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
NIL
NIL
-(-1076 R E V P TS)
+(-1077 R E V P TS)
((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\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.}")))
NIL
NIL
-(-1077 R E V P)
+(-1078 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.}")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-1078)
+(-1079)
((|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| (|Integer|)) (|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| (|Integer|)) (|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| (|Integer|))) "\\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 \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{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,{}\\spad{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 \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber.")))
NIL
NIL
-(-1079 S)
+(-1080 S)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-1080)
+(-1081)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-1081 |dimtot| |dim1| S)
+(-1082 |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}.")))
-((-4336 |has| |#3| (-1020)) (-4337 |has| |#3| (-1020)) (-4339 |has| |#3| (-6 -4339)) ((-4344 "*") |has| |#3| (-170)) (-4342 . T))
-((-1561 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-227))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-823))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (LIST (QUOTE 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|#3| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#3| (QUOTE (-356))) (-1561 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356))) (|HasCategory| |#3| (QUOTE (-1020)))) (-1561 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-356)))) (|HasCategory| |#3| (QUOTE (-1020))) (|HasCategory| |#3| (QUOTE (-771))) (-1561 (|HasCategory| |#3| (QUOTE (-771))) (|HasCategory| |#3| (QUOTE (-823)))) (|HasCategory| |#3| (QUOTE (-823))) (|HasCategory| |#3| (QUOTE (-705))) (|HasCategory| |#3| (QUOTE (-170))) (-1561 (|HasCategory| |#3| (QUOTE (-170))) (|HasCategory| |#3| (QUOTE (-1020)))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#3| (LIST (QUOTE -873) (QUOTE (-1144)))) (-1561 (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#3| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-170))) 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-(-1082 R |x|)
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(QUOTE (-550)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#3| (QUOTE (-1069)))) (|HasAttribute| |#3| (QUOTE -4341)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (LIST (QUOTE -302) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1083 R |x|)
((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}")))
NIL
((|HasCategory| |#1| (QUOTE (-444))))
-(-1083)
+(-1084)
((|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
-(-1084 R -3260)
+(-1085 R -3327)
((|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
-(-1085 R)
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((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1086)
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((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}.")))
NIL
NIL
-(-1087)
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((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}")))
NIL
NIL
-(-1088)
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((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|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.")))
-((-4330 . T) (-4334 . T) (-4329 . T) (-4340 . T) (-4341 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4332 . T) (-4336 . T) (-4331 . T) (-4342 . T) (-4343 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1089 S)
+(-1090 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-4342 . T) (-4343 . T) (-1964 . T))
+((-4344 . T) (-4345 . T) (-2836 . T))
NIL
-(-1090 S |ndim| R |Row| |Col|)
+(-1091 S |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-356))) (|HasAttribute| |#3| (QUOTE (-4344 "*"))) (|HasCategory| |#3| (QUOTE (-170))))
-(-1091 |ndim| R |Row| |Col|)
+((|HasCategory| |#3| (QUOTE (-356))) (|HasAttribute| |#3| (QUOTE (-4346 "*"))) (|HasCategory| |#3| (QUOTE (-170))))
+(-1092 |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.")))
-((-1964 . T) (-4342 . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-2836 . T) (-4344 . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1092 R |Row| |Col| M)
+(-1093 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}.")))
NIL
NIL
-(-1093 R |VarSet|)
+(-1094 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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-882))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4340)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-882)))) (|HasCategory| |#1| (QUOTE (-143)))))
-(-1094 |Coef| |Var| SMP)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-883))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (|HasCategory| |#1| (QUOTE (-444))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-372))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -860) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -860) (QUOTE (-550))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-372)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4342)) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-883)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-1095 |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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356))))
-(-1095 R E V P)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356))))
+(-1096 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}")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-1096 UP -3260)
+(-1097 UP -3327)
((|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
-(-1097 R)
+(-1098 R)
((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,{}lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,{}x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function.")))
NIL
NIL
-(-1098 R)
+(-1099 R)
((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned.")))
NIL
NIL
-(-1099 R)
+(-1100 R)
((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,{}x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq.")))
NIL
NIL
-(-1100 S A)
+(-1101 S A)
((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented")))
NIL
((|HasCategory| |#1| (QUOTE (-825))))
-(-1101 R)
+(-1102 R)
((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")))
NIL
NIL
-(-1102 R)
+(-1103 R)
((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} [props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination.")))
NIL
NIL
-(-1103)
+(-1104)
((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}")))
NIL
NIL
-(-1104)
+(-1105)
((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful.")))
NIL
NIL
-(-1105)
+(-1106)
((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-1106)
+(-1107)
((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.")))
NIL
NIL
-(-1107)
+(-1108)
((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")))
NIL
NIL
-(-1108 V C)
+(-1109 V C)
((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}")))
NIL
NIL
-(-1109 V C)
+(-1110 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-1108 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1108) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1108 |#1| |#2|) (QUOTE (-1068)))) (|HasCategory| (-1108 |#1| |#2|) (QUOTE (-1068))) (-1561 (|HasCategory| (-1108 |#1| |#2|) (LIST (QUOTE -595) (QUOTE (-836)))) (-12 (|HasCategory| (-1108 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1108) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1108 |#1| |#2|) (QUOTE (-1068))))) (|HasCategory| (-1108 |#1| |#2|) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1110 |ndim| R)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-1109 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1109) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1109 |#1| |#2|) (QUOTE (-1069)))) (|HasCategory| (-1109 |#1| |#2|) (QUOTE (-1069))) (-1489 (|HasCategory| (-1109 |#1| |#2|) (LIST (QUOTE -595) (QUOTE (-837)))) (-12 (|HasCategory| (-1109 |#1| |#2|) (LIST (QUOTE -302) (LIST (QUOTE -1109) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1109 |#1| |#2|) (QUOTE (-1069))))) (|HasCategory| (-1109 |#1| |#2|) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1111 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}.")))
-((-4339 . T) (-4331 |has| |#2| (-6 (-4344 "*"))) (-4342 . T) (-4336 . T) (-4337 . T))
-((|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4344 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (-1561 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-356))) (-1561 (|HasAttribute| |#2| (QUOTE (-4344 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-170))))
-(-1111 S)
+((-4341 . T) (-4333 |has| |#2| (-6 (-4346 "*"))) (-4344 . T) (-4338 . T) (-4339 . T))
+((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE (-4346 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-550)))) (-1489 (-12 (|HasCategory| |#2| (QUOTE (-227))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (QUOTE (-300))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-356))) (-1489 (|HasAttribute| |#2| (QUOTE (-4346 "*"))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasCategory| |#2| (QUOTE (-227)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-170))))
+(-1112 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
NIL
NIL
-(-1112)
+(-1113)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-1113 R E V P TS)
+(-1114 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.}")))
NIL
NIL
-(-1114 R E V P)
+(-1115 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.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1115 S)
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1116 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}.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1116 A S)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1117 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
NIL
-(-1117 S)
+(-1118 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})}.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-1118 |Key| |Ent| |dent|)
+(-1119 |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.")))
-((-4343 . T))
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-(-1119)
+((-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-825))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1120)
((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping.")))
NIL
NIL
-(-1120 |Coef|)
+(-1121 |Coef|)
((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|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| (((|Stream| |#1|) (|Stream| |#1|)) "\\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| (((|Stream| |#1|) (|Stream| |#1|)) "\\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| (((|Stream| |#1|) (|Stream| |#1|)) "\\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
-(-1121 S)
+(-1122 S)
((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}.")))
NIL
NIL
-(-1122 A B)
+(-1123 A B)
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}.")))
NIL
NIL
-(-1123 A B C)
+(-1124 A B C)
((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}.")))
NIL
NIL
-(-1124 S)
+(-1125 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}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries.")))
-((-4343 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1125)
+((-4345 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1126)
((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-1126)
+(-1127)
NIL
-((-4343 . T) (-4342 . T))
-((-1561 (-12 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1068))) (-12 (|HasCategory| (-142) (QUOTE (-1068))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1127 |Entry|)
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| (-142) (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| (-142) (QUOTE (-1069))) (-12 (|HasCategory| (-142) (QUOTE (-1069))) (|HasCategory| (-142) (LIST (QUOTE -302) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1128 |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (QUOTE (-1126))) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#1|)))))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (QUOTE (-1068))) (|HasCategory| (-1126) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 (-1126)) (|:| -2119 |#1|)) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1128 A)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (QUOTE (-1127))) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#1|)))))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (QUOTE (-1069))) (|HasCategory| (-1127) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 (-1127)) (|:| -3859 |#1|)) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1129 A)
((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}")))
NIL
((|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))))
-(-1129 |Coef|)
+(-1130 |Coef|)
((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}.")))
NIL
NIL
-(-1130 |Coef|)
+(-1131 |Coef|)
((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}.")))
NIL
NIL
-(-1131 R UP)
+(-1132 R UP)
((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}.")))
NIL
((|HasCategory| |#1| (QUOTE (-300))))
-(-1132 |n| R)
+(-1133 |n| R)
((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,{}s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,{}n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented")))
NIL
NIL
-(-1133 S1 S2)
+(-1134 S1 S2)
((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} makes a form \\spad{s:t}")))
NIL
NIL
-(-1134)
+(-1135)
((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'.")))
NIL
NIL
-(-1135 |Coef| |var| |cen|)
+(-1136 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series.")))
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((|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
-(-1137 R)
+(-1138 R)
((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.")))
NIL
NIL
-(-1138 R S)
+(-1139 R S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
-(-1139 E OV R P)
+(-1140 E OV R P)
((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}.")))
NIL
NIL
-(-1140 R)
+(-1141 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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4338 |has| |#1| (-356)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
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-(-1141 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
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(-1142 |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.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-550)) (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasSignature| |#1| (LIST (QUOTE -2233) (LIST (|devaluate| |#1|) (QUOTE (-1145)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1489 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -2149) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1145))))) (|HasSignature| |#1| (LIST (QUOTE -1516) (LIST (LIST (QUOTE -623) (QUOTE (-1145))) (|devaluate| |#1|)))))))
+(-1143 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}.")))
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+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-749)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-749)) (|devaluate| |#1|)))) (|HasCategory| (-749) (QUOTE (-1081))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-749))))) (|HasSignature| |#1| (LIST (QUOTE -2233) (LIST (|devaluate| |#1|) (QUOTE (-1145)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-749))))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -2149) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1145))))) (|HasSignature| |#1| (LIST (QUOTE -1516) (LIST (LIST (QUOTE -623) (QUOTE (-1145))) (|devaluate| |#1|)))))))
+(-1144)
((|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
NIL
-(-1144)
+(-1145)
((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s,{} [a,{}b,{}c])} is equivalent to \\spad{script(s,{}[a,{}b,{}c,{}[],{}[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts the string \\spad{s} to a symbol.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%.")))
NIL
NIL
-(-1145 R)
+(-1146 R)
((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r,{} n)} returns the vector of the elementary symmetric functions in \\spad{[r,{}r,{}...,{}r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,{}...,{}rn])} returns the vector of the elementary symmetric functions in the \\spad{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}.")))
NIL
NIL
-(-1146 R)
+(-1147 R)
((|constructor| (NIL "This domain implements symmetric polynomial")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-6 -4340)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| (-944) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-542)))) (-1561 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4340)))
-(-1147)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-6 -4342)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-444))) (-12 (|HasCategory| (-945) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-542)))) (-1489 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasAttribute| |#1| (QUOTE -4342)))
+(-1148)
((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table.")))
NIL
NIL
-(-1148)
+(-1149)
((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,{}tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,{}tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,{}t,{}tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,{}t,{}tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}")))
NIL
NIL
-(-1149)
+(-1150)
((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} building complete representation of Spad programs as objects of a term algebra built from ground terms of type integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity in a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} Symbol,{} String,{} SExpression. See Also: SExpression,{} SetCategory. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (($ (|String|)) "\\spad{coerce(s)} injects the string value \\spad{`s'} into the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (($ (|Symbol|)) "\\spad{coerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (($ (|DoubleFloat|)) "\\spad{coerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}") (($ (|Integer|)) "\\spad{coerce(i)} injects the integer value `i' into the Syntax domain.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax.")))
NIL
NIL
-(-1150 R)
+(-1151 R)
((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,{}lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,{}v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,{}v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,{}lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")))
NIL
NIL
-(-1151)
+(-1152)
((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system.")))
NIL
NIL
-(-1152 S)
+(-1153 S)
((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record")))
NIL
NIL
-(-1153 S)
+(-1154 S)
((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau.")))
NIL
NIL
-(-1154 |Key| |Entry|)
+(-1155 |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}")))
-((-4342 . T) (-4343 . T))
-((-12 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2763) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2119) (|devaluate| |#2|)))))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1068)))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1068))) (-1561 (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-836)))) (|HasCategory| (-2 (|:| -2763 |#1|) (|:| -2119 |#2|)) (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1155 R)
+((-4344 . T) (-4345 . T))
+((-12 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -302) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3549) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3859) (|devaluate| |#2|)))))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-1069)))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -596) (QUOTE (-526)))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (LIST (QUOTE -302) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-1069))) (-1489 (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#2| (LIST (QUOTE -595) (QUOTE (-837)))) (|HasCategory| (-2 (|:| -3549 |#1|) (|:| -3859 |#2|)) (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1156 R)
((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}.")))
NIL
NIL
-(-1156 S |Key| |Entry|)
+(-1157 S |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| |#3| |#3| |#3|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\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| ((|#3| $ |#2| |#3|) "\\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})}.")))
NIL
NIL
-(-1157 |Key| |Entry|)
+(-1158 |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})}.")))
-((-4343 . T) (-1964 . T))
+((-4345 . T) (-2836 . T))
NIL
-(-1158 |Key| |Entry|)
+(-1159 |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.")))
NIL
NIL
-(-1159)
+(-1160)
((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it.")))
NIL
NIL
-(-1160 S)
+(-1161 S)
((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format.")))
NIL
NIL
-(-1161)
+(-1162)
((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format.")))
NIL
NIL
-(-1162)
+(-1163)
((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,{}\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,{}s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned.")))
NIL
NIL
-(-1163 R)
+(-1164 R)
((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented")))
NIL
NIL
-(-1164)
+(-1165)
((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination.")))
NIL
NIL
-(-1165 S)
+(-1166 S)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1166)
+(-1167)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1167 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}.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1068))) (-1561 (-12 (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
(-1168 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1069))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1169 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1169)
+(-1170)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1170 R -3260)
+(-1171 R -3327)
((|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
-(-1171 R |Row| |Col| M)
+(-1172 R |Row| |Col| M)
((|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
-(-1172 R -3260)
+(-1173 R -3327)
((|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 -596) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -859) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -859) (|devaluate| |#1|)))))
-(-1173 S R E V P)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -596) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -860) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -860) (|devaluate| |#1|)))))
+(-1174 S R E V P)
((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
NIL
((|HasCategory| |#4| (QUOTE (-361))))
-(-1174 R E V P)
+(-1175 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
+((-4345 . T) (-4344 . T) (-2836 . T))
NIL
-(-1175 |Coef|)
+(-1176 |Coef|)
((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356))))
-(-1176 |Curve|)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-356))))
+(-1177 |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
NIL
-(-1177)
+(-1178)
((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,{}sin(n - 1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point.")))
NIL
NIL
-(-1178 S)
+(-1179 S)
((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a")))
NIL
-((|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1179 -3260)
+((|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1180 -3327)
((|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
-(-1180)
+(-1181)
((|constructor| (NIL "This domain represents a type AST.")))
NIL
NIL
-(-1181)
+(-1182)
((|constructor| (NIL "The fundamental Type.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-1182 S)
+(-1183 S)
((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}")))
NIL
((|HasCategory| |#1| (QUOTE (-825))))
-(-1183)
+(-1184)
((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}.")))
NIL
NIL
-(-1184 S)
+(-1185 S)
((|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.")))
NIL
NIL
-(-1185)
+(-1186)
((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
-((-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1186 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
+(-1187 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}.")))
NIL
NIL
-(-1187 |Coef|)
+(-1188 |Coef|)
((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1188 S |Coef| UTS)
+(-1189 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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}.")))
NIL
((|HasCategory| |#2| (QUOTE (-356))))
-(-1189 |Coef| UTS)
+(-1190 |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| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|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)}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-1964 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-2836 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1190 |Coef| UTS)
+(-1191 |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)}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
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-(-1192 ZP)
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(QUOTE -1012) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1489 (-12 (|HasCategory| (-1220 |#1| |#2| |#3|) (QUOTE (-798))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| (-1220 |#1| |#2| |#3|) (QUOTE (-883))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-170)))) (-12 (|HasCategory| (-1220 |#1| |#2| |#3|) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1220 |#1| |#2| |#3|) (QUOTE (-883))) (|HasCategory| |#1| (QUOTE (-356)))) (-1489 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-1220 |#1| |#2| |#3|) (QUOTE (-883))) (|HasCategory| |#1| (QUOTE (-356)))) (-12 (|HasCategory| (-1220 |#1| |#2| |#3|) (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-356)))) (|HasCategory| |#1| (QUOTE (-143)))))
+(-1193 ZP)
((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}")))
NIL
NIL
-(-1193 R S)
+(-1194 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}.")))
NIL
((|HasCategory| |#1| (QUOTE (-823))))
-(-1194 S)
+(-1195 S)
((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound.")))
NIL
-((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1068))))
-(-1195 |x| R |y| S)
+((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1069))))
+(-1196 |x| R |y| S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
-(-1196 R Q UP)
+(-1197 R Q UP)
((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}.")))
NIL
NIL
-(-1197 R UP)
+(-1198 R UP)
((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")))
NIL
NIL
-(-1198 R UP)
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((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded.")))
NIL
NIL
-(-1199 R U)
+(-1200 R U)
((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all.")))
NIL
NIL
-(-1200 |x| R)
+(-1201 |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| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial.")))
-(((-4344 "*") |has| |#2| (-170)) (-4335 |has| |#2| (-542)) (-4338 |has| |#2| (-356)) (-4340 |has| |#2| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-882))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (-1561 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-542)))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -859) (QUOTE (-372)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-372))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -859) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -859) (QUOTE (-550))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-372)))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -596) (LIST (QUOTE -865) (QUOTE (-550)))))) (-12 (|HasCategory| (-1050) (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#2| (LIST (QUOTE -596) (QUOTE (-526))))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (-1561 (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-1119))) (|HasCategory| |#2| (LIST (QUOTE -873) (QUOTE (-1144)))) (-1561 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasCategory| |#2| (QUOTE (-227))) (|HasAttribute| |#2| (QUOTE -4340)) (|HasCategory| |#2| (QUOTE (-444))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (-1561 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-882)))) (|HasCategory| |#2| (QUOTE (-143)))))
-(-1201 R PR S PS)
+(((-4346 "*") |has| |#2| (-170)) (-4337 |has| |#2| (-542)) (-4340 |has| |#2| (-356)) (-4342 |has| |#2| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
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+(-1202 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
NIL
-(-1202 S R)
+(-1203 S R)
((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1119))))
-(-1203 R)
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))) (|HasCategory| |#2| (QUOTE (-444))) (|HasCategory| |#2| (QUOTE (-542))) (|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (QUOTE (-1120))))
+(-1204 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}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4338 |has| |#1| (-356)) (-4340 |has| |#1| (-6 -4340)) (-4337 . T) (-4336 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4342 |has| |#1| (-6 -4342)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
-(-1204 S |Coef| |Expon|)
+(-1205 S |Coef| |Expon|)
((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
NIL
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-(-1205 |Coef| |Expon|)
+((|HasCategory| |#2| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1081))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2233) (LIST (|devaluate| |#2|) (QUOTE (-1145))))))
+(-1206 |Coef| |Expon|)
((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1206 RC P)
+(-1207 RC P)
((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-1207 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
+(-1208 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}.")))
NIL
NIL
-(-1208 |Coef|)
+(-1209 |Coef|)
((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1209 S |Coef| ULS)
+(-1210 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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}.")))
NIL
NIL
-(-1210 |Coef| ULS)
+(-1211 |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| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|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)}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1211 |Coef| ULS)
+(-1212 |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)}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
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-(-1212 |Coef| |var| |cen|)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-550)) (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasSignature| |#1| (LIST (QUOTE -2233) (LIST (|devaluate| |#1|) (QUOTE (-1145)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1489 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -2149) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1145))))) (|HasSignature| |#1| (LIST (QUOTE -1516) (LIST (LIST (QUOTE -623) (QUOTE (-1145))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))))
+(-1213 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4340 |has| |#1| (-356)) (-4334 |has| |#1| (-356)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-550)) (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-1561 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (QUOTE (-1144)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1561 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-1166))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -1489) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1144))))) (|HasSignature| |#1| (LIST (QUOTE -3141) (LIST (LIST (QUOTE -623) (QUOTE (-1144))) (|devaluate| |#1|)))))))
-(-1213 R FE |var| |cen|)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4342 |has| |#1| (-356)) (-4336 |has| |#1| (-356)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#1| (QUOTE (-170))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -874) (QUOTE (-1145)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550))) (|devaluate| |#1|)))) (|HasCategory| (-400 (-550)) (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-356))) (-1489 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-1489 (|HasCategory| |#1| (QUOTE (-356))) (|HasCategory| |#1| (QUOTE (-542)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasSignature| |#1| (LIST (QUOTE -2233) (LIST (|devaluate| |#1|) (QUOTE (-1145)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -400) (QUOTE (-550)))))) (-1489 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -2149) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1145))))) (|HasSignature| |#1| (LIST (QUOTE -1516) (LIST (LIST (QUOTE -623) (QUOTE (-1145))) (|devaluate| |#1|)))))))
+(-1214 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))}.")))
-(((-4344 "*") |has| (-1212 |#2| |#3| |#4|) (-170)) (-4335 |has| (-1212 |#2| |#3| |#4|) (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1011) (QUOTE (-550)))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-356))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-444))) (-1561 (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (LIST (QUOTE -1011) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasCategory| (-1212 |#2| |#3| |#4|) (QUOTE (-542))))
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+(((-4346 "*") |has| (-1213 |#2| |#3| |#4|) (-170)) (-4337 |has| (-1213 |#2| |#3| |#4|) (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
+((|HasCategory| (-1213 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-1213 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1213 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1213 |#2| |#3| |#4|) (QUOTE (-170))) (|HasCategory| (-1213 |#2| |#3| |#4|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-1213 |#2| |#3| |#4|) (LIST (QUOTE -1012) (QUOTE (-550)))) (|HasCategory| (-1213 |#2| |#3| |#4|) (QUOTE (-356))) (|HasCategory| (-1213 |#2| |#3| |#4|) (QUOTE (-444))) (-1489 (|HasCategory| (-1213 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| (-1213 |#2| |#3| |#4|) (LIST (QUOTE -1012) (LIST (QUOTE -400) (QUOTE (-550)))))) (|HasCategory| (-1213 |#2| |#3| |#4|) (QUOTE (-542))))
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((|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4343)))
-(-1215 S)
+((|HasAttribute| |#1| (QUOTE -4345)))
+(-1216 S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
-((-1964 . T))
+((-2836 . T))
NIL
-(-1216 |Coef1| |Coef2| UTS1 UTS2)
+(-1217 |Coef1| |Coef2| UTS1 UTS2)
((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}")))
NIL
NIL
-(-1217 S |Coef|)
+(-1218 S |Coef|)
((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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
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-(-1218 |Coef|)
+((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-1167))) (|HasSignature| |#2| (LIST (QUOTE -1516) (LIST (LIST (QUOTE -623) (QUOTE (-1145))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2149) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1145))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#2| (QUOTE (-356))))
+(-1219 |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.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1219 |Coef| |var| |cen|)
+(-1220 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}.")))
-(((-4344 "*") |has| |#1| (-170)) (-4335 |has| |#1| (-542)) (-4336 . T) (-4337 . T) (-4339 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasCategory| |#1| (QUOTE (-542))) (-1561 (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-542)))) (|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -873) (QUOTE (-1144)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-749)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-749)) (|devaluate| |#1|)))) (|HasCategory| (-749) (QUOTE (-1080))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-749))))) (|HasSignature| |#1| (LIST (QUOTE -1518) (LIST (|devaluate| |#1|) (QUOTE (-1144)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-749))))) (|HasCategory| |#1| (QUOTE (-356))) (-1561 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-1166))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasSignature| |#1| (LIST (QUOTE -1489) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1144))))) (|HasSignature| |#1| (LIST (QUOTE -3141) (LIST (LIST (QUOTE -623) (QUOTE (-1144))) (|devaluate| |#1|)))))))
-(-1220 |Coef| UTS)
+(((-4346 "*") |has| |#1| (-170)) (-4337 |has| |#1| (-542)) (-4338 . T) (-4339 . T) (-4341 . T))
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((|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
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+(-1222 -3327 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 (-542))))
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((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators.")))
-((-1964 . T))
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NIL
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((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol")))
NIL
NIL
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((|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| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "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| |#2|) $ $) "\\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| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|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.")))
NIL
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-(-1225 R)
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((|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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-4343 . T) (-4342 . T) (-1964 . T))
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NIL
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((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}.")))
NIL
NIL
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((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-4343 . T) (-4342 . T))
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-(-1228)
+((-4345 . T) (-4344 . T))
+((-1489 (-12 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|))))) (-1489 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837))))) (|HasCategory| |#1| (LIST (QUOTE -596) (QUOTE (-526)))) (-1489 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-550) (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-705))) (|HasCategory| |#1| (QUOTE (-1021))) (-12 (|HasCategory| |#1| (QUOTE (-976))) (|HasCategory| |#1| (QUOTE (-1021)))) (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -302) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -595) (QUOTE (-837)))))
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((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc.")))
NIL
NIL
-(-1229)
+(-1230)
((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians.")))
NIL
NIL
-(-1230)
+(-1231)
((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport.")))
NIL
NIL
-(-1231)
+(-1232)
((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}.")))
NIL
NIL
-(-1232)
+(-1233)
((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object.")))
NIL
NIL
-(-1233 A S)
+(-1234 A S)
((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}.")))
NIL
NIL
-(-1234 S)
+(-1235 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}.")))
-((-4337 . T) (-4336 . T))
+((-4339 . T) (-4338 . T))
NIL
-(-1235 R)
+(-1236 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
-(-1236 K R UP -3260)
+(-1237 K R UP -3327)
((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")))
NIL
NIL
-(-1237)
+(-1238)
((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'.")))
NIL
NIL
-(-1238)
+(-1239)
((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'.")))
NIL
NIL
-(-1239 R |VarSet| E P |vl| |wl| |wtlevel|)
+(-1240 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights")))
-((-4337 |has| |#1| (-170)) (-4336 |has| |#1| (-170)) (-4339 . T))
+((-4339 |has| |#1| (-170)) (-4338 |has| |#1| (-170)) (-4341 . T))
((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))))
-(-1240 R E V P)
+(-1241 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}}.")))
-((-4343 . T) (-4342 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-836)))))
-(-1241 R)
+((-4345 . T) (-4344 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#4| (LIST (QUOTE -302) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -596) (QUOTE (-526)))) (|HasCategory| |#4| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-542))) (|HasCategory| |#3| (QUOTE (-361))) (|HasCategory| |#4| (LIST (QUOTE -595) (QUOTE (-837)))))
+(-1242 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})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}.")))
-((-4336 . T) (-4337 . T) (-4339 . T))
+((-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1242 |vl| R)
+(-1243 |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.")))
-((-4339 . T) (-4335 |has| |#2| (-6 -4335)) (-4337 . T) (-4336 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4335)))
-(-1243 R |VarSet| XPOLY)
+((-4341 . T) (-4337 |has| |#2| (-6 -4337)) (-4339 . T) (-4338 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4337)))
+(-1244 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
-(-1244 |vl| R)
+(-1245 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}.")))
-((-4335 |has| |#2| (-6 -4335)) (-4337 . T) (-4336 . T) (-4339 . T))
+((-4337 |has| |#2| (-6 -4337)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
-(-1245 S -3260)
+(-1246 S -3327)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
NIL
((|HasCategory| |#2| (QUOTE (-361))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))))
-(-1246 -3260)
+(-1247 -3327)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
-((-4334 . T) (-4340 . T) (-4335 . T) ((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+((-4336 . T) (-4342 . T) (-4337 . T) ((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
-(-1247 |VarSet| R)
+(-1248 |VarSet| R)
((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}.")))
-((-4335 |has| |#2| (-6 -4335)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -696) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasAttribute| |#2| (QUOTE -4335)))
-(-1248 |vl| R)
+((-4337 |has| |#2| (-6 -4337)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasCategory| |#2| (LIST (QUOTE -696) (LIST (QUOTE -400) (QUOTE (-550))))) (|HasAttribute| |#2| (QUOTE -4337)))
+(-1249 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}.")))
-((-4335 |has| |#2| (-6 -4335)) (-4337 . T) (-4336 . T) (-4339 . T))
+((-4337 |has| |#2| (-6 -4337)) (-4339 . T) (-4338 . T) (-4341 . T))
NIL
-(-1249 R)
+(-1250 R)
((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute.")))
-((-4335 |has| |#1| (-6 -4335)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4335)))
-(-1250 R E)
+((-4337 |has| |#1| (-6 -4337)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasAttribute| |#1| (QUOTE -4337)))
+(-1251 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}.")))
-((-4339 . T) (-4340 |has| |#1| (-6 -4340)) (-4335 |has| |#1| (-6 -4335)) (-4337 . T) (-4336 . T))
-((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasAttribute| |#1| (QUOTE -4339)) (|HasAttribute| |#1| (QUOTE -4340)) (|HasAttribute| |#1| (QUOTE -4335)))
-(-1251 |VarSet| R)
+((-4341 . T) (-4342 |has| |#1| (-6 -4342)) (-4337 |has| |#1| (-6 -4337)) (-4339 . T) (-4338 . T))
+((|HasCategory| |#1| (QUOTE (-170))) (|HasCategory| |#1| (QUOTE (-356))) (|HasAttribute| |#1| (QUOTE -4341)) (|HasAttribute| |#1| (QUOTE -4342)) (|HasAttribute| |#1| (QUOTE -4337)))
+(-1252 |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.")))
-((-4335 |has| |#2| (-6 -4335)) (-4337 . T) (-4336 . T) (-4339 . T))
-((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4335)))
-(-1252 A)
+((-4337 |has| |#2| (-6 -4337)) (-4339 . T) (-4338 . T) (-4341 . T))
+((|HasCategory| |#2| (QUOTE (-170))) (|HasAttribute| |#2| (QUOTE -4337)))
+(-1253 A)
((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}.")))
NIL
NIL
-(-1253 R |ls| |ls2|)
+(-1254 R |ls| |ls2|)
((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} 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{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.")))
NIL
NIL
-(-1254 R)
+(-1255 R)
((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([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 the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise.")))
NIL
NIL
-(-1255 |p|)
+(-1256 |p|)
((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}.")))
-(((-4344 "*") . T) (-4336 . T) (-4337 . T) (-4339 . T))
+(((-4346 "*") . T) (-4338 . T) (-4339 . T) (-4341 . T))
NIL
NIL
NIL
@@ -4968,4 +4972,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 2267173 2267178 2267183 2267188) (-2 NIL 2267153 2267158 2267163 2267168) (-1 NIL 2267133 2267138 2267143 2267148) (0 NIL 2267113 2267118 2267123 2267128) (-1255 "ZMOD.spad" 2266922 2266935 2267051 2267108) (-1254 "ZLINDEP.spad" 2265966 2265977 2266912 2266917) (-1253 "ZDSOLVE.spad" 2255815 2255837 2265956 2265961) (-1252 "YSTREAM.spad" 2255308 2255319 2255805 2255810) (-1251 "XRPOLY.spad" 2254528 2254548 2255164 2255233) (-1250 "XPR.spad" 2252257 2252270 2254246 2254345) (-1249 "XPOLY.spad" 2251812 2251823 2252113 2252182) (-1248 "XPOLYC.spad" 2251129 2251145 2251738 2251807) (-1247 "XPBWPOLY.spad" 2249566 2249586 2250909 2250978) (-1246 "XF.spad" 2248027 2248042 2249468 2249561) (-1245 "XF.spad" 2246468 2246485 2247911 2247916) (-1244 "XFALG.spad" 2243492 2243508 2246394 2246463) (-1243 "XEXPPKG.spad" 2242743 2242769 2243482 2243487) (-1242 "XDPOLY.spad" 2242357 2242373 2242599 2242668) (-1241 "XALG.spad" 2241955 2241966 2242313 2242352) (-1240 "WUTSET.spad" 2237794 2237811 2241601 2241628) (-1239 "WP.spad" 2236808 2236852 2237652 2237719) (-1238 "WHILEAST.spad" 2236606 2236615 2236798 2236803) (-1237 "WHEREAST.spad" 2236277 2236286 2236596 2236601) (-1236 "WFFINTBS.spad" 2233840 2233862 2236267 2236272) (-1235 "WEIER.spad" 2232054 2232065 2233830 2233835) (-1234 "VSPACE.spad" 2231727 2231738 2232022 2232049) (-1233 "VSPACE.spad" 2231420 2231433 2231717 2231722) (-1232 "VOID.spad" 2231010 2231019 2231410 2231415) (-1231 "VIEW.spad" 2228632 2228641 2231000 2231005) (-1230 "VIEWDEF.spad" 2223829 2223838 2228622 2228627) (-1229 "VIEW3D.spad" 2207664 2207673 2223819 2223824) (-1228 "VIEW2D.spad" 2195401 2195410 2207654 2207659) (-1227 "VECTOR.spad" 2194076 2194087 2194327 2194354) (-1226 "VECTOR2.spad" 2192703 2192716 2194066 2194071) (-1225 "VECTCAT.spad" 2190591 2190602 2192659 2192698) (-1224 "VECTCAT.spad" 2188299 2188312 2190369 2190374) (-1223 "VARIABLE.spad" 2188079 2188094 2188289 2188294) (-1222 "UTYPE.spad" 2187713 2187722 2188059 2188074) (-1221 "UTSODETL.spad" 2187006 2187030 2187669 2187674) (-1220 "UTSODE.spad" 2185194 2185214 2186996 2187001) (-1219 "UTS.spad" 2179983 2180011 2183661 2183758) (-1218 "UTSCAT.spad" 2177434 2177450 2179881 2179978) (-1217 "UTSCAT.spad" 2174529 2174547 2176978 2176983) (-1216 "UTS2.spad" 2174122 2174157 2174519 2174524) (-1215 "URAGG.spad" 2168744 2168755 2174102 2174117) (-1214 "URAGG.spad" 2163340 2163353 2168700 2168705) (-1213 "UPXSSING.spad" 2160983 2161009 2162421 2162554) (-1212 "UPXS.spad" 2158010 2158038 2159115 2159264) (-1211 "UPXSCONS.spad" 2155767 2155787 2156142 2156291) (-1210 "UPXSCCA.spad" 2154225 2154245 2155613 2155762) (-1209 "UPXSCCA.spad" 2152825 2152847 2154215 2154220) (-1208 "UPXSCAT.spad" 2151406 2151422 2152671 2152820) (-1207 "UPXS2.spad" 2150947 2151000 2151396 2151401) (-1206 "UPSQFREE.spad" 2149359 2149373 2150937 2150942) (-1205 "UPSCAT.spad" 2146952 2146976 2149257 2149354) (-1204 "UPSCAT.spad" 2144251 2144277 2146558 2146563) (-1203 "UPOLYC.spad" 2139229 2139240 2144093 2144246) (-1202 "UPOLYC.spad" 2134099 2134112 2138965 2138970) (-1201 "UPOLYC2.spad" 2133568 2133587 2134089 2134094) (-1200 "UP.spad" 2130610 2130625 2131118 2131271) (-1199 "UPMP.spad" 2129500 2129513 2130600 2130605) (-1198 "UPDIVP.spad" 2129063 2129077 2129490 2129495) (-1197 "UPDECOMP.spad" 2127300 2127314 2129053 2129058) (-1196 "UPCDEN.spad" 2126507 2126523 2127290 2127295) (-1195 "UP2.spad" 2125869 2125890 2126497 2126502) (-1194 "UNISEG.spad" 2125222 2125233 2125788 2125793) (-1193 "UNISEG2.spad" 2124715 2124728 2125178 2125183) (-1192 "UNIFACT.spad" 2123816 2123828 2124705 2124710) (-1191 "ULS.spad" 2114370 2114398 2115463 2115892) (-1190 "ULSCONS.spad" 2108409 2108429 2108781 2108930) (-1189 "ULSCCAT.spad" 2106006 2106026 2108229 2108404) (-1188 "ULSCCAT.spad" 2103737 2103759 2105962 2105967) (-1187 "ULSCAT.spad" 2101953 2101969 2103583 2103732) (-1186 "ULS2.spad" 2101465 2101518 2101943 2101948) (-1185 "UFD.spad" 2100530 2100539 2101391 2101460) (-1184 "UFD.spad" 2099657 2099668 2100520 2100525) (-1183 "UDVO.spad" 2098504 2098513 2099647 2099652) (-1182 "UDPO.spad" 2095931 2095942 2098460 2098465) (-1181 "TYPE.spad" 2095853 2095862 2095911 2095926) (-1180 "TYPEAST.spad" 2095772 2095781 2095843 2095848) (-1179 "TWOFACT.spad" 2094422 2094437 2095762 2095767) (-1178 "TUPLE.spad" 2093808 2093819 2094321 2094326) (-1177 "TUBETOOL.spad" 2090645 2090654 2093798 2093803) (-1176 "TUBE.spad" 2089286 2089303 2090635 2090640) (-1175 "TS.spad" 2087875 2087891 2088851 2088948) (-1174 "TSETCAT.spad" 2074990 2075007 2087831 2087870) (-1173 "TSETCAT.spad" 2062103 2062122 2074946 2074951) (-1172 "TRMANIP.spad" 2056469 2056486 2061809 2061814) (-1171 "TRIMAT.spad" 2055428 2055453 2056459 2056464) (-1170 "TRIGMNIP.spad" 2053945 2053962 2055418 2055423) (-1169 "TRIGCAT.spad" 2053457 2053466 2053935 2053940) (-1168 "TRIGCAT.spad" 2052967 2052978 2053447 2053452) (-1167 "TREE.spad" 2051538 2051549 2052574 2052601) (-1166 "TRANFUN.spad" 2051369 2051378 2051528 2051533) (-1165 "TRANFUN.spad" 2051198 2051209 2051359 2051364) (-1164 "TOPSP.spad" 2050872 2050881 2051188 2051193) (-1163 "TOOLSIGN.spad" 2050535 2050546 2050862 2050867) (-1162 "TEXTFILE.spad" 2049092 2049101 2050525 2050530) (-1161 "TEX.spad" 2046109 2046118 2049082 2049087) (-1160 "TEX1.spad" 2045665 2045676 2046099 2046104) (-1159 "TEMUTL.spad" 2045220 2045229 2045655 2045660) (-1158 "TBCMPPK.spad" 2043313 2043336 2045210 2045215) (-1157 "TBAGG.spad" 2042337 2042360 2043281 2043308) (-1156 "TBAGG.spad" 2041381 2041406 2042327 2042332) (-1155 "TANEXP.spad" 2040757 2040768 2041371 2041376) (-1154 "TABLE.spad" 2039168 2039191 2039438 2039465) (-1153 "TABLEAU.spad" 2038649 2038660 2039158 2039163) (-1152 "TABLBUMP.spad" 2035432 2035443 2038639 2038644) (-1151 "SYSTEM.spad" 2034706 2034715 2035422 2035427) (-1150 "SYSSOLP.spad" 2032179 2032190 2034696 2034701) (-1149 "SYNTAX.spad" 2028371 2028380 2032169 2032174) (-1148 "SYMTAB.spad" 2026427 2026436 2028361 2028366) (-1147 "SYMS.spad" 2022412 2022421 2026417 2026422) (-1146 "SYMPOLY.spad" 2021419 2021430 2021501 2021628) (-1145 "SYMFUNC.spad" 2020894 2020905 2021409 2021414) (-1144 "SYMBOL.spad" 2018230 2018239 2020884 2020889) (-1143 "SWITCH.spad" 2014987 2014996 2018220 2018225) (-1142 "SUTS.spad" 2011886 2011914 2013454 2013551) (-1141 "SUPXS.spad" 2008900 2008928 2010018 2010167) (-1140 "SUP.spad" 2005669 2005680 2006450 2006603) (-1139 "SUPFRACF.spad" 2004774 2004792 2005659 2005664) (-1138 "SUP2.spad" 2004164 2004177 2004764 2004769) (-1137 "SUMRF.spad" 2003130 2003141 2004154 2004159) (-1136 "SUMFS.spad" 2002763 2002780 2003120 2003125) (-1135 "SULS.spad" 1993304 1993332 1994410 1994839) (-1134 "SUCHTAST.spad" 1993073 1993082 1993294 1993299) (-1133 "SUCH.spad" 1992753 1992768 1993063 1993068) (-1132 "SUBSPACE.spad" 1984760 1984775 1992743 1992748) (-1131 "SUBRESP.spad" 1983920 1983934 1984716 1984721) (-1130 "STTF.spad" 1980019 1980035 1983910 1983915) (-1129 "STTFNC.spad" 1976487 1976503 1980009 1980014) (-1128 "STTAYLOR.spad" 1968885 1968896 1976368 1976373) (-1127 "STRTBL.spad" 1967390 1967407 1967539 1967566) (-1126 "STRING.spad" 1966799 1966808 1966813 1966840) (-1125 "STRICAT.spad" 1966575 1966584 1966755 1966794) (-1124 "STREAM.spad" 1963343 1963354 1966100 1966115) (-1123 "STREAM3.spad" 1962888 1962903 1963333 1963338) (-1122 "STREAM2.spad" 1961956 1961969 1962878 1962883) (-1121 "STREAM1.spad" 1961660 1961671 1961946 1961951) (-1120 "STINPROD.spad" 1960566 1960582 1961650 1961655) (-1119 "STEP.spad" 1959767 1959776 1960556 1960561) (-1118 "STBL.spad" 1958293 1958321 1958460 1958475) (-1117 "STAGG.spad" 1957358 1957369 1958273 1958288) (-1116 "STAGG.spad" 1956431 1956444 1957348 1957353) (-1115 "STACK.spad" 1955782 1955793 1956038 1956065) (-1114 "SREGSET.spad" 1953486 1953503 1955428 1955455) (-1113 "SRDCMPK.spad" 1952031 1952051 1953476 1953481) (-1112 "SRAGG.spad" 1947116 1947125 1951987 1952026) (-1111 "SRAGG.spad" 1942233 1942244 1947106 1947111) (-1110 "SQMATRIX.spad" 1939849 1939867 1940765 1940852) (-1109 "SPLTREE.spad" 1934401 1934414 1939285 1939312) (-1108 "SPLNODE.spad" 1930989 1931002 1934391 1934396) (-1107 "SPFCAT.spad" 1929766 1929775 1930979 1930984) (-1106 "SPECOUT.spad" 1928316 1928325 1929756 1929761) (-1105 "SPADXPT.spad" 1920445 1920454 1928296 1928311) (-1104 "spad-parser.spad" 1919910 1919919 1920435 1920440) (-1103 "SPADAST.spad" 1919611 1919620 1919900 1919905) (-1102 "SPACEC.spad" 1903624 1903635 1919601 1919606) (-1101 "SPACE3.spad" 1903400 1903411 1903614 1903619) (-1100 "SORTPAK.spad" 1902945 1902958 1903356 1903361) (-1099 "SOLVETRA.spad" 1900702 1900713 1902935 1902940) (-1098 "SOLVESER.spad" 1899222 1899233 1900692 1900697) (-1097 "SOLVERAD.spad" 1895232 1895243 1899212 1899217) (-1096 "SOLVEFOR.spad" 1893652 1893670 1895222 1895227) (-1095 "SNTSCAT.spad" 1893240 1893257 1893608 1893647) (-1094 "SMTS.spad" 1891500 1891526 1892805 1892902) (-1093 "SMP.spad" 1888939 1888959 1889329 1889456) (-1092 "SMITH.spad" 1887782 1887807 1888929 1888934) (-1091 "SMATCAT.spad" 1885880 1885910 1887714 1887777) (-1090 "SMATCAT.spad" 1883922 1883954 1885758 1885763) (-1089 "SKAGG.spad" 1882871 1882882 1883878 1883917) (-1088 "SINT.spad" 1881179 1881188 1882737 1882866) (-1087 "SIMPAN.spad" 1880907 1880916 1881169 1881174) (-1086 "SIG.spad" 1880235 1880244 1880897 1880902) (-1085 "SIGNRF.spad" 1879343 1879354 1880225 1880230) (-1084 "SIGNEF.spad" 1878612 1878629 1879333 1879338) (-1083 "SIGAST.spad" 1877993 1878002 1878602 1878607) (-1082 "SHP.spad" 1875911 1875926 1877949 1877954) (-1081 "SHDP.spad" 1866896 1866923 1867405 1867536) (-1080 "SGROUP.spad" 1866504 1866513 1866886 1866891) (-1079 "SGROUP.spad" 1866110 1866121 1866494 1866499) (-1078 "SGCF.spad" 1858991 1859000 1866100 1866105) (-1077 "SFRTCAT.spad" 1857907 1857924 1858947 1858986) (-1076 "SFRGCD.spad" 1856970 1856990 1857897 1857902) (-1075 "SFQCMPK.spad" 1851607 1851627 1856960 1856965) (-1074 "SFORT.spad" 1851042 1851056 1851597 1851602) (-1073 "SEXOF.spad" 1850885 1850925 1851032 1851037) (-1072 "SEX.spad" 1850777 1850786 1850875 1850880) (-1071 "SEXCAT.spad" 1847881 1847921 1850767 1850772) (-1070 "SET.spad" 1846181 1846192 1847302 1847341) (-1069 "SETMN.spad" 1844615 1844632 1846171 1846176) (-1068 "SETCAT.spad" 1844100 1844109 1844605 1844610) (-1067 "SETCAT.spad" 1843583 1843594 1844090 1844095) (-1066 "SETAGG.spad" 1840092 1840103 1843551 1843578) (-1065 "SETAGG.spad" 1836621 1836634 1840082 1840087) (-1064 "SEQAST.spad" 1836324 1836333 1836611 1836616) (-1063 "SEGXCAT.spad" 1835436 1835449 1836304 1836319) (-1062 "SEG.spad" 1835249 1835260 1835355 1835360) (-1061 "SEGCAT.spad" 1834068 1834079 1835229 1835244) (-1060 "SEGBIND.spad" 1833140 1833151 1834023 1834028) (-1059 "SEGBIND2.spad" 1832836 1832849 1833130 1833135) (-1058 "SEGAST.spad" 1832550 1832559 1832826 1832831) (-1057 "SEG2.spad" 1831975 1831988 1832506 1832511) (-1056 "SDVAR.spad" 1831251 1831262 1831965 1831970) (-1055 "SDPOL.spad" 1828641 1828652 1828932 1829059) (-1054 "SCPKG.spad" 1826720 1826731 1828631 1828636) (-1053 "SCOPE.spad" 1825865 1825874 1826710 1826715) (-1052 "SCACHE.spad" 1824547 1824558 1825855 1825860) (-1051 "SASTCAT.spad" 1824456 1824465 1824537 1824542) (-1050 "SAOS.spad" 1824328 1824337 1824446 1824451) (-1049 "SAERFFC.spad" 1824041 1824061 1824318 1824323) (-1048 "SAE.spad" 1822216 1822232 1822827 1822962) (-1047 "SAEFACT.spad" 1821917 1821937 1822206 1822211) (-1046 "RURPK.spad" 1819558 1819574 1821907 1821912) (-1045 "RULESET.spad" 1818999 1819023 1819548 1819553) (-1044 "RULE.spad" 1817203 1817227 1818989 1818994) (-1043 "RULECOLD.spad" 1817055 1817068 1817193 1817198) (-1042 "RSTRCAST.spad" 1816772 1816781 1817045 1817050) (-1041 "RSETGCD.spad" 1813150 1813170 1816762 1816767) (-1040 "RSETCAT.spad" 1802922 1802939 1813106 1813145) (-1039 "RSETCAT.spad" 1792726 1792745 1802912 1802917) (-1038 "RSDCMPK.spad" 1791178 1791198 1792716 1792721) (-1037 "RRCC.spad" 1789562 1789592 1791168 1791173) (-1036 "RRCC.spad" 1787944 1787976 1789552 1789557) (-1035 "RPTAST.spad" 1787646 1787655 1787934 1787939) (-1034 "RPOLCAT.spad" 1767006 1767021 1787514 1787641) (-1033 "RPOLCAT.spad" 1746080 1746097 1766590 1766595) (-1032 "ROUTINE.spad" 1741943 1741952 1744727 1744754) (-1031 "ROMAN.spad" 1741175 1741184 1741809 1741938) (-1030 "ROIRC.spad" 1740255 1740287 1741165 1741170) (-1029 "RNS.spad" 1739158 1739167 1740157 1740250) (-1028 "RNS.spad" 1738147 1738158 1739148 1739153) (-1027 "RNG.spad" 1737882 1737891 1738137 1738142) (-1026 "RMODULE.spad" 1737520 1737531 1737872 1737877) (-1025 "RMCAT2.spad" 1736928 1736985 1737510 1737515) (-1024 "RMATRIX.spad" 1735607 1735626 1736095 1736134) (-1023 "RMATCAT.spad" 1731128 1731159 1735551 1735602) (-1022 "RMATCAT.spad" 1726551 1726584 1730976 1730981) (-1021 "RINTERP.spad" 1726439 1726459 1726541 1726546) (-1020 "RING.spad" 1725796 1725805 1726419 1726434) (-1019 "RING.spad" 1725161 1725172 1725786 1725791) (-1018 "RIDIST.spad" 1724545 1724554 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126005 130523 130528) (-113 "BOP1.spad" 123383 123393 125953 125958) (-112 "BOOLEAN.spad" 122707 122715 123373 123378) (-111 "BMODULE.spad" 122419 122431 122675 122702) (-110 "BITS.spad" 121838 121846 122055 122082) (-109 "BINFILE.spad" 121181 121189 121828 121833) (-108 "BINDING.spad" 120600 120608 121171 121176) (-107 "BINARY.spad" 118491 118499 119068 119161) (-106 "BGAGG.spad" 117676 117686 118459 118486) (-105 "BGAGG.spad" 116881 116893 117666 117671) (-104 "BFUNCT.spad" 116445 116453 116861 116876) (-103 "BEZOUT.spad" 115579 115606 116395 116400) (-102 "BBTREE.spad" 112398 112408 115186 115213) (-101 "BASTYPE.spad" 112070 112078 112388 112393) (-100 "BASTYPE.spad" 111740 111750 112060 112065) (-99 "BALFACT.spad" 111180 111192 111730 111735) (-98 "AUTOMOR.spad" 110627 110636 111160 111175) (-97 "ATTREG.spad" 107346 107353 110379 110622) (-96 "ATTRBUT.spad" 103369 103376 107326 107341) (-95 "ATTRAST.spad" 103086 103093 103359 103364) (-94 "ATRIG.spad" 102556 102563 103076 103081) (-93 "ATRIG.spad" 102024 102033 102546 102551) (-92 "ASTCAT.spad" 101928 101935 102014 102019) (-91 "ASTCAT.spad" 101830 101839 101918 101923) (-90 "ASTACK.spad" 101163 101172 101437 101464) (-89 "ASSOCEQ.spad" 99963 99974 101119 101124) (-88 "ASP9.spad" 99044 99057 99953 99958) (-87 "ASP8.spad" 98087 98100 99034 99039) (-86 "ASP80.spad" 97409 97422 98077 98082) (-85 "ASP7.spad" 96569 96582 97399 97404) (-84 "ASP78.spad" 96020 96033 96559 96564) (-83 "ASP77.spad" 95389 95402 96010 96015) (-82 "ASP74.spad" 94481 94494 95379 95384) (-81 "ASP73.spad" 93752 93765 94471 94476) (-80 "ASP6.spad" 92384 92397 93742 93747) (-79 "ASP55.spad" 90893 90906 92374 92379) (-78 "ASP50.spad" 88710 88723 90883 90888) (-77 "ASP4.spad" 88005 88018 88700 88705) (-76 "ASP49.spad" 87004 87017 87995 88000) (-75 "ASP42.spad" 85411 85450 86994 86999) (-74 "ASP41.spad" 83990 84029 85401 85406) (-73 "ASP35.spad" 82978 82991 83980 83985) (-72 "ASP34.spad" 82279 82292 82968 82973) (-71 "ASP33.spad" 81839 81852 82269 82274) (-70 "ASP31.spad" 80979 80992 81829 81834) (-69 "ASP30.spad" 79871 79884 80969 80974) (-68 "ASP29.spad" 79337 79350 79861 79866) (-67 "ASP28.spad" 70610 70623 79327 79332) (-66 "ASP27.spad" 69507 69520 70600 70605) (-65 "ASP24.spad" 68594 68607 69497 69502) (-64 "ASP20.spad" 67810 67823 68584 68589) (-63 "ASP1.spad" 67191 67204 67800 67805) (-62 "ASP19.spad" 61877 61890 67181 67186) (-61 "ASP12.spad" 61291 61304 61867 61872) (-60 "ASP10.spad" 60562 60575 61281 61286) (-59 "ARRAY2.spad" 59922 59931 60169 60196) (-58 "ARRAY1.spad" 58757 58766 59105 59132) (-57 "ARRAY12.spad" 57426 57437 58747 58752) (-56 "ARR2CAT.spad" 53076 53097 57382 57421) (-55 "ARR2CAT.spad" 48758 48781 53066 53071) (-54 "APPRULE.spad" 48002 48024 48748 48753) (-53 "APPLYORE.spad" 47617 47630 47992 47997) (-52 "ANY.spad" 45959 45966 47607 47612) (-51 "ANY1.spad" 45030 45039 45949 45954) (-50 "ANTISYM.spad" 43469 43485 45010 45025) (-49 "ANON.spad" 43166 43173 43459 43464) (-48 "AN.spad" 41467 41474 42982 43075) (-47 "AMR.spad" 39646 39657 41365 41462) (-46 "AMR.spad" 37662 37675 39383 39388) (-45 "ALIST.spad" 35074 35095 35424 35451) (-44 "ALGSC.spad" 34197 34223 34946 34999) (-43 "ALGPKG.spad" 29906 29917 34153 34158) (-42 "ALGMFACT.spad" 29095 29109 29896 29901) (-41 "ALGMANIP.spad" 26515 26530 28892 28897) (-40 "ALGFF.spad" 24830 24857 25047 25203) (-39 "ALGFACT.spad" 23951 23961 24820 24825) (-38 "ALGEBRA.spad" 23682 23691 23907 23946) (-37 "ALGEBRA.spad" 23445 23456 23672 23677) (-36 "ALAGG.spad" 22943 22964 23401 23440) (-35 "AHYP.spad" 22324 22331 22933 22938) (-34 "AGG.spad" 20623 20630 22304 22319) (-33 "AGG.spad" 18896 18905 20579 20584) (-32 "AF.spad" 17321 17336 18831 18836) (-31 "ADDAST.spad" 16999 17006 17311 17316) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file
+((-3 NIL 2267735 2267740 2267745 2267750) (-2 NIL 2267715 2267720 2267725 2267730) (-1 NIL 2267695 2267700 2267705 2267710) (0 NIL 2267675 2267680 2267685 2267690) (-1256 "ZMOD.spad" 2267484 2267497 2267613 2267670) (-1255 "ZLINDEP.spad" 2266528 2266539 2267474 2267479) (-1254 "ZDSOLVE.spad" 2256377 2256399 2266518 2266523) (-1253 "YSTREAM.spad" 2255870 2255881 2256367 2256372) (-1252 "XRPOLY.spad" 2255090 2255110 2255726 2255795) (-1251 "XPR.spad" 2252819 2252832 2254808 2254907) (-1250 "XPOLY.spad" 2252374 2252385 2252675 2252744) (-1249 "XPOLYC.spad" 2251691 2251707 2252300 2252369) (-1248 "XPBWPOLY.spad" 2250128 2250148 2251471 2251540) (-1247 "XF.spad" 2248589 2248604 2250030 2250123) (-1246 "XF.spad" 2247030 2247047 2248473 2248478) (-1245 "XFALG.spad" 2244054 2244070 2246956 2247025) (-1244 "XEXPPKG.spad" 2243305 2243331 2244044 2244049) (-1243 "XDPOLY.spad" 2242919 2242935 2243161 2243230) (-1242 "XALG.spad" 2242517 2242528 2242875 2242914) (-1241 "WUTSET.spad" 2238356 2238373 2242163 2242190) (-1240 "WP.spad" 2237370 2237414 2238214 2238281) (-1239 "WHILEAST.spad" 2237168 2237177 2237360 2237365) (-1238 "WHEREAST.spad" 2236839 2236848 2237158 2237163) (-1237 "WFFINTBS.spad" 2234402 2234424 2236829 2236834) (-1236 "WEIER.spad" 2232616 2232627 2234392 2234397) (-1235 "VSPACE.spad" 2232289 2232300 2232584 2232611) (-1234 "VSPACE.spad" 2231982 2231995 2232279 2232284) (-1233 "VOID.spad" 2231572 2231581 2231972 2231977) (-1232 "VIEW.spad" 2229194 2229203 2231562 2231567) (-1231 "VIEWDEF.spad" 2224391 2224400 2229184 2229189) (-1230 "VIEW3D.spad" 2208226 2208235 2224381 2224386) (-1229 "VIEW2D.spad" 2195963 2195972 2208216 2208221) (-1228 "VECTOR.spad" 2194638 2194649 2194889 2194916) (-1227 "VECTOR2.spad" 2193265 2193278 2194628 2194633) (-1226 "VECTCAT.spad" 2191153 2191164 2193221 2193260) (-1225 "VECTCAT.spad" 2188861 2188874 2190931 2190936) (-1224 "VARIABLE.spad" 2188641 2188656 2188851 2188856) (-1223 "UTYPE.spad" 2188275 2188284 2188621 2188636) (-1222 "UTSODETL.spad" 2187568 2187592 2188231 2188236) (-1221 "UTSODE.spad" 2185756 2185776 2187558 2187563) (-1220 "UTS.spad" 2180545 2180573 2184223 2184320) (-1219 "UTSCAT.spad" 2177996 2178012 2180443 2180540) (-1218 "UTSCAT.spad" 2175091 2175109 2177540 2177545) (-1217 "UTS2.spad" 2174684 2174719 2175081 2175086) (-1216 "URAGG.spad" 2169306 2169317 2174664 2174679) (-1215 "URAGG.spad" 2163902 2163915 2169262 2169267) (-1214 "UPXSSING.spad" 2161545 2161571 2162983 2163116) (-1213 "UPXS.spad" 2158572 2158600 2159677 2159826) (-1212 "UPXSCONS.spad" 2156329 2156349 2156704 2156853) (-1211 "UPXSCCA.spad" 2154787 2154807 2156175 2156324) (-1210 "UPXSCCA.spad" 2153387 2153409 2154777 2154782) (-1209 "UPXSCAT.spad" 2151968 2151984 2153233 2153382) (-1208 "UPXS2.spad" 2151509 2151562 2151958 2151963) (-1207 "UPSQFREE.spad" 2149921 2149935 2151499 2151504) (-1206 "UPSCAT.spad" 2147514 2147538 2149819 2149916) (-1205 "UPSCAT.spad" 2144813 2144839 2147120 2147125) (-1204 "UPOLYC.spad" 2139791 2139802 2144655 2144808) (-1203 "UPOLYC.spad" 2134661 2134674 2139527 2139532) (-1202 "UPOLYC2.spad" 2134130 2134149 2134651 2134656) (-1201 "UP.spad" 2131172 2131187 2131680 2131833) (-1200 "UPMP.spad" 2130062 2130075 2131162 2131167) (-1199 "UPDIVP.spad" 2129625 2129639 2130052 2130057) (-1198 "UPDECOMP.spad" 2127862 2127876 2129615 2129620) (-1197 "UPCDEN.spad" 2127069 2127085 2127852 2127857) (-1196 "UP2.spad" 2126431 2126452 2127059 2127064) (-1195 "UNISEG.spad" 2125784 2125795 2126350 2126355) (-1194 "UNISEG2.spad" 2125277 2125290 2125740 2125745) (-1193 "UNIFACT.spad" 2124378 2124390 2125267 2125272) (-1192 "ULS.spad" 2114932 2114960 2116025 2116454) (-1191 "ULSCONS.spad" 2108971 2108991 2109343 2109492) (-1190 "ULSCCAT.spad" 2106568 2106588 2108791 2108966) (-1189 "ULSCCAT.spad" 2104299 2104321 2106524 2106529) (-1188 "ULSCAT.spad" 2102515 2102531 2104145 2104294) (-1187 "ULS2.spad" 2102027 2102080 2102505 2102510) (-1186 "UFD.spad" 2101092 2101101 2101953 2102022) (-1185 "UFD.spad" 2100219 2100230 2101082 2101087) (-1184 "UDVO.spad" 2099066 2099075 2100209 2100214) (-1183 "UDPO.spad" 2096493 2096504 2099022 2099027) (-1182 "TYPE.spad" 2096415 2096424 2096473 2096488) (-1181 "TYPEAST.spad" 2096334 2096343 2096405 2096410) (-1180 "TWOFACT.spad" 2094984 2094999 2096324 2096329) (-1179 "TUPLE.spad" 2094370 2094381 2094883 2094888) (-1178 "TUBETOOL.spad" 2091207 2091216 2094360 2094365) (-1177 "TUBE.spad" 2089848 2089865 2091197 2091202) (-1176 "TS.spad" 2088437 2088453 2089413 2089510) (-1175 "TSETCAT.spad" 2075552 2075569 2088393 2088432) (-1174 "TSETCAT.spad" 2062665 2062684 2075508 2075513) (-1173 "TRMANIP.spad" 2057031 2057048 2062371 2062376) (-1172 "TRIMAT.spad" 2055990 2056015 2057021 2057026) (-1171 "TRIGMNIP.spad" 2054507 2054524 2055980 2055985) (-1170 "TRIGCAT.spad" 2054019 2054028 2054497 2054502) (-1169 "TRIGCAT.spad" 2053529 2053540 2054009 2054014) (-1168 "TREE.spad" 2052100 2052111 2053136 2053163) (-1167 "TRANFUN.spad" 2051931 2051940 2052090 2052095) (-1166 "TRANFUN.spad" 2051760 2051771 2051921 2051926) (-1165 "TOPSP.spad" 2051434 2051443 2051750 2051755) (-1164 "TOOLSIGN.spad" 2051097 2051108 2051424 2051429) (-1163 "TEXTFILE.spad" 2049654 2049663 2051087 2051092) (-1162 "TEX.spad" 2046671 2046680 2049644 2049649) (-1161 "TEX1.spad" 2046227 2046238 2046661 2046666) (-1160 "TEMUTL.spad" 2045782 2045791 2046217 2046222) (-1159 "TBCMPPK.spad" 2043875 2043898 2045772 2045777) (-1158 "TBAGG.spad" 2042899 2042922 2043843 2043870) (-1157 "TBAGG.spad" 2041943 2041968 2042889 2042894) (-1156 "TANEXP.spad" 2041319 2041330 2041933 2041938) (-1155 "TABLE.spad" 2039730 2039753 2040000 2040027) (-1154 "TABLEAU.spad" 2039211 2039222 2039720 2039725) (-1153 "TABLBUMP.spad" 2035994 2036005 2039201 2039206) (-1152 "SYSTEM.spad" 2035268 2035277 2035984 2035989) (-1151 "SYSSOLP.spad" 2032741 2032752 2035258 2035263) (-1150 "SYNTAX.spad" 2028933 2028942 2032731 2032736) (-1149 "SYMTAB.spad" 2026989 2026998 2028923 2028928) (-1148 "SYMS.spad" 2022974 2022983 2026979 2026984) (-1147 "SYMPOLY.spad" 2021981 2021992 2022063 2022190) (-1146 "SYMFUNC.spad" 2021456 2021467 2021971 2021976) (-1145 "SYMBOL.spad" 2018792 2018801 2021446 2021451) (-1144 "SWITCH.spad" 2015549 2015558 2018782 2018787) (-1143 "SUTS.spad" 2012448 2012476 2014016 2014113) (-1142 "SUPXS.spad" 2009462 2009490 2010580 2010729) (-1141 "SUP.spad" 2006231 2006242 2007012 2007165) (-1140 "SUPFRACF.spad" 2005336 2005354 2006221 2006226) (-1139 "SUP2.spad" 2004726 2004739 2005326 2005331) (-1138 "SUMRF.spad" 2003692 2003703 2004716 2004721) (-1137 "SUMFS.spad" 2003325 2003342 2003682 2003687) (-1136 "SULS.spad" 1993866 1993894 1994972 1995401) (-1135 "SUCHTAST.spad" 1993635 1993644 1993856 1993861) (-1134 "SUCH.spad" 1993315 1993330 1993625 1993630) (-1133 "SUBSPACE.spad" 1985322 1985337 1993305 1993310) (-1132 "SUBRESP.spad" 1984482 1984496 1985278 1985283) (-1131 "STTF.spad" 1980581 1980597 1984472 1984477) (-1130 "STTFNC.spad" 1977049 1977065 1980571 1980576) (-1129 "STTAYLOR.spad" 1969447 1969458 1976930 1976935) (-1128 "STRTBL.spad" 1967952 1967969 1968101 1968128) (-1127 "STRING.spad" 1967361 1967370 1967375 1967402) (-1126 "STRICAT.spad" 1967137 1967146 1967317 1967356) (-1125 "STREAM.spad" 1963905 1963916 1966662 1966677) (-1124 "STREAM3.spad" 1963450 1963465 1963895 1963900) (-1123 "STREAM2.spad" 1962518 1962531 1963440 1963445) (-1122 "STREAM1.spad" 1962222 1962233 1962508 1962513) (-1121 "STINPROD.spad" 1961128 1961144 1962212 1962217) (-1120 "STEP.spad" 1960329 1960338 1961118 1961123) (-1119 "STBL.spad" 1958855 1958883 1959022 1959037) (-1118 "STAGG.spad" 1957920 1957931 1958835 1958850) (-1117 "STAGG.spad" 1956993 1957006 1957910 1957915) (-1116 "STACK.spad" 1956344 1956355 1956600 1956627) (-1115 "SREGSET.spad" 1954048 1954065 1955990 1956017) (-1114 "SRDCMPK.spad" 1952593 1952613 1954038 1954043) (-1113 "SRAGG.spad" 1947678 1947687 1952549 1952588) (-1112 "SRAGG.spad" 1942795 1942806 1947668 1947673) (-1111 "SQMATRIX.spad" 1940411 1940429 1941327 1941414) (-1110 "SPLTREE.spad" 1934963 1934976 1939847 1939874) (-1109 "SPLNODE.spad" 1931551 1931564 1934953 1934958) (-1108 "SPFCAT.spad" 1930328 1930337 1931541 1931546) (-1107 "SPECOUT.spad" 1928878 1928887 1930318 1930323) (-1106 "SPADXPT.spad" 1921007 1921016 1928858 1928873) (-1105 "spad-parser.spad" 1920472 1920481 1920997 1921002) (-1104 "SPADAST.spad" 1920173 1920182 1920462 1920467) (-1103 "SPACEC.spad" 1904186 1904197 1920163 1920168) (-1102 "SPACE3.spad" 1903962 1903973 1904176 1904181) (-1101 "SORTPAK.spad" 1903507 1903520 1903918 1903923) (-1100 "SOLVETRA.spad" 1901264 1901275 1903497 1903502) (-1099 "SOLVESER.spad" 1899784 1899795 1901254 1901259) (-1098 "SOLVERAD.spad" 1895794 1895805 1899774 1899779) (-1097 "SOLVEFOR.spad" 1894214 1894232 1895784 1895789) (-1096 "SNTSCAT.spad" 1893802 1893819 1894170 1894209) (-1095 "SMTS.spad" 1892062 1892088 1893367 1893464) (-1094 "SMP.spad" 1889501 1889521 1889891 1890018) (-1093 "SMITH.spad" 1888344 1888369 1889491 1889496) (-1092 "SMATCAT.spad" 1886442 1886472 1888276 1888339) (-1091 "SMATCAT.spad" 1884484 1884516 1886320 1886325) (-1090 "SKAGG.spad" 1883433 1883444 1884440 1884479) (-1089 "SINT.spad" 1881741 1881750 1883299 1883428) (-1088 "SIMPAN.spad" 1881469 1881478 1881731 1881736) (-1087 "SIG.spad" 1880797 1880806 1881459 1881464) (-1086 "SIGNRF.spad" 1879905 1879916 1880787 1880792) (-1085 "SIGNEF.spad" 1879174 1879191 1879895 1879900) (-1084 "SIGAST.spad" 1878555 1878564 1879164 1879169) (-1083 "SHP.spad" 1876473 1876488 1878511 1878516) (-1082 "SHDP.spad" 1867458 1867485 1867967 1868098) (-1081 "SGROUP.spad" 1867066 1867075 1867448 1867453) (-1080 "SGROUP.spad" 1866672 1866683 1867056 1867061) (-1079 "SGCF.spad" 1859553 1859562 1866662 1866667) (-1078 "SFRTCAT.spad" 1858469 1858486 1859509 1859548) (-1077 "SFRGCD.spad" 1857532 1857552 1858459 1858464) (-1076 "SFQCMPK.spad" 1852169 1852189 1857522 1857527) (-1075 "SFORT.spad" 1851604 1851618 1852159 1852164) (-1074 "SEXOF.spad" 1851447 1851487 1851594 1851599) (-1073 "SEX.spad" 1851339 1851348 1851437 1851442) (-1072 "SEXCAT.spad" 1848443 1848483 1851329 1851334) (-1071 "SET.spad" 1846743 1846754 1847864 1847903) (-1070 "SETMN.spad" 1845177 1845194 1846733 1846738) (-1069 "SETCAT.spad" 1844662 1844671 1845167 1845172) (-1068 "SETCAT.spad" 1844145 1844156 1844652 1844657) (-1067 "SETAGG.spad" 1840654 1840665 1844113 1844140) (-1066 "SETAGG.spad" 1837183 1837196 1840644 1840649) (-1065 "SEQAST.spad" 1836886 1836895 1837173 1837178) (-1064 "SEGXCAT.spad" 1835998 1836011 1836866 1836881) (-1063 "SEG.spad" 1835811 1835822 1835917 1835922) (-1062 "SEGCAT.spad" 1834630 1834641 1835791 1835806) (-1061 "SEGBIND.spad" 1833702 1833713 1834585 1834590) (-1060 "SEGBIND2.spad" 1833398 1833411 1833692 1833697) (-1059 "SEGAST.spad" 1833112 1833121 1833388 1833393) (-1058 "SEG2.spad" 1832537 1832550 1833068 1833073) (-1057 "SDVAR.spad" 1831813 1831824 1832527 1832532) (-1056 "SDPOL.spad" 1829203 1829214 1829494 1829621) (-1055 "SCPKG.spad" 1827282 1827293 1829193 1829198) (-1054 "SCOPE.spad" 1826427 1826436 1827272 1827277) (-1053 "SCACHE.spad" 1825109 1825120 1826417 1826422) (-1052 "SASTCAT.spad" 1825018 1825027 1825099 1825104) (-1051 "SAOS.spad" 1824890 1824899 1825008 1825013) (-1050 "SAERFFC.spad" 1824603 1824623 1824880 1824885) (-1049 "SAE.spad" 1822778 1822794 1823389 1823524) (-1048 "SAEFACT.spad" 1822479 1822499 1822768 1822773) (-1047 "RURPK.spad" 1820120 1820136 1822469 1822474) (-1046 "RULESET.spad" 1819561 1819585 1820110 1820115) (-1045 "RULE.spad" 1817765 1817789 1819551 1819556) (-1044 "RULECOLD.spad" 1817617 1817630 1817755 1817760) (-1043 "RSTRCAST.spad" 1817334 1817343 1817607 1817612) (-1042 "RSETGCD.spad" 1813712 1813732 1817324 1817329) (-1041 "RSETCAT.spad" 1803484 1803501 1813668 1813707) (-1040 "RSETCAT.spad" 1793288 1793307 1803474 1803479) (-1039 "RSDCMPK.spad" 1791740 1791760 1793278 1793283) (-1038 "RRCC.spad" 1790124 1790154 1791730 1791735) 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1725713 1725718) (-1018 "RGCHAIN.spad" 1723686 1723702 1724592 1724619) (-1017 "RF.spad" 1721300 1721311 1723676 1723681) (-1016 "RFFACTOR.spad" 1720762 1720773 1721290 1721295) (-1015 "RFFACT.spad" 1720497 1720509 1720752 1720757) (-1014 "RFDIST.spad" 1719485 1719494 1720487 1720492) (-1013 "RETSOL.spad" 1718902 1718915 1719475 1719480) (-1012 "RETRACT.spad" 1718251 1718262 1718892 1718897) (-1011 "RETRACT.spad" 1717598 1717611 1718241 1718246) (-1010 "RETAST.spad" 1717410 1717419 1717588 1717593) (-1009 "RESULT.spad" 1715470 1715479 1716057 1716084) (-1008 "RESRING.spad" 1714817 1714864 1715408 1715465) (-1007 "RESLATC.spad" 1714141 1714152 1714807 1714812) (-1006 "REPSQ.spad" 1713870 1713881 1714131 1714136) (-1005 "REP.spad" 1711422 1711431 1713860 1713865) (-1004 "REPDB.spad" 1711127 1711138 1711412 1711417) (-1003 "REP2.spad" 1700699 1700710 1710969 1710974) (-1002 "REP1.spad" 1694689 1694700 1700649 1700654) (-1001 "REGSET.spad" 1692486 1692503 1694335 1694362) (-1000 "REF.spad" 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1037653) (-643 "LSAGG.spad" 1037004 1037016 1037305 1037310) (-642 "LPOLY.spad" 1035958 1035977 1036860 1036929) (-641 "LPEFRAC.spad" 1035215 1035225 1035948 1035953) (-640 "LO.spad" 1034616 1034630 1035149 1035176) (-639 "LOGIC.spad" 1034218 1034226 1034606 1034611) (-638 "LOGIC.spad" 1033818 1033828 1034208 1034213) (-637 "LODOOPS.spad" 1032736 1032748 1033808 1033813) (-636 "LODO.spad" 1032120 1032136 1032416 1032455) (-635 "LODOF.spad" 1031164 1031181 1032077 1032082) (-634 "LODOCAT.spad" 1029822 1029832 1031120 1031159) (-633 "LODOCAT.spad" 1028478 1028490 1029778 1029783) (-632 "LODO2.spad" 1027751 1027763 1028158 1028197) (-631 "LODO1.spad" 1027151 1027161 1027431 1027470) (-630 "LODEEF.spad" 1025923 1025941 1027141 1027146) (-629 "LNAGG.spad" 1021715 1021725 1025903 1025918) (-628 "LNAGG.spad" 1017481 1017493 1021671 1021676) (-627 "LMOPS.spad" 1014217 1014234 1017471 1017476) (-626 "LMODULE.spad" 1013859 1013869 1014207 1014212) (-625 "LMDICT.spad" 1013142 1013152 1013410 1013437) (-624 "LITERAL.spad" 1013048 1013059 1013132 1013137) (-623 "LIST.spad" 1010766 1010776 1012195 1012222) (-622 "LIST3.spad" 1010057 1010071 1010756 1010761) (-621 "LIST2.spad" 1008697 1008709 1010047 1010052) (-620 "LIST2MAP.spad" 1005574 1005586 1008687 1008692) (-619 "LINEXP.spad" 1005006 1005016 1005554 1005569) (-618 "LINDEP.spad" 1003783 1003795 1004918 1004923) (-617 "LIMITRF.spad" 1001697 1001707 1003773 1003778) (-616 "LIMITPS.spad" 1000580 1000593 1001687 1001692) (-615 "LIE.spad" 998594 998606 999870 1000015) (-614 "LIECAT.spad" 998070 998080 998520 998589) (-613 "LIECAT.spad" 997574 997586 998026 998031) (-612 "LIB.spad" 995622 995630 996233 996248) (-611 "LGROBP.spad" 992975 992994 995612 995617) (-610 "LF.spad" 991894 991910 992965 992970) (-609 "LFCAT.spad" 990913 990921 991884 991889) (-608 "LEXTRIPK.spad" 986416 986431 990903 990908) (-607 "LEXP.spad" 984419 984446 986396 986411) (-606 "LETAST.spad" 984118 984126 984409 984414) (-605 "LEADCDET.spad" 982502 982519 984108 984113) (-604 "LAZM3PK.spad" 981206 981228 982492 982497) (-603 "LAUPOL.spad" 979895 979908 980799 980868) (-602 "LAPLACE.spad" 979468 979484 979885 979890) (-601 "LA.spad" 978908 978922 979390 979429) (-600 "LALG.spad" 978684 978694 978888 978903) (-599 "LALG.spad" 978468 978480 978674 978679) (-598 "KTVLOGIC.spad" 977891 977899 978458 978463) (-597 "KOVACIC.spad" 976604 976621 977881 977886) (-596 "KONVERT.spad" 976326 976336 976594 976599) (-595 "KOERCE.spad" 976063 976073 976316 976321) (-594 "KERNEL.spad" 974598 974608 975847 975852) (-593 "KERNEL2.spad" 974301 974313 974588 974593) (-592 "KDAGG.spad" 973392 973414 974269 974296) (-591 "KDAGG.spad" 972503 972527 973382 973387) (-590 "KAFILE.spad" 971466 971482 971701 971728) (-589 "JORDAN.spad" 969293 969305 970756 970901) (-588 "JOINAST.spad" 968987 968995 969283 969288) (-587 "JAVACODE.spad" 968753 968761 968977 968982) (-586 "IXAGG.spad" 966866 966890 968733 968748) (-585 "IXAGG.spad" 964844 964870 966713 966718) (-584 "IVECTOR.spad" 963615 963630 963770 963797) (-583 "ITUPLE.spad" 962760 962770 963605 963610) (-582 "ITRIGMNP.spad" 961571 961590 962750 962755) (-581 "ITFUN3.spad" 961065 961079 961561 961566) (-580 "ITFUN2.spad" 960795 960807 961055 961060) (-579 "ITAYLOR.spad" 958587 958602 960631 960756) (-578 "ISUPS.spad" 950998 951013 957561 957658) (-577 "ISUMP.spad" 950495 950511 950988 950993) (-576 "ISTRING.spad" 949498 949511 949664 949691) (-575 "ISAST.spad" 949217 949225 949488 949493) (-574 "IRURPK.spad" 947930 947949 949207 949212) (-573 "IRSN.spad" 945890 945898 947920 947925) (-572 "IRRF2F.spad" 944365 944375 945846 945851) (-571 "IRREDFFX.spad" 943966 943977 944355 944360) (-570 "IROOT.spad" 942297 942307 943956 943961) (-569 "IR.spad" 940086 940100 942152 942179) (-568 "IR2.spad" 939106 939122 940076 940081) (-567 "IR2F.spad" 938306 938322 939096 939101) (-566 "IPRNTPK.spad" 938066 938074 938296 938301) (-565 "IPF.spad" 937631 937643 937871 937964) (-564 "IPADIC.spad" 937392 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diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index f1560383..7af81219 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
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. -542) 123696) ((-1140 . -47) 123673) ((-348 . -1020) T) ((-345 . -1020) T) ((-474 . -23) 123543) ((-337 . -1020) T) ((-257 . -1020) T) ((-241 . -1020) T) ((-1093 . -47) 123515) ((-117 . -1027) T) ((-1007 . -626) 123489) ((-931 . -34) T) ((-348 . -227) 123468) ((-348 . -237) T) ((-345 . -227) 123447) ((-345 . -237) T) ((-241 . -319) 123404) ((-337 . -227) 123383) ((-337 . -237) T) ((-257 . -319) 123355) ((-257 . -227) 123334) ((-1124 . -149) 123318) ((-244 . -873) 123250) ((-243 . -873) 123182) ((-1050 . -825) T) ((-1194 . -1181) T) ((-407 . -1080) T) ((-1024 . -23) T) ((-883 . -1020) T) ((-315 . -626) 123164) ((-997 . -823) T) ((-1175 . -975) 123130) ((-1141 . -893) 123109) ((-1135 . -893) 123088) ((-883 . -237) T) ((-795 . -356) 123067) ((-378 . -23) T) ((-127 . -1068) 123045) ((-121 . -1068) 123023) ((-883 . -227) T) ((-1135 . -798) NIL) ((-372 . -626) 122988) ((-843 . -696) 122975) ((-1017 . -149) 122940) ((-40 . -170) T) ((-672 . -404) 122922) ((-691 . -302) 122909) ((-812 . 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121767) ((-1227 . -1225) 121751) ((-344 . -395) T) ((-1227 . -1068) 121701) ((-564 . -696) 121688) ((-550 . -696) 121675) ((-486 . -696) 121640) ((-309 . -609) 121619) ((-812 . -705) T) ((-805 . -705) T) ((-623 . -1181) T) ((-1048 . -619) 121567) ((-1140 . -873) 121510) ((-1093 . -873) 121494) ((-640 . -1026) 121478) ((-107 . -619) 121460) ((-474 . -130) 121330) ((-1146 . -1080) T) ((-925 . -47) 121299) ((-603 . -1068) T) ((-640 . -111) 121278) ((-482 . -595) 121244) ((-320 . -281) 121221) ((-473 . -47) 121178) ((-1146 . -23) T) ((-117 . -1068) T) ((-102 . -101) 121156) ((-1239 . -1080) T) ((-1024 . -130) T) ((-997 . -1027) T) ((-797 . -1011) 121140) ((-976 . -703) 121112) ((-1239 . -23) T) ((-677 . -696) 121077) ((-569 . -595) 121059) ((-379 . -1011) 121043) ((-347 . -1027) T) ((-378 . -130) T) ((-317 . -1011) 121027) ((-219 . -859) 121009) ((-977 . -893) T) ((-90 . -34) T) ((-977 . -798) T) ((-887 . -893) T) ((-479 . -1185) T) ((-1161 . -595) 120991) ((-1073 . -1068) T) ((-211 . -1185) T) ((-972 . -302) 120956) ((-219 . -1011) 120916) ((-40 . -283) T) ((-1048 . -21) T) ((-1048 . -25) T) ((-1088 . -806) T) ((-479 . -542) T) ((-352 . -25) T) ((-211 . -542) T) ((-352 . -21) T) ((-346 . -25) T) ((-346 . -21) T) ((-693 . -626) 120876) ((-338 . -25) T) ((-338 . -21) T) ((-107 . -25) T) ((-107 . -21) T) ((-48 . -1027) T) ((-564 . -170) T) ((-550 . -170) T) ((-486 . -170) T) ((-636 . -595) 120858) ((-716 . -715) 120842) ((-329 . -595) 120824) ((-67 . -376) T) ((-67 . -388) T) ((-1070 . -106) 120808) ((-1031 . -859) 120790) ((-925 . -859) 120715) ((-631 . -1080) T) ((-603 . -696) 120702) ((-473 . -859) NIL) ((-1114 . -101) T) ((-1031 . -1011) 120684) ((-96 . -595) 120666) ((-469 . -145) T) ((-925 . -1011) 120546) ((-117 . -696) 120491) ((-631 . -23) T) ((-473 . -1011) 120367) ((-1055 . -596) NIL) ((-1055 . -595) 120349) ((-760 . -596) NIL) ((-760 . -595) 120310) ((-758 . -596) 119944) ((-758 . -595) 119858) ((-1081 . -619) 119764) ((-453 . -595) 119746) ((-446 . -595) 119728) ((-446 . -596) 119589) ((-1008 . -223) 119535) ((-845 . -882) 119514) ((-126 . -34) T) ((-795 . -130) T) ((-627 . -595) 119496) ((-563 . -101) T) ((-348 . -1246) 119480) ((-345 . -1246) 119464) ((-337 . -1246) 119448) ((-127 . -505) 119381) ((-121 . -505) 119314) ((-502 . -770) T) ((-502 . -773) T) ((-501 . -772) T) ((-102 . -302) 119252) ((-216 . -101) 119230) ((-672 . -1068) T) ((-677 . -170) T) ((-845 . -626) 119182) ((-64 . -377) T) ((-268 . -595) 119164) ((-64 . -388) T) ((-925 . -370) 119148) ((-843 . -283) T) ((-50 . -595) 119130) ((-972 . -38) 119078) ((-565 . -595) 119060) ((-473 . -370) 119044) ((-565 . -596) 119026) ((-509 . -595) 119008) ((-883 . -1246) 118995) ((-844 . -1181) T) ((-679 . -444) T) ((-486 . -505) 118961) ((-479 . -356) T) ((-348 . -361) 118940) ((-345 . -361) 118919) ((-337 . -361) 118898) ((-211 . -356) T) ((-693 . -705) T) ((-116 . -444) T) ((-1250 . -1241) 118882) ((-844 . -857) 118859) ((-844 . -859) NIL) ((-937 . -825) 118758) ((-793 . -825) 118709) ((-632 . -634) 118693) ((-1167 . -34) T) ((-169 . -595) 118675) ((-1081 . -21) 118585) ((-1081 . -25) 118436) ((-844 . -1011) 118413) ((-925 . -873) 118394) ((-1200 . -47) 118371) ((-883 . -361) T) ((-58 . -629) 118355) ((-507 . -629) 118339) ((-473 . -873) 118316) ((-70 . -433) T) ((-70 . -388) T) ((-487 . -629) 118300) ((-58 . -366) 118284) ((-603 . -170) T) ((-507 . -366) 118268) ((-487 . -366) 118252) ((-805 . -687) 118236) ((-1140 . -300) 118215) ((-1146 . -130) T) ((-117 . -170) T) ((-1114 . -302) 118153) ((-167 . -1181) T) ((-615 . -723) 118137) ((-589 . -723) 118121) ((-1239 . -130) T) ((-1212 . -893) 118100) ((-1191 . -893) 118079) ((-1191 . -798) NIL) ((-672 . -696) 118029) ((-1190 . -882) 117982) ((-997 . -1068) T) ((-844 . -370) 117959) ((-844 . -331) 117936) ((-878 . -1080) T) ((-167 . -857) 117920) ((-167 . -859) 117845) ((-479 . -1080) T) ((-347 . -1068) T) ((-211 . -1080) T) ((-75 . -433) T) ((-75 . -388) T) ((-167 . -1011) 117741) ((-312 . -825) T) ((-1227 . -505) 117674) ((-1211 . -626) 117571) ((-1190 . -626) 117441) ((-845 . -772) 117420) ((-845 . -769) 117399) ((-845 . -705) T) ((-479 . -23) T) ((-217 . -595) 117381) ((-172 . -444) T) ((-216 . -302) 117319) ((-85 . -433) T) ((-85 . -388) T) ((-211 . -23) T) ((-1251 . -1244) 117298) ((-564 . -283) T) ((-550 . -283) T) ((-655 . -1011) 117282) ((-486 . -283) T) ((-135 . -462) 117237) ((-48 . -1068) T) ((-691 . -225) 117221) ((-844 . -873) NIL) ((-1200 . -859) NIL) ((-862 . -101) T) ((-858 . -101) T) ((-381 . -1068) T) ((-167 . -370) 117205) ((-167 . -331) 117189) ((-1200 . -1011) 117069) ((-830 . -1011) 116965) ((-1110 . -101) T) ((-631 . -130) T) ((-117 . -505) 116873) ((-640 . -770) 116852) ((-640 . -773) 116831) ((-557 . -1011) 116813) ((-287 . -1234) 116783) ((-839 . -101) T) ((-936 . -542) 116762) ((-1175 . -1026) 116645) ((-474 . -619) 116551) ((-877 . -1068) T) ((-997 . -696) 116488) ((-690 . -1026) 116453) ((-598 . -101) T) ((-584 . -34) T) ((-1115 . -1181) T) ((-1175 . -111) 116322) ((-466 . -626) 116219) ((-347 . -696) 116164) ((-167 . -873) 116123) ((-677 . -283) T) ((-672 . -170) T) ((-690 . -111) 116079) ((-1255 . -1027) T) ((-1200 . -370) 116063) ((-411 . -1185) 116041) ((-1086 . -595) 116023) ((-306 . -823) NIL) ((-411 . -542) T) ((-219 . -300) T) ((-1190 . -769) 115976) ((-1190 . -772) 115929) ((-1211 . -705) T) ((-1190 . -705) T) ((-48 . -696) 115894) ((-219 . -995) T) ((-344 . -1234) 115871) ((-1213 . -404) 115837) ((-697 . -705) T) ((-1200 . -873) 115780) ((-112 . -595) 115762) ((-112 . -596) 115744) ((-697 . -465) T) ((-474 . -21) 115654) ((-127 . -481) 115638) ((-121 . -481) 115622) ((-474 . -25) 115473) ((-603 . -283) T) ((-569 . -1026) 115448) ((-430 . -1068) T) ((-1031 . -300) T) ((-117 . -283) T) ((-1072 . -101) T) ((-976 . -101) T) ((-569 . -111) 115416) ((-1110 . -302) 115354) ((-1175 . -1020) T) ((-1031 . -995) T) ((-65 . -1181) T) ((-1024 . -25) T) ((-1024 . -21) T) ((-690 . -1020) T) ((-378 . -21) T) ((-378 . -25) T) ((-672 . -505) NIL) ((-997 . -170) T) ((-690 . -237) T) ((-1031 . -535) T) ((-497 . -101) T) ((-493 . -101) T) ((-347 . -170) T) ((-336 . -595) 115336) ((-387 . -595) 115318) ((-466 . -705) T) ((-1088 . -823) T) ((-865 . -1011) 115286) ((-107 . -825) T) ((-636 . -1026) 115270) ((-479 . -130) T) ((-1213 . -1027) T) ((-211 . -130) T) ((-1124 . -101) 115248) ((-98 . -1068) T) ((-239 . -644) 115232) ((-239 . -629) 115216) ((-636 . -111) 115195) ((-309 . -404) 115179) ((-239 . -366) 115163) ((-1127 . -229) 115110) ((-972 . -225) 115094) ((-73 . -1181) T) ((-48 . -170) T) ((-679 . -380) T) ((-679 . -141) T) ((-1250 . -101) T) ((-1055 . -1026) 114937) ((-257 . -882) 114916) ((-241 . -882) 114895) ((-760 . -1026) 114718) ((-758 . -1026) 114561) ((-590 . -1181) T) ((-1132 . -595) 114543) ((-1055 . -111) 114372) ((-1017 . -101) T) ((-467 . -1181) T) ((-453 . -1026) 114343) ((-446 . -1026) 114186) ((-642 . -626) 114170) ((-844 . -300) T) ((-760 . -111) 113979) ((-758 . -111) 113808) ((-348 . -626) 113760) 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-1020) T) ((-1239 . -21) T) ((-1239 . -25) T) ((-1142 . -542) 111869) ((-1141 . -1185) 111848) ((-565 . -1020) T) ((-509 . -1020) T) ((-1135 . -1185) 111827) ((-354 . -1011) 111811) ((-315 . -1011) 111795) ((-997 . -283) T) ((-372 . -859) 111777) ((-1141 . -542) 111728) ((-1135 . -542) 111679) ((-976 . -38) 111624) ((-777 . -1080) T) ((-883 . -705) T) ((-565 . -237) T) ((-565 . -227) T) ((-509 . -227) T) ((-509 . -237) T) ((-1094 . -542) 111603) ((-347 . -283) T) ((-625 . -673) 111587) ((-372 . -1011) 111547) ((-1088 . -1027) T) ((-102 . -125) 111531) ((-777 . -23) T) ((-1227 . -279) 111508) ((-400 . -302) 111473) ((-1249 . -1244) 111449) ((-1247 . -1244) 111428) ((-1213 . -1068) T) ((-843 . -595) 111410) ((-812 . -1011) 111379) ((-197 . -765) T) ((-196 . -765) T) ((-195 . -765) T) ((-194 . -765) T) ((-193 . -765) T) ((-192 . -765) T) ((-191 . -765) T) ((-190 . -765) T) ((-189 . -765) T) ((-188 . -765) T) ((-486 . -975) T) ((-267 . -814) T) ((-266 . -814) T) ((-265 . -814) T) ((-264 . -814) T) ((-48 . -283) T) ((-263 . -814) T) ((-262 . -814) T) ((-261 . -814) T) ((-187 . -765) T) ((-594 . -825) T) ((-632 . -404) 111363) ((-110 . -825) T) ((-631 . -21) T) ((-631 . -25) T) ((-1250 . -38) 111333) ((-117 . -279) 111284) ((-1227 . -19) 111268) ((-1227 . -586) 111245) ((-1240 . -1068) T) ((-1045 . -1068) T) ((-960 . -1068) T) ((-936 . -130) T) ((-716 . -1068) T) ((-714 . -130) T) ((-694 . -130) T) ((-502 . -771) T) ((-400 . -1119) 111223) ((-445 . -130) T) ((-502 . -772) T) ((-217 . -1020) T) ((-287 . -101) 111005) ((-139 . -1068) T) ((-677 . -975) T) ((-90 . -1181) T) ((-127 . -595) 110937) ((-121 . -595) 110869) ((-1255 . -170) T) ((-1141 . -356) 110848) ((-1135 . -356) 110827) ((-309 . -1068) T) ((-411 . -130) T) ((-306 . -1068) T) ((-400 . -38) 110779) ((-1101 . -101) T) ((-1213 . -696) 110671) ((-632 . -1027) T) ((-1103 . -1222) T) ((-312 . -143) 110650) ((-312 . -145) 110629) ((-135 . -1068) T) ((-114 . -1068) T) ((-833 . -101) T) ((-564 . -595) 110611) ((-550 . -596) 110510) ((-550 . -595) 110492) ((-486 . -595) 110474) ((-486 . -596) 110419) ((-477 . -23) T) ((-474 . -825) 110370) ((-479 . -619) 110352) ((-938 . -595) 110334) ((-211 . -619) 110316) ((-219 . -397) T) ((-640 . -626) 110300) ((-1140 . -893) 110279) ((-710 . -1080) T) ((-344 . -101) T) ((-1180 . -1051) T) ((-796 . -825) T) ((-710 . -23) T) ((-336 . -1026) 110224) ((-1126 . -1125) T) ((-1115 . -106) 110208) ((-1142 . -1080) T) ((-1141 . -1080) T) ((-506 . -1011) 110192) ((-1135 . -1080) T) ((-1094 . -1080) T) ((-336 . -111) 110121) ((-977 . -1185) T) ((-126 . -1181) T) ((-887 . -1185) T) ((-672 . -279) NIL) ((-1228 . -595) 110103) ((-1142 . -23) T) ((-1141 . -23) T) ((-1135 . -23) T) ((-977 . -542) T) ((-1110 . -225) 110087) ((-887 . -542) T) ((-1094 . -23) T) ((-242 . -595) 110069) ((-1043 . -1068) T) ((-777 . -130) T) ((-689 . -595) 110051) ((-309 . -696) 109961) ((-306 . -696) 109890) ((-677 . -595) 109872) ((-677 . -596) 109817) ((-400 . -393) 109801) ((-431 . -1068) T) 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. -111) 81757) ((-445 . -723) 81727) ((-839 . -1026) 81697) ((-795 . -38) 81639) ((-672 . -857) 81621) ((-672 . -859) 81603) ((-288 . -302) 81407) ((-883 . -1185) T) ((-648 . -404) 81391) ((-839 . -111) 81356) ((-672 . -1011) 81301) ((-977 . -444) T) ((-883 . -542) T) ((-565 . -893) T) ((-466 . -1080) T) ((-509 . -893) T) ((-1124 . -281) 81278) ((-887 . -444) T) ((-64 . -595) 81260) ((-612 . -223) 81206) ((-466 . -23) T) ((-1088 . -772) T) ((-845 . -130) T) ((-1088 . -769) T) ((-1242 . -1244) 81185) ((-1088 . -705) T) ((-632 . -626) 81159) ((-287 . -595) 80900) ((-1008 . -34) T) ((-793 . -823) 80879) ((-564 . -300) T) ((-550 . -300) T) ((-486 . -300) T) ((-1251 . -696) 80849) ((-672 . -370) 80831) ((-672 . -331) 80813) ((-469 . -170) T) ((-374 . -696) 80783) ((-844 . -825) NIL) ((-550 . -995) T) ((-486 . -995) T) ((-1101 . -595) 80765) ((-1081 . -232) 80744) ((-208 . -101) T) ((-1118 . -101) T) ((-70 . -595) 80726) ((-1110 . -1020) T) ((-1146 . -38) 80623) ((-833 . -595) 80605) ((-550 . -535) T) ((-648 . -1027) T) ((-710 . -922) 80558) ((-1110 . -227) 80537) ((-1050 . -1068) T) ((-1007 . -25) T) ((-1007 . -21) T) ((-976 . -1026) 80482) ((-878 . -101) T) ((-839 . -1020) T) ((-672 . -873) NIL) ((-348 . -322) 80466) ((-348 . -356) T) ((-345 . -322) 80450) ((-345 . -356) T) ((-337 . -322) 80434) ((-337 . -356) T) ((-479 . -101) T) ((-1239 . -38) 80404) ((-514 . -665) 80354) ((-211 . -101) T) ((-997 . -1011) 80234) ((-976 . -111) 80163) ((-1142 . -946) 80132) ((-1141 . -946) 80094) ((-511 . -149) 80078) ((-1048 . -363) 80057) ((-344 . -595) 80039) ((-315 . -21) T) ((-347 . -1011) 80016) ((-315 . -25) T) ((-1135 . -946) 79985) ((-1094 . -946) 79952) ((-75 . -595) 79934) ((-677 . -300) T) ((-167 . -825) 79913) ((-883 . -356) T) ((-372 . -25) T) ((-372 . -21) T) ((-883 . -322) 79900) ((-85 . -595) 79882) ((-677 . -995) T) ((-655 . -825) T) ((-1211 . -130) T) ((-1190 . -130) T) ((-874 . -983) 79866) ((-812 . -21) T) ((-48 . -1011) 79809) ((-812 . -25) T) ((-805 . -25) T) 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73448) ((-241 . -619) 73396) ((-679 . -1026) 73383) ((-578 . -1205) 73360) ((-1094 . -277) 73326) ((-312 . -170) 73257) ((-352 . -1068) T) ((-346 . -1068) T) ((-338 . -1068) T) ((-491 . -19) 73239) ((-1088 . -1011) 73221) ((-1070 . -149) 73205) ((-107 . -1068) T) ((-116 . -1026) 73192) ((-690 . -356) T) ((-491 . -586) 73167) ((-679 . -111) 73152) ((-429 . -101) T) ((-45 . -1117) 73102) ((-116 . -111) 73087) ((-615 . -699) T) ((-589 . -699) T) ((-793 . -505) 73020) ((-1008 . -1181) T) ((-916 . -149) 73004) ((-516 . -101) T) ((-511 . -101) 72954) ((-1140 . -444) 72885) ((-1134 . -1068) T) ((-1055 . -1185) 72864) ((-760 . -1185) 72843) ((-758 . -1185) 72822) ((-61 . -1181) T) ((-469 . -595) 72774) ((-469 . -596) 72696) ((-1126 . -1068) T) ((-1110 . -626) 72670) ((-1093 . -444) 72621) ((-1055 . -542) 72552) ((-474 . -404) 72521) ((-603 . -893) 72500) ((-446 . -1185) 72479) ((-967 . -1068) T) ((-760 . -542) 72390) ((-391 . -595) 72372) ((-758 . -542) 72303) ((-653 . -505) 72236) ((-710 . 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T) ((-679 . -1020) T) ((-263 . -1068) T) ((-262 . -1068) T) ((-261 . -1068) T) ((-206 . -1068) T) ((-205 . -1068) T) ((-203 . -1068) T) ((-167 . -1169) 71314) ((-167 . -1166) 71292) ((-202 . -1068) T) ((-201 . -1068) T) ((-116 . -1020) T) ((-200 . -1068) T) ((-197 . -1068) T) ((-679 . -227) T) ((-196 . -1068) T) ((-195 . -1068) T) ((-194 . -1068) T) ((-193 . -1068) T) ((-192 . -1068) T) ((-191 . -1068) T) ((-190 . -1068) T) ((-189 . -1068) T) ((-188 . -1068) T) ((-187 . -1068) T) ((-234 . -101) 71082) ((-167 . -35) 71060) ((-167 . -94) 71038) ((-632 . -1011) 70934) ((-474 . -1027) 70864) ((-1081 . -1068) 70654) ((-1110 . -34) T) ((-648 . -481) 70638) ((-72 . -1181) T) ((-104 . -595) 70620) ((-1251 . -595) 70602) ((-374 . -595) 70584) ((-710 . -38) 70433) ((-557 . -1169) T) ((-557 . -1166) T) ((-522 . -595) 70415) ((-511 . -302) 70353) ((-491 . -595) 70335) ((-491 . -596) 70317) ((-1180 . -595) 70283) ((-1135 . -1119) NIL) ((-1000 . -1040) 70252) ((-1000 . -1068) T) ((-977 . -101) T) 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. -92) T) ((-154 . -92) T) ((-152 . -92) T) ((-1191 . -696) 40895) ((-976 . -893) T) ((-681 . -595) 40864) ((-150 . -705) T) ((-1081 . -361) 40843) ((-977 . -505) NIL) ((-244 . -404) 40812) ((-243 . -404) 40781) ((-997 . -25) T) ((-997 . -21) T) ((-579 . -696) 40754) ((-578 . -696) 40651) ((-777 . -279) 40609) ((-126 . -101) 40587) ((-811 . -1011) 40483) ((-167 . -806) 40462) ((-312 . -626) 40359) ((-793 . -34) T) ((-693 . -101) T) ((-1088 . -1080) T) ((-128 . -505) NIL) ((-999 . -1181) T) ((-372 . -38) 40324) ((-347 . -25) T) ((-347 . -21) T) ((-160 . -101) T) ((-155 . -101) T) ((-348 . -1234) 40308) ((-345 . -1234) 40292) ((-337 . -1234) 40276) ((-167 . -342) 40255) ((-550 . -825) T) ((-486 . -825) T) ((-1088 . -23) T) ((-86 . -595) 40237) ((-679 . -300) T) ((-812 . -38) 40207) ((-805 . -38) 40177) ((-1213 . -130) T) ((-1118 . -281) 40156) ((-937 . -771) 40109) ((-937 . -772) 40062) ((-793 . -769) 40041) ((-116 . -300) T) ((-90 . -302) 39979) ((-653 . -34) T) ((-536 . -586) 39958) 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. -595) 37410) ((-536 . -596) NIL) ((-536 . -595) 37392) ((-520 . -595) 37374) ((-1135 . -279) 37222) ((-479 . -1026) 37172) ((-690 . -444) T) ((-502 . -500) 37151) ((-498 . -500) 37130) ((-211 . -1026) 37080) ((-352 . -626) 37032) ((-346 . -626) 36984) ((-219 . -823) T) ((-338 . -626) 36936) ((-584 . -101) 36886) ((-474 . -361) 36865) ((-107 . -626) 36815) ((-479 . -111) 36749) ((-234 . -481) 36733) ((-336 . -145) 36715) ((-336 . -143) T) ((-167 . -363) 36686) ((-916 . -1225) 36670) ((-211 . -111) 36604) ((-845 . -302) 36569) ((-916 . -1068) 36519) ((-777 . -596) 36480) ((-777 . -595) 36462) ((-697 . -101) T) ((-324 . -1068) T) ((-1088 . -130) T) ((-693 . -38) 36432) ((-309 . -484) 36411) ((-491 . -1181) T) ((-1211 . -277) 36377) ((-1190 . -277) 36343) ((-320 . -149) 36327) ((-1032 . -281) 36302) ((-1242 . -696) 36272) ((-1127 . -34) T) ((-1251 . -1011) 36249) ((-460 . -595) 36231) ((-476 . -34) T) ((-374 . -1011) 36215) ((-1140 . -1027) T) ((-1093 . -1027) T) ((-829 . -1027) T) 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126788) ((-648 . -25) T) ((-648 . -21) T) ((-466 . -1021) T) ((-615 . -410) 126753) ((-589 . -410) 126718) ((-1089 . -1120) T) ((-565 . -283) T) ((-509 . -283) T) ((-1213 . -300) 126697) ((-466 . -227) 126649) ((-466 . -237) 126628) ((-1192 . -300) 126607) ((-1192 . -996) NIL) ((-1049 . -130) T) ((-846 . -773) 126586) ((-142 . -101) T) ((-40 . -1069) T) ((-846 . -770) 126565) ((-623 . -984) 126549) ((-564 . -1028) T) ((-550 . -1028) T) ((-486 . -1028) T) ((-400 . -444) T) ((-352 . -130) T) ((-309 . -393) 126533) ((-306 . -393) 126494) ((-346 . -130) T) ((-338 . -130) T) ((-1150 . -1069) T) ((-1089 . -38) 126481) ((-1063 . -595) 126448) ((-107 . -130) T) ((-928 . -1069) T) ((-895 . -1069) T) ((-749 . -1069) T) ((-650 . -1069) T) ((-497 . -1052) T) ((-679 . -145) T) ((-116 . -145) T) ((-1250 . -21) T) ((-1250 . -25) T) ((-1248 . -21) T) ((-1248 . -25) T) ((-642 . -1027) 126432) ((-522 . -825) T) ((-491 . -825) T) ((-348 . -1027) 126384) ((-345 . -1027) 126336) ((-337 . -1027) 126288) 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. -542) 123714) ((-1141 . -47) 123691) ((-348 . -1021) T) ((-345 . -1021) T) ((-474 . -23) 123561) ((-337 . -1021) T) ((-257 . -1021) T) ((-241 . -1021) T) ((-1094 . -47) 123533) ((-117 . -1028) T) ((-1008 . -626) 123507) ((-932 . -34) T) ((-348 . -227) 123486) ((-348 . -237) T) ((-345 . -227) 123465) ((-345 . -237) T) ((-241 . -319) 123422) ((-337 . -227) 123401) ((-337 . -237) T) ((-257 . -319) 123373) ((-257 . -227) 123352) ((-1125 . -149) 123336) ((-244 . -874) 123268) ((-243 . -874) 123200) ((-1051 . -825) T) ((-1195 . -1182) T) ((-407 . -1081) T) ((-1025 . -23) T) ((-884 . -1021) T) ((-315 . -626) 123182) ((-998 . -823) T) ((-1176 . -976) 123148) ((-1142 . -894) 123127) ((-1136 . -894) 123106) ((-884 . -237) T) ((-795 . -356) 123085) ((-378 . -23) T) ((-127 . -1069) 123063) ((-121 . -1069) 123041) ((-884 . -227) T) ((-1136 . -798) NIL) ((-372 . -626) 123006) ((-844 . -696) 122993) ((-1018 . -149) 122958) ((-40 . -170) T) ((-672 . -404) 122940) ((-691 . -302) 122927) ((-812 . -626) 122887) ((-805 . -626) 122861) ((-312 . -25) T) ((-312 . -21) T) ((-636 . -279) 122840) ((-564 . -1069) T) ((-550 . -1069) T) ((-486 . -1069) T) ((-239 . -281) 122817) ((-306 . -225) 122778) ((-1141 . -860) NIL) ((-1094 . -860) 122637) ((-129 . -825) T) ((-1141 . -1012) 122517) ((-1094 . -1012) 122400) ((-181 . -595) 122382) ((-829 . -1012) 122278) ((-760 . -279) 122205) ((-795 . -1081) T) ((-1008 . -705) T) ((-584 . -629) 122189) ((-1018 . -950) 122118) ((-973 . -101) T) ((-795 . -23) T) ((-691 . -1120) 122096) ((-672 . -1028) T) ((-584 . -366) 122080) ((-344 . -444) T) ((-336 . -283) T) ((-1229 . -1069) T) ((-242 . -1069) T) ((-392 . -101) T) ((-282 . -21) T) ((-282 . -25) T) ((-354 . -705) T) ((-689 . -1069) T) ((-677 . -1069) T) ((-354 . -465) T) ((-1176 . -595) 122062) ((-1141 . -370) 122046) ((-1094 . -370) 122030) ((-998 . -404) 121992) ((-139 . -223) 121974) ((-372 . -772) T) ((-372 . -769) T) ((-844 . -170) T) ((-372 . -705) T) ((-690 . -595) 121956) ((-691 . -38) 121785) ((-1228 . -1226) 121769) ((-344 . -395) T) ((-1228 . -1069) 121719) ((-564 . -696) 121706) ((-550 . -696) 121693) ((-486 . -696) 121658) ((-309 . -609) 121637) ((-812 . -705) T) ((-805 . -705) T) ((-623 . -1182) T) ((-1049 . -619) 121585) ((-1141 . -874) 121528) ((-1094 . -874) 121512) ((-640 . -1027) 121496) ((-107 . -619) 121478) ((-474 . -130) 121348) ((-1147 . -1081) T) ((-926 . -47) 121317) ((-603 . -1069) T) ((-640 . -111) 121296) ((-482 . -595) 121262) ((-320 . -281) 121239) ((-473 . -47) 121196) ((-1147 . -23) T) ((-117 . -1069) T) ((-102 . -101) 121174) ((-1240 . -1081) T) ((-1025 . -130) T) ((-998 . -1028) T) ((-797 . -1012) 121158) ((-977 . -703) 121130) ((-1240 . -23) T) ((-677 . -696) 121095) ((-569 . -595) 121077) ((-379 . -1012) 121061) ((-347 . -1028) T) ((-378 . -130) T) ((-317 . -1012) 121045) ((-219 . -860) 121027) ((-978 . -894) T) ((-90 . -34) T) ((-978 . -798) T) ((-888 . -894) T) ((-479 . -1186) T) ((-1162 . -595) 121009) ((-1074 . -1069) T) ((-211 . -1186) T) ((-973 . -302) 120974) ((-219 . -1012) 120934) ((-40 . -283) T) ((-1049 . -21) T) ((-1049 . -25) T) ((-1089 . -806) T) ((-479 . -542) T) ((-352 . -25) T) ((-211 . -542) T) ((-352 . -21) T) ((-346 . -25) T) ((-346 . -21) T) ((-693 . -626) 120894) ((-338 . -25) T) ((-338 . -21) T) ((-107 . -25) T) ((-107 . -21) T) ((-48 . -1028) T) ((-564 . -170) T) ((-550 . -170) T) ((-486 . -170) T) ((-636 . -595) 120876) ((-716 . -715) 120860) ((-329 . -595) 120842) ((-67 . -376) T) ((-67 . -388) T) ((-1071 . -106) 120826) ((-1032 . -860) 120808) ((-926 . -860) 120733) ((-631 . -1081) T) ((-603 . -696) 120720) ((-473 . -860) NIL) ((-1115 . -101) T) ((-1032 . -1012) 120702) ((-96 . -595) 120684) ((-469 . -145) T) ((-926 . -1012) 120564) ((-117 . -696) 120509) ((-631 . -23) T) ((-473 . -1012) 120385) ((-1056 . -596) NIL) ((-1056 . -595) 120367) ((-760 . -596) NIL) ((-760 . -595) 120328) ((-758 . -596) 119962) ((-758 . -595) 119876) ((-1082 . -619) 119782) ((-453 . -595) 119764) ((-446 . -595) 119746) ((-446 . -596) 119607) ((-1009 . -223) 119553) ((-846 . -883) 119532) ((-126 . -34) T) ((-795 . -130) T) ((-627 . -595) 119514) ((-563 . -101) T) ((-348 . -1247) 119498) ((-345 . -1247) 119482) ((-337 . -1247) 119466) ((-127 . -505) 119399) ((-121 . -505) 119332) ((-502 . -770) T) ((-502 . -773) T) ((-501 . -772) T) ((-102 . -302) 119270) ((-216 . -101) 119248) ((-672 . -1069) T) ((-677 . -170) T) ((-846 . -626) 119200) ((-64 . -377) T) ((-268 . -595) 119182) ((-64 . -388) T) ((-926 . -370) 119166) ((-844 . -283) T) ((-50 . -595) 119148) ((-973 . -38) 119096) ((-565 . -595) 119078) ((-473 . -370) 119062) ((-565 . -596) 119044) ((-509 . -595) 119026) ((-884 . -1247) 119013) ((-845 . -1182) T) ((-679 . -444) T) ((-486 . -505) 118979) ((-479 . -356) T) ((-348 . -361) 118958) ((-345 . -361) 118937) ((-337 . -361) 118916) ((-211 . -356) T) ((-693 . -705) T) ((-116 . -444) T) ((-1251 . -1242) 118900) ((-845 . -858) 118877) ((-845 . -860) NIL) ((-938 . -825) 118776) ((-793 . -825) 118727) ((-632 . -634) 118711) ((-1168 . -34) T) ((-169 . -595) 118693) ((-1082 . -21) 118603) ((-1082 . -25) 118454) ((-845 . -1012) 118431) ((-926 . -874) 118412) ((-1201 . -47) 118389) ((-884 . -361) T) ((-58 . -629) 118373) ((-507 . -629) 118357) ((-473 . -874) 118334) ((-70 . -433) T) ((-70 . -388) T) ((-487 . -629) 118318) ((-58 . -366) 118302) ((-603 . -170) T) ((-507 . -366) 118286) ((-487 . -366) 118270) ((-805 . -687) 118254) ((-1141 . -300) 118233) ((-1147 . -130) T) ((-117 . -170) T) ((-1115 . -302) 118171) ((-167 . -1182) T) ((-615 . -723) 118155) ((-589 . -723) 118139) ((-1240 . -130) T) ((-1213 . -894) 118118) ((-1192 . -894) 118097) ((-1192 . -798) NIL) ((-672 . -696) 118047) ((-1191 . -883) 118000) ((-998 . -1069) T) ((-845 . -370) 117977) ((-845 . -331) 117954) ((-879 . -1081) T) ((-167 . -858) 117938) ((-167 . -860) 117863) ((-479 . -1081) T) ((-347 . -1069) T) ((-211 . -1081) T) ((-75 . -433) T) ((-75 . -388) T) ((-167 . -1012) 117759) ((-312 . -825) T) ((-1228 . -505) 117692) ((-1212 . -626) 117589) ((-1191 . -626) 117459) ((-846 . -772) 117438) ((-846 . -769) 117417) ((-846 . -705) T) ((-479 . -23) T) ((-217 . -595) 117399) ((-172 . -444) T) ((-216 . -302) 117337) ((-85 . -433) T) ((-85 . -388) T) ((-211 . -23) T) ((-1252 . -1245) 117316) ((-564 . -283) T) ((-550 . -283) T) ((-655 . -1012) 117300) ((-486 . -283) T) ((-135 . -462) 117255) ((-48 . -1069) T) ((-691 . -225) 117239) ((-845 . -874) NIL) ((-1201 . -860) NIL) ((-863 . -101) T) ((-859 . -101) T) ((-381 . -1069) T) ((-167 . -370) 117223) ((-167 . -331) 117207) ((-1201 . -1012) 117087) ((-830 . -1012) 116983) ((-1111 . -101) T) ((-631 . -130) T) ((-117 . -505) 116891) ((-640 . -770) 116870) ((-640 . -773) 116849) ((-557 . -1012) 116831) ((-287 . -1235) 116801) ((-840 . -101) T) ((-937 . -542) 116780) ((-1176 . -1027) 116663) ((-474 . -619) 116569) ((-878 . -1069) T) ((-998 . -696) 116506) ((-690 . -1027) 116471) ((-598 . -101) T) ((-584 . -34) T) ((-1116 . -1182) T) ((-1176 . -111) 116340) ((-466 . -626) 116237) ((-347 . -696) 116182) ((-167 . -874) 116141) ((-677 . -283) T) ((-672 . -170) T) ((-690 . -111) 116097) ((-1256 . -1028) T) ((-1201 . -370) 116081) ((-411 . -1186) 116059) ((-1087 . -595) 116041) ((-306 . -823) NIL) ((-411 . -542) T) ((-219 . -300) T) ((-1191 . -769) 115994) ((-1191 . -772) 115947) ((-1212 . -705) T) ((-1191 . -705) T) ((-48 . -696) 115912) ((-219 . -996) T) ((-344 . -1235) 115889) ((-1214 . -404) 115855) ((-697 . -705) T) ((-1201 . -874) 115798) ((-112 . -595) 115780) ((-112 . -596) 115762) ((-697 . -465) T) ((-474 . -21) 115672) ((-127 . -481) 115656) ((-121 . -481) 115640) ((-474 . -25) 115491) ((-603 . -283) T) ((-569 . -1027) 115466) ((-430 . -1069) T) ((-1032 . -300) T) ((-117 . -283) T) ((-1073 . -101) T) ((-977 . -101) T) ((-569 . -111) 115434) ((-1111 . -302) 115372) ((-1176 . -1021) T) ((-1032 . -996) T) ((-65 . -1182) T) ((-1025 . -25) T) ((-1025 . -21) T) ((-690 . -1021) T) ((-378 . -21) T) ((-378 . -25) T) ((-672 . -505) NIL) ((-998 . -170) T) ((-690 . -237) T) ((-1032 . -535) T) ((-497 . -101) T) ((-493 . -101) T) ((-347 . -170) T) ((-336 . -595) 115354) ((-387 . -595) 115336) ((-466 . -705) T) ((-1089 . -823) T) ((-866 . -1012) 115304) ((-107 . -825) T) ((-636 . -1027) 115288) ((-479 . -130) T) ((-1214 . -1028) T) ((-211 . -130) T) ((-1125 . -101) 115266) ((-98 . -1069) T) ((-239 . -644) 115250) ((-239 . -629) 115234) ((-636 . -111) 115213) ((-309 . -404) 115197) ((-239 . -366) 115181) ((-1128 . -229) 115128) ((-973 . -225) 115112) ((-73 . -1182) T) ((-48 . -170) T) ((-679 . -380) T) ((-679 . -141) T) ((-1251 . -101) T) ((-1056 . -1027) 114955) ((-257 . -883) 114934) ((-241 . -883) 114913) ((-760 . -1027) 114736) ((-758 . -1027) 114579) ((-590 . -1182) T) ((-1133 . -595) 114561) ((-1056 . -111) 114390) ((-1018 . -101) T) ((-467 . -1182) T) ((-453 . -1027) 114361) ((-446 . -1027) 114204) ((-642 . -626) 114188) ((-845 . -300) T) ((-760 . -111) 113997) ((-758 . -111) 113826) ((-348 . -626) 113778) ((-345 . -626) 113730) ((-337 . -626) 113682) ((-257 . -626) 113607) ((-241 . -626) 113532) ((-1127 . -825) T) ((-1057 . -1012) 113516) ((-453 . -111) 113477) ((-446 . -111) 113306) ((-1045 . -1012) 113283) ((-974 . -34) T) ((-940 . -595) 113265) ((-932 . -1182) T) ((-126 . -984) 113249) ((-937 . -1081) T) ((-845 . -996) NIL) ((-714 . -1081) T) ((-694 . -1081) T) ((-1228 . -481) 113233) ((-1111 . -38) 113193) ((-937 . -23) T) ((-818 . -101) T) ((-795 . -21) T) ((-795 . -25) T) ((-714 . -23) T) ((-694 . -23) T) ((-110 . -639) T) ((-884 . -626) 113158) ((-565 . -1027) 113123) ((-509 . -1027) 113068) ((-221 . -56) 113026) ((-445 . -23) T) ((-400 . -101) T) ((-256 . -101) T) ((-672 . -283) T) ((-840 . -38) 112996) ((-565 . -111) 112952) ((-509 . -111) 112881) ((-411 . -1081) T) ((-309 . -1028) 112771) ((-306 . -1028) T) ((-636 . -1021) T) ((-1256 . -1069) T) ((-167 . -300) 112702) ((-411 . -23) T) ((-40 . -595) 112684) ((-40 . -596) 112668) ((-107 . -966) 112650) ((-116 . -843) 112634) 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-1021) T) ((-1240 . -21) T) ((-1240 . -25) T) ((-1143 . -542) 111887) ((-1142 . -1186) 111866) ((-565 . -1021) T) ((-509 . -1021) T) ((-1136 . -1186) 111845) ((-354 . -1012) 111829) ((-315 . -1012) 111813) ((-998 . -283) T) ((-372 . -860) 111795) ((-1142 . -542) 111746) ((-1136 . -542) 111697) ((-977 . -38) 111642) ((-777 . -1081) T) ((-884 . -705) T) ((-565 . -237) T) ((-565 . -227) T) ((-509 . -227) T) ((-509 . -237) T) ((-1095 . -542) 111621) ((-347 . -283) T) ((-625 . -673) 111605) ((-372 . -1012) 111565) ((-1089 . -1028) T) ((-102 . -125) 111549) ((-777 . -23) T) ((-1228 . -279) 111526) ((-400 . -302) 111491) ((-1250 . -1245) 111467) ((-1248 . -1245) 111446) ((-1214 . -1069) T) ((-844 . -595) 111428) ((-812 . -1012) 111397) ((-197 . -765) T) ((-196 . -765) T) ((-195 . -765) T) ((-194 . -765) T) ((-193 . -765) T) ((-192 . -765) T) ((-191 . -765) T) ((-190 . -765) T) ((-189 . -765) T) ((-188 . -765) T) ((-486 . -976) T) ((-267 . -814) T) ((-266 . -814) T) ((-265 . -814) T) ((-264 . -814) T) ((-48 . -283) T) ((-263 . -814) T) ((-262 . -814) T) ((-261 . -814) T) ((-187 . -765) T) ((-594 . -825) T) ((-632 . -404) 111381) ((-110 . -825) T) ((-631 . -21) T) ((-631 . -25) T) ((-1251 . -38) 111351) ((-117 . -279) 111302) ((-1228 . -19) 111286) ((-1228 . -586) 111263) ((-1241 . -1069) T) ((-1046 . -1069) T) ((-961 . -1069) T) ((-937 . -130) T) ((-716 . -1069) T) ((-714 . -130) T) ((-694 . -130) T) ((-502 . -771) T) ((-400 . -1120) 111241) ((-445 . -130) T) ((-502 . -772) T) ((-217 . -1021) T) ((-287 . -101) 111023) ((-139 . -1069) T) ((-677 . -976) T) ((-90 . -1182) T) ((-127 . -595) 110955) ((-121 . -595) 110887) ((-1256 . -170) T) ((-1142 . -356) 110866) ((-1136 . -356) 110845) ((-309 . -1069) T) ((-411 . -130) T) ((-306 . -1069) T) ((-400 . -38) 110797) ((-1102 . -101) T) ((-1214 . -696) 110689) ((-632 . -1028) T) ((-1104 . -1223) T) ((-312 . -143) 110668) ((-312 . -145) 110647) ((-135 . -1069) T) ((-114 . -1069) T) ((-833 . -101) T) ((-564 . -595) 110629) ((-550 . -596) 110528) ((-550 . -595) 110510) ((-486 . -595) 110492) ((-486 . -596) 110437) ((-477 . -23) T) ((-474 . -825) 110388) ((-479 . -619) 110370) ((-939 . -595) 110352) ((-211 . -619) 110334) ((-219 . -397) T) ((-640 . -626) 110318) ((-1141 . -894) 110297) ((-710 . -1081) T) ((-344 . -101) T) ((-1181 . -1052) T) ((-796 . -825) T) ((-710 . -23) T) ((-336 . -1027) 110242) ((-1127 . -1126) T) ((-1116 . -106) 110226) ((-1143 . -1081) T) ((-1142 . -1081) T) ((-506 . -1012) 110210) ((-1136 . -1081) T) ((-1095 . -1081) T) ((-336 . -111) 110139) ((-978 . -1186) T) ((-126 . -1182) T) ((-888 . -1186) T) ((-672 . -279) NIL) ((-1229 . -595) 110121) ((-1143 . -23) T) ((-1142 . -23) T) ((-1136 . -23) T) ((-978 . -542) T) ((-1111 . -225) 110105) ((-888 . -542) T) ((-1095 . -23) T) ((-242 . -595) 110087) ((-1044 . -1069) T) ((-777 . -130) T) ((-689 . -595) 110069) ((-309 . -696) 109979) ((-306 . -696) 109908) ((-677 . -595) 109890) ((-677 . -596) 109835) ((-400 . -393) 109819) ((-431 . -1069) T) 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. -111) 81775) ((-445 . -723) 81745) ((-840 . -1027) 81715) ((-795 . -38) 81657) ((-672 . -858) 81639) ((-672 . -860) 81621) ((-288 . -302) 81425) ((-884 . -1186) T) ((-648 . -404) 81409) ((-840 . -111) 81374) ((-672 . -1012) 81319) ((-978 . -444) T) ((-884 . -542) T) ((-565 . -894) T) ((-466 . -1081) T) ((-509 . -894) T) ((-1125 . -281) 81296) ((-888 . -444) T) ((-64 . -595) 81278) ((-612 . -223) 81224) ((-466 . -23) T) ((-1089 . -772) T) ((-846 . -130) T) ((-1089 . -769) T) ((-1243 . -1245) 81203) ((-1089 . -705) T) ((-632 . -626) 81177) ((-287 . -595) 80918) ((-1009 . -34) T) ((-793 . -823) 80897) ((-564 . -300) T) ((-550 . -300) T) ((-486 . -300) T) ((-1252 . -696) 80867) ((-672 . -370) 80849) ((-672 . -331) 80831) ((-469 . -170) T) ((-374 . -696) 80801) ((-845 . -825) NIL) ((-550 . -996) T) ((-486 . -996) T) ((-1102 . -595) 80783) ((-1082 . -232) 80762) ((-208 . -101) T) ((-1119 . -101) T) ((-70 . -595) 80744) ((-1111 . -1021) T) ((-1147 . -38) 80641) ((-833 . -595) 80623) ((-550 . -535) T) ((-648 . -1028) T) ((-710 . -923) 80576) ((-1111 . -227) 80555) ((-1051 . -1069) T) ((-1008 . -25) T) ((-1008 . -21) T) ((-977 . -1027) 80500) ((-879 . -101) T) ((-840 . -1021) T) ((-672 . -874) NIL) ((-348 . -322) 80484) ((-348 . -356) T) ((-345 . -322) 80468) ((-345 . -356) T) ((-337 . -322) 80452) ((-337 . -356) T) ((-479 . -101) T) ((-1240 . -38) 80422) ((-514 . -665) 80372) ((-211 . -101) T) ((-998 . -1012) 80252) ((-977 . -111) 80181) ((-1143 . -947) 80150) ((-1142 . -947) 80112) ((-511 . -149) 80096) ((-1049 . -363) 80075) ((-344 . -595) 80057) ((-315 . -21) T) ((-347 . -1012) 80034) ((-315 . -25) T) ((-1136 . -947) 80003) ((-1095 . -947) 79970) ((-75 . -595) 79952) ((-677 . -300) T) ((-167 . -825) 79931) ((-884 . -356) T) ((-372 . -25) T) ((-372 . -21) T) ((-884 . -322) 79918) ((-85 . -595) 79900) ((-677 . -996) T) ((-655 . -825) T) ((-1212 . -130) T) ((-1191 . -130) T) ((-875 . -984) 79884) ((-812 . -21) T) ((-48 . -1012) 79827) ((-812 . -25) T) ((-805 . -25) T) 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73466) ((-241 . -619) 73414) ((-679 . -1027) 73401) ((-578 . -1206) 73378) ((-1095 . -277) 73344) ((-312 . -170) 73275) ((-352 . -1069) T) ((-346 . -1069) T) ((-338 . -1069) T) ((-491 . -19) 73257) ((-1089 . -1012) 73239) ((-1071 . -149) 73223) ((-107 . -1069) T) ((-116 . -1027) 73210) ((-690 . -356) T) ((-491 . -586) 73185) ((-679 . -111) 73170) ((-429 . -101) T) ((-45 . -1118) 73120) ((-116 . -111) 73105) ((-615 . -699) T) ((-589 . -699) T) ((-793 . -505) 73038) ((-1009 . -1182) T) ((-917 . -149) 73022) ((-516 . -101) T) ((-511 . -101) 72972) ((-1141 . -444) 72903) ((-1135 . -1069) T) ((-1056 . -1186) 72882) ((-760 . -1186) 72861) ((-758 . -1186) 72840) ((-61 . -1182) T) ((-469 . -595) 72792) ((-469 . -596) 72714) ((-1127 . -1069) T) ((-1111 . -626) 72688) ((-1094 . -444) 72639) ((-1056 . -542) 72570) ((-474 . -404) 72539) ((-603 . -894) 72518) ((-446 . -1186) 72497) ((-968 . -1069) T) ((-760 . -542) 72408) ((-391 . -595) 72390) ((-758 . -542) 72321) ((-653 . -505) 72254) ((-710 . -302) 72241) ((-642 . -25) T) ((-642 . -21) T) ((-446 . -542) 72172) ((-117 . -894) T) ((-117 . -798) NIL) ((-348 . -25) T) ((-348 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-337 . -25) T) ((-337 . -21) T) ((-257 . -25) T) ((-257 . -21) T) ((-82 . -377) T) ((-82 . -388) T) ((-241 . -25) T) ((-241 . -21) T) ((-1230 . -595) 72154) ((-1176 . -1081) T) ((-1176 . -23) T) ((-1136 . -302) 72039) ((-1095 . -302) 72026) ((-1049 . -696) 71894) ((-840 . -626) 71854) ((-917 . -954) 71838) ((-884 . -21) T) ((-282 . -170) T) ((-884 . -25) T) ((-304 . -92) T) ((-846 . -825) 71789) ((-690 . -1081) T) ((-690 . -23) T) ((-625 . -1069) 71767) ((-612 . -592) 71742) ((-612 . -1069) T) ((-565 . -1186) T) ((-509 . -1186) T) ((-565 . -542) T) ((-509 . -542) T) ((-352 . -696) 71694) ((-346 . -696) 71646) ((-338 . -696) 71598) ((-332 . -1027) 71582) ((-172 . -111) 71493) ((-172 . -1027) 71425) ((-107 . -696) 71375) ((-332 . -111) 71354) ((-267 . -1069) T) ((-266 . -1069) T) ((-265 . -1069) T) ((-264 . -1069) T) ((-679 . -1021) T) ((-263 . -1069) T) ((-262 . -1069) T) ((-261 . -1069) T) ((-206 . -1069) T) ((-205 . -1069) T) ((-203 . -1069) T) ((-167 . -1170) 71332) ((-167 . -1167) 71310) ((-202 . -1069) T) ((-201 . -1069) T) ((-116 . -1021) T) ((-200 . -1069) T) ((-197 . -1069) T) ((-679 . -227) T) ((-196 . -1069) T) ((-195 . -1069) T) ((-194 . -1069) T) ((-193 . -1069) T) ((-192 . -1069) T) ((-191 . -1069) T) ((-190 . -1069) T) ((-189 . -1069) T) ((-188 . -1069) T) ((-187 . -1069) T) ((-234 . -101) 71100) ((-167 . -35) 71078) ((-167 . -94) 71056) ((-632 . -1012) 70952) ((-474 . -1028) 70882) ((-1082 . -1069) 70672) ((-1111 . -34) T) ((-648 . -481) 70656) ((-72 . -1182) T) ((-104 . -595) 70638) ((-1252 . -595) 70620) ((-374 . -595) 70602) ((-710 . -38) 70451) ((-557 . -1170) T) ((-557 . -1167) T) ((-522 . -595) 70433) ((-511 . -302) 70371) ((-491 . -595) 70353) ((-491 . -596) 70335) ((-1181 . -595) 70301) ((-1136 . -1120) NIL) ((-1001 . -1041) 70270) ((-1001 . -1069) T) ((-978 . -101) T) 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NIL) ((-329 . -23) T) ((-102 . -984) 69097) ((-45 . -36) 69076) ((-594 . -1069) T) ((-344 . -361) T) ((-515 . -101) T) ((-486 . -27) T) ((-234 . -302) 69014) ((-1056 . -1081) T) ((-1251 . -626) 68988) ((-760 . -1081) T) ((-758 . -1081) T) ((-446 . -1081) T) ((-1032 . -444) T) ((-926 . -444) 68939) ((-1084 . -1052) T) ((-110 . -1069) T) ((-1056 . -23) T) ((-795 . -1028) T) ((-760 . -23) T) ((-758 . -23) T) ((-473 . -444) 68890) ((-1128 . -505) 68673) ((-374 . -375) 68652) ((-1147 . -404) 68636) ((-453 . -23) T) ((-446 . -23) T) ((-95 . -1069) T) ((-476 . -505) 68569) ((-282 . -283) T) ((-1051 . -595) 68551) ((-400 . -883) 68530) ((-50 . -1081) T) ((-998 . -894) T) ((-977 . -705) T) ((-691 . -860) NIL) ((-565 . -1081) T) ((-509 . -1081) T) ((-818 . -626) 68503) ((-1176 . -130) T) ((-1136 . -393) 68455) ((-978 . -302) NIL) ((-793 . -481) 68439) ((-347 . -894) T) ((-1125 . -34) T) ((-400 . -626) 68391) ((-50 . -23) T) ((-690 . -130) T) ((-691 . -1012) 68271) ((-565 . -23) T) ((-107 . -505) NIL) ((-509 . -23) T) ((-167 . -402) 68242) ((-128 . -302) NIL) ((-1109 . -1069) T) ((-1243 . -1242) 68226) ((-679 . -773) T) ((-679 . -770) T) ((-1089 . -300) T) ((-372 . -145) T) ((-273 . -595) 68208) ((-1191 . -966) 68178) ((-48 . -894) T) ((-653 . -481) 68162) ((-244 . -1235) 68132) ((-243 . -1235) 68102) ((-1145 . -825) T) ((-1082 . -170) 68081) ((-1089 . -996) T) ((-1018 . -34) T) ((-812 . -145) 68060) ((-812 . -143) 68039) ((-716 . -106) 68023) ((-594 . -131) T) ((-474 . -1069) 67813) ((-1147 . -1028) T) ((-845 . -444) T) ((-84 . -1182) T) ((-234 . -38) 67783) ((-139 . -106) 67765) ((-691 . -370) 67749) ((-1089 . -535) T) ((-383 . -1027) 67733) ((-1251 . -705) T) ((-1141 . -923) 67702) ((-129 . -595) 67669) ((-52 . -595) 67651) ((-1094 . -923) 67618) ((-631 . -404) 67602) ((-1240 . -1028) T) ((-601 . -1027) 67586) ((-640 . -25) T) ((-640 . -21) T) ((-1127 . -505) NIL) ((-1220 . -101) T) ((-1213 . -101) T) ((-383 . -111) 67565) ((-216 . -247) 67549) ((-1192 . -101) T) ((-1025 . -1069) T) ((-978 . -1120) T) ((-1025 . -1024) 67489) ((-796 . -1069) T) ((-336 . -1186) T) ((-615 . -626) 67473) ((-601 . -111) 67452) ((-589 . -626) 67436) ((-579 . -101) T) ((-569 . -130) T) ((-578 . -101) T) ((-407 . -1069) T) ((-378 . -1069) T) ((-304 . -595) 67402) ((-221 . -1069) 67380) ((-625 . -505) 67313) ((-612 . -505) 67157) ((-811 . -1021) 67136) ((-623 . -149) 67120) ((-336 . -542) T) ((-691 . -874) 67063) ((-536 . -223) 67013) ((-1220 . -277) 66979) ((-1049 . -283) 66930) ((-479 . -823) T) ((-217 . -1081) T) ((-1213 . -277) 66896) ((-1192 . -277) 66862) ((-978 . -38) 66812) ((-211 . -823) T) ((-1176 . -484) 66778) ((-888 . -38) 66730) ((-818 . -772) 66709) ((-818 . -769) 66688) ((-818 . -705) 66667) ((-352 . -283) T) ((-346 . -283) T) ((-338 . -283) T) ((-167 . -444) 66598) ((-420 . -38) 66582) ((-107 . -283) T) ((-217 . -23) T) ((-400 . -772) 66561) ((-400 . -769) 66540) ((-400 . -705) T) ((-491 . -281) 66515) ((-469 . -1027) 66480) ((-636 . -130) T) ((-1082 . -505) 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. -145) 42287) ((-509 . -145) 42269) ((-509 . -143) T) ((-309 . -23) 42121) ((-40 . -335) 42095) ((-306 . -23) T) ((-1127 . -629) 42077) ((-1243 . -1028) T) ((-1127 . -366) 42059) ((-793 . -626) 41907) ((-1065 . -101) T) ((-1059 . -101) T) ((-1043 . -101) T) ((-167 . -225) 41891) ((-1036 . -101) T) ((-1010 . -101) T) ((-993 . -101) T) ((-576 . -481) 41873) ((-606 . -101) T) ((-234 . -505) 41806) ((-475 . -101) T) ((-1250 . -705) T) ((-1248 . -705) T) ((-212 . -101) T) ((-1147 . -1027) 41689) ((-1147 . -111) 41558) ((-836 . -171) T) ((-795 . -1021) T) ((-659 . -1052) T) ((-654 . -1052) T) ((-506 . -101) T) ((-501 . -101) T) ((-48 . -619) 41518) ((-499 . -101) T) ((-470 . -1052) T) ((-1240 . -1027) 41488) ((-137 . -1052) T) ((-136 . -1052) T) ((-132 . -1052) T) ((-1008 . -38) 41472) ((-795 . -227) T) ((-795 . -237) 41451) ((-1240 . -111) 41416) ((-1220 . -696) 41313) ((-536 . -279) 41292) ((-1213 . -696) 41133) ((-1201 . -225) 41117) ((-588 . -92) T) ((-1033 . -596) NIL) ((-1033 . -595) 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39979) ((-653 . -34) T) ((-536 . -586) 39958) ((-48 . -25) T) ((-48 . -21) T) ((-793 . -772) 39909) ((-793 . -771) 39888) ((-679 . -996) T) ((-631 . -1027) 39872) ((-938 . -705) 39771) ((-793 . -705) 39681) ((-938 . -465) 39634) ((-474 . -773) 39585) ((-474 . -770) 39536) ((-884 . -1235) 39523) ((-1147 . -1021) T) ((-631 . -111) 39502) ((-1147 . -319) 39479) ((-1168 . -101) 39457) ((-1070 . -595) 39439) ((-679 . -535) T) ((-794 . -1069) T) ((-1240 . -1021) T) ((-406 . -1069) T) ((-1104 . -595) 39405) ((-244 . -1028) 39335) ((-243 . -1028) 39265) ((-282 . -626) 39252) ((-576 . -279) 39227) ((-667 . -665) 39185) ((-937 . -595) 39167) ((-846 . -101) T) ((-714 . -595) 39149) ((-694 . -595) 39131) ((-1220 . -170) 39082) ((-1213 . -170) 39013) ((-1192 . -170) 38944) ((-677 . -825) T) ((-978 . -283) T) ((-445 . -595) 38926) ((-607 . -705) T) ((-59 . -1069) 38904) ((-239 . -149) 38888) ((-888 . -283) T) ((-998 . -986) T) ((-607 . -465) T) ((-691 . -1186) 38867) ((-579 . -170) 38846) ((-578 . 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. -595) 37467) ((-667 . -596) 37428) ((-583 . -595) 37410) ((-536 . -596) NIL) ((-536 . -595) 37392) ((-520 . -595) 37374) ((-1136 . -279) 37222) ((-479 . -1027) 37172) ((-690 . -444) T) ((-502 . -500) 37151) ((-498 . -500) 37130) ((-211 . -1027) 37080) ((-352 . -626) 37032) ((-346 . -626) 36984) ((-219 . -823) T) ((-338 . -626) 36936) ((-584 . -101) 36886) ((-474 . -361) 36865) ((-107 . -626) 36815) ((-479 . -111) 36749) ((-234 . -481) 36733) ((-336 . -145) 36715) ((-336 . -143) T) ((-167 . -363) 36686) ((-917 . -1226) 36670) ((-211 . -111) 36604) ((-846 . -302) 36569) ((-917 . -1069) 36519) ((-777 . -596) 36480) ((-777 . -595) 36462) ((-697 . -101) T) ((-324 . -1069) T) ((-1089 . -130) T) ((-693 . -38) 36432) ((-309 . -484) 36411) ((-491 . -1182) T) ((-1212 . -277) 36377) ((-1191 . -277) 36343) ((-320 . -149) 36327) ((-1033 . -281) 36302) ((-1243 . -696) 36272) ((-1128 . -34) T) ((-1252 . -1012) 36249) ((-460 . -595) 36231) ((-476 . -34) T) ((-374 . -1012) 36215) ((-1141 . -1028) T) 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. -34) T) ((-1195 . -1062) 33839) ((-565 . -444) T) ((-509 . -444) T) ((-1195 . -1069) 33817) ((-1195 . -1064) 33774) ((-234 . -586) 33751) ((-1143 . -595) 33733) ((-1142 . -595) 33715) ((-1136 . -595) 33697) ((-1136 . -596) NIL) ((-1095 . -595) 33679) ((-128 . -279) 33654) ((-846 . -393) 33638) ((-526 . -101) T) ((-1212 . -38) 33479) ((-1191 . -38) 33293) ((-844 . -145) T) ((-565 . -395) T) ((-48 . -825) T) ((-509 . -395) T) ((-1224 . -101) T) ((-1214 . -21) T) ((-1214 . -25) T) ((-1082 . -769) 33272) ((-1082 . -772) 33223) ((-1082 . -771) 33202) ((-967 . -1069) T) ((-1001 . -34) T) ((-837 . -1069) T) ((-1082 . -705) 33112) ((-642 . -101) T) ((-624 . -101) T) ((-536 . -281) 33091) ((-1155 . -101) T) ((-468 . -34) T) ((-455 . -34) T) ((-348 . -101) T) ((-345 . -101) T) ((-337 . -101) T) ((-257 . -101) T) ((-241 . -101) T) ((-469 . -300) T) ((-1032 . -1028) T) ((-926 . -1028) T) ((-309 . -619) 32997) ((-306 . -619) 32958) ((-473 . -1028) T) ((-471 . -101) T) ((-429 . -595) 32940) 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-302) 29097) ((-487 . -302) 29035) ((-411 . -227) 29014) ((-474 . -34) T) ((-978 . -596) 28944) ((-219 . -1069) T) ((-978 . -595) 28926) ((-945 . -595) 28908) ((-945 . -596) 28883) ((-888 . -595) 28865) ((-677 . -145) T) ((-679 . -894) T) ((-679 . -798) T) ((-420 . -595) 28847) ((-1089 . -21) T) ((-128 . -596) NIL) ((-128 . -595) 28829) ((-1089 . -25) T) ((-648 . -370) 28813) ((-116 . -894) T) ((-846 . -225) 28797) ((-77 . -1182) T) ((-126 . -125) 28781) ((-1025 . -34) T) ((-1250 . -1012) 28755) ((-1248 . -1012) 28712) ((-1201 . -1028) T) ((-830 . -1028) T) ((-474 . -769) 28691) ((-348 . -1120) 28670) ((-345 . -1120) 28649) ((-337 . -1120) 28628) ((-474 . -772) 28579) ((-474 . -771) 28558) ((-221 . -34) T) ((-474 . -705) 28468) ((-59 . -481) 28452) ((-557 . -1028) T) ((-1141 . -170) 28343) ((-1094 . -170) 28254) ((-1032 . -1069) T) ((-1056 . -923) 28199) ((-926 . -1069) T) ((-795 . -626) 28150) ((-760 . -923) 28119) ((-692 . -1069) T) ((-758 . -923) 28086) ((-507 . -275) 28070) ((-648 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. -101) T) ((-309 . -933) 10466) ((-133 . -1081) T) ((-116 . -1081) T) ((-584 . -1226) 10450) ((-679 . -23) T) ((-584 . -1069) 10400) ((-90 . -505) 10333) ((-172 . -356) T) ((-309 . -94) 10312) ((-309 . -35) 10291) ((-590 . -481) 10225) ((-133 . -23) T) ((-116 . -23) T) ((-940 . -101) T) ((-697 . -1069) T) ((-467 . -481) 10162) ((-400 . -619) 10110) ((-631 . -1012) 10006) ((-932 . -481) 9990) ((-348 . -1028) T) ((-345 . -1028) T) ((-337 . -1028) T) ((-257 . -1028) T) ((-241 . -1028) T) ((-845 . -596) NIL) ((-845 . -595) 9972) ((-1251 . -21) T) ((-1239 . -595) 9938) ((-1238 . -595) 9904) ((-557 . -976) T) ((-710 . -705) T) ((-1251 . -25) T) ((-244 . -1021) 9834) ((-243 . -1021) 9764) ((-71 . -1182) T) ((-244 . -227) 9716) ((-243 . -227) 9668) ((-40 . -101) T) ((-884 . -1028) T) ((-1150 . -101) T) ((-1143 . -705) T) ((-1142 . -705) T) ((-1136 . -705) T) ((-1136 . -769) NIL) ((-1136 . -772) NIL) ((-928 . -101) T) ((-895 . -101) T) ((-1095 . -705) T) ((-749 . -101) T) ((-650 . -101) T) 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. -894) T) ((-795 . -300) 7651) ((-844 . -101) T) ((-760 . -225) 7635) ((-978 . -626) 7585) ((-932 . -279) 7562) ((-888 . -626) 7514) ((-615 . -21) T) ((-615 . -25) T) ((-589 . -21) T) ((-336 . -38) 7479) ((-672 . -703) 7446) ((-479 . -858) 7428) ((-479 . -860) 7410) ((-466 . -696) 7251) ((-211 . -858) 7233) ((-63 . -1182) T) ((-211 . -860) 7215) ((-589 . -25) T) ((-420 . -626) 7189) ((-479 . -1012) 7149) ((-846 . -505) 7061) ((-211 . -1012) 7021) ((-234 . -34) T) ((-974 . -1069) 6999) ((-1212 . -170) 6930) ((-1191 . -170) 6861) ((-691 . -143) 6840) ((-691 . -145) 6819) ((-679 . -130) T) ((-135 . -457) 6796) ((-636 . -634) 6780) ((-1116 . -595) 6712) ((-116 . -130) T) ((-469 . -1186) T) ((-590 . -586) 6688) ((-467 . -586) 6667) ((-329 . -328) 6636) ((-526 . -1069) T) ((-469 . -542) T) ((-1141 . -1021) T) ((-1094 . -1021) T) ((-829 . -1021) T) ((-234 . -769) 6615) ((-234 . -772) 6566) ((-234 . -771) 6545) ((-1141 . -319) 6522) ((-234 . -705) 6432) ((-932 . -19) 6416) ((-479 . -370) 6398) ((-479 . -331) 6380) ((-1094 . -319) 6352) ((-347 . -1235) 6329) ((-211 . -370) 6311) ((-211 . -331) 6293) ((-932 . -586) 6270) ((-1141 . -227) T) ((-642 . -1069) T) ((-624 . -1069) T) ((-1224 . -1069) T) ((-1155 . -1069) T) ((-1056 . -246) 6207) ((-348 . -1069) T) ((-345 . -1069) T) ((-337 . -1069) T) ((-257 . -1069) T) ((-241 . -1069) T) ((-83 . -1182) T) ((-127 . -101) 6185) ((-121 . -101) 6163) ((-128 . -34) T) ((-1155 . -592) 6142) ((-471 . -1069) T) ((-1110 . -1069) T) ((-471 . -592) 6121) ((-244 . -773) 6072) ((-244 . -770) 6023) ((-243 . -773) 5974) ((-40 . -1120) NIL) ((-243 . -770) 5925) ((-1049 . -894) 5876) ((-978 . -772) T) ((-978 . -769) T) ((-978 . -705) T) ((-945 . -772) T) ((-888 . -705) T) ((-90 . -481) 5860) ((-479 . -874) NIL) ((-884 . -1069) T) ((-219 . -1027) 5825) ((-846 . -283) T) ((-211 . -874) NIL) ((-811 . -1081) 5804) ((-58 . -1069) 5754) ((-510 . -1069) 5732) ((-507 . -1069) 5682) ((-488 . -1069) 5660) ((-487 . -1069) 5610) ((-564 . -101) T) ((-550 . -101) T) ((-486 . -101) T) ((-466 . -170) 5541) ((-352 . -894) T) ((-346 . -894) T) ((-338 . -894) T) ((-219 . -111) 5497) ((-811 . -23) 5449) ((-420 . -705) T) ((-107 . -894) T) ((-40 . -38) 5394) ((-107 . -798) T) ((-565 . -342) T) ((-509 . -342) T) ((-1191 . -505) 5254) ((-309 . -444) 5233) ((-306 . -444) T) ((-812 . -279) 5212) ((-332 . -130) T) ((-172 . -130) T) ((-287 . -25) 5076) ((-287 . -21) 4959) ((-45 . -1158) 4938) ((-65 . -595) 4920) ((-866 . -595) 4902) ((-584 . -505) 4835) ((-45 . -106) 4785) ((-1071 . -418) 4769) ((-1071 . -361) 4748) ((-1033 . -1182) T) ((-1032 . -1027) 4735) ((-926 . -1027) 4578) ((-1229 . -101) T) ((-1228 . -101) 4528) ((-473 . -1027) 4371) ((-642 . -696) 4355) ((-1032 . -111) 4340) ((-926 . -111) 4169) ((-469 . -356) T) ((-348 . -696) 4121) ((-345 . -696) 4073) ((-337 . -696) 4025) ((-257 . -696) 3874) ((-241 . -696) 3723) ((-1220 . -626) 3648) ((-1192 . -883) NIL) ((-1065 . -92) T) ((-1059 . -92) T) ((-917 . -629) 3632) ((-1043 . -92) T) ((-473 . -111) 3461) ((-1036 . -92) T) ((-1010 . -92) T) ((-917 . -366) 3445) ((-242 . -101) T) ((-993 . -92) T) ((-73 . -595) 3427) ((-937 . -47) 3406) ((-601 . -1081) T) ((-1 . -1069) T) ((-689 . -101) T) ((-677 . -101) T) ((-1213 . -626) 3303) ((-606 . -92) T) ((-1163 . -595) 3285) ((-1057 . -595) 3267) ((-126 . -481) 3251) ((-475 . -92) T) ((-1045 . -595) 3233) ((-383 . -23) T) ((-86 . -1182) T) ((-212 . -92) T) ((-1192 . -626) 3085) ((-884 . -696) 3050) ((-601 . -23) T) ((-590 . -595) 3032) ((-590 . -596) NIL) ((-467 . -596) NIL) ((-467 . -595) 3014) ((-502 . -1069) T) ((-498 . -1069) T) ((-344 . -25) T) ((-344 . -21) T) ((-127 . -302) 2952) ((-121 . -302) 2890) ((-579 . -626) 2877) ((-219 . -1021) T) ((-578 . -626) 2802) ((-372 . -976) T) ((-219 . -237) T) ((-219 . -227) T) ((-932 . -596) 2763) ((-932 . -595) 2675) ((-844 . -38) 2662) ((-1212 . -283) 2613) ((-1191 . -283) 2564) ((-1089 . -444) T) ((-493 . -825) T) ((-309 . -1108) 2543) ((-973 . -145) 2522) ((-973 . -143) 2501) ((-486 . -302) 2488) ((-288 . -1158) 2467) ((-469 . -1081) T) ((-845 . -1027) 2412) ((-603 . -101) T) ((-1168 . -481) 2396) ((-244 . -361) 2375) ((-243 . -361) 2354) ((-288 . -106) 2304) ((-1032 . -1021) T) ((-117 . -101) T) ((-926 . -1021) T) ((-845 . -111) 2233) ((-469 . -23) T) ((-473 . -1021) T) ((-1032 . -227) T) ((-926 . -319) 2202) ((-473 . -319) 2159) ((-348 . -170) T) ((-345 . -170) T) ((-337 . -170) T) ((-257 . -170) 2070) ((-241 . -170) 1981) ((-937 . -1012) 1877) ((-714 . -1012) 1848) ((-508 . -595) 1814) ((-1074 . -101) T) ((-1061 . -595) 1781) ((-1008 . -595) 1763) ((-1220 . -705) T) ((-1213 . -705) T) ((-1192 . -769) NIL) ((-167 . -1027) 1673) ((-1192 . -772) NIL) ((-884 . -170) T) ((-1192 . -705) T) ((-1241 . -149) 1657) ((-977 . -335) 1631) ((-974 . -505) 1564) ((-818 . -825) 1543) ((-550 . -1120) T) ((-466 . -283) 1494) ((-579 . -705) T) ((-354 . -595) 1476) ((-315 . -595) 1458) ((-411 . -1012) 1354) ((-578 . -705) T) ((-400 . -825) 1305) ((-167 . -111) 1201) ((-811 . -130) 1153) ((-716 . -149) 1137) ((-1228 . -302) 1075) ((-479 . -300) T) ((-372 . -595) 1042) ((-511 . -984) 1026) ((-372 . -596) 940) ((-211 . -300) T) ((-139 . -149) 922) ((-693 . -279) 901) ((-479 . -996) T) ((-564 . -38) 888) ((-550 . -38) 875) ((-486 . -38) 840) ((-211 . -996) T) ((-845 . -1021) T) ((-812 . -595) 822) ((-805 . -595) 804) ((-803 . -595) 786) ((-794 . -883) 765) ((-1252 . -1081) T) ((-1201 . -1027) 588) ((-830 . -1027) 572) ((-845 . -237) T) ((-845 . -227) NIL) ((-667 . -1182) T) ((-1252 . -23) T) ((-794 . -626) 497) ((-536 . -1182) T) ((-411 . -331) 481) ((-557 . -1027) 468) ((-1201 . -111) 277) ((-679 . -619) 259) ((-830 . -111) 238) ((-374 . -23) T) ((-1155 . -505) 30) ((-640 . -1069) T) ((-659 . -1069) T) ((-654 . -1069) T)) \ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 8d4faa5e..d0afd9e6 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
-(30 . 3431822559)
-(4345 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3431897904)
+(4347 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
|ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
|OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -307,8 +307,8 @@
|UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial|
|UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions|
|OrderedSemiGroup| |OrdSetInts| |OutputByteConduit&|
- |OutputByteConduit| |OutputForm| |OutputPackage| |OrderedVariableList|
- |OrdinaryWeightedPolynomials| |PadeApproximants|
+ |OutputByteConduit| |OutputBinaryFile| |OutputForm| |OutputPackage|
+ |OrderedVariableList| |OrdinaryWeightedPolynomials| |PadeApproximants|
|PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger|
|PAdicRational| |PAdicRationalConstructor| |Pair| |Palette|
|PolynomialAN2Expression| |ParametricPlaneCurveFunctions2|
@@ -469,653 +469,649 @@
|XPolynomial| |XPolynomialRing| |XRecursivePolynomial|
|ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
|IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |LyndonWordsList| |internal?| |and| |tanhIfCan|
- |isMult| |structuralConstants| |createNormalPoly| |mapdiv| |OMgetType|
- |createGenericMatrix| |conjugate| |externalList| |in?|
- |createNormalElement| |goodnessOfFit| |poisson| |bfEntry|
- |setProperties| |morphism| |setFormula!| |addMatch|
- |removeRedundantFactorsInPols| |setelt!| |pile| |exptMod| |PDESolve|
- |csch2sinh| |iicsch| |algebraic?| |factorial| |An| |epilogue|
- |composite| |first| |symmetric?| |antisymmetric?| |initiallyReduced?|
- |tryFunctionalDecomposition| |lazyResidueClass| SEGMENT |setlast!|
- |changeName| |palgLODE| |mkIntegral| |complexZeros|
- |leftMinimalPolynomial| |logical?| |critBonD| |rest| |cycles|
- |definingPolynomial| |mathieu11| |basisOfNucleus| |e01sef| |OMgetAttr|
- |linearPolynomials| |ranges| |substitute| |c06gqf| |f01mcf| |lambert|
- |viewPosDefault| |zoom| |deleteProperty!| |stoseInvertible?reg|
- |continuedFraction| |tanNa| |int| |removeDuplicates|
- |subscriptedVariables| |adaptive?| |integer?| |sortConstraints|
- |scalarMatrix| |denominators| |extractBottom!| |idealiser|
- |tableForDiscreteLogarithm| |factorSquareFree| |uncouplingMatrices|
- |mat| |inRadical?| |s17dcf| |triangSolve| |backOldPos| |associates?|
- |genericLeftNorm| |dimensionOfIrreducibleRepresentation|
- |patternMatchTimes| |hexDigit| |exprToXXP| |yellow| |getIdentifier|
- |seriesToOutputForm| |sturmVariationsOf| |airyAi| |pToDmp| |powers|
- |antiCommutator| |cothIfCan| |normDeriv2| |c02agf|
- |rootOfIrreduciblePoly| |yCoordinates| |vark| |checkPrecision|
- |realEigenvectors| |OMcloseConn| |queue| |lazyVariations| |divergence|
- |whatInfinity| |transcendentalDecompose| |coordinates| |low|
- |curryRight| |complexLimit| |linear| |irreducibleFactors| |showAll?|
- |paren| |typeList| |lazyPseudoQuotient| |nextsubResultant2| |zerosOf|
- |sec2cos| |recip| |setProperty| |iiasinh| |norm| |showTypeInOutput|
- |OMencodingBinary| |symmetricTensors| |linkToFortran| |headReduced?|
- |nthFractionalTerm| |setRow!| |btwFact| |LyndonWordsList1|
- |splitConstant| |sh| |strongGenerators| |polynomial| |critMTonD1|
- |UnVectorise| |viewport2D| |nor| |e01sff| |geometric|
- |exprHasWeightCosWXorSinWX| |bivariate?| |linGenPos| |fixedPointExquo|
- |cons| |hasHi| |f01qcf| |positive?| |separant| |numberOfHues|
- |leftFactor| |stoseInvertibleSetreg| |mapUnivariate| |light|
- |innerint| |exprToGenUPS| |deref| |hermite| |viewSizeDefault|
- |minimalPolynomial| |doublyTransitive?| |nextPrimitiveNormalPoly|
- |setrest!| |chebyshevU| |henselFact| |contract| |c05nbf| |shuffle|
- |sumOfSquares| |neglist| |and?| |property| |const| |exprToUPS|
- |OMgetBind| |isPlus| |symmetricDifference| |leftFactorIfCan|
- |unitCanonical| |iCompose| |branchPointAtInfinity?| |imagi| |notelem|
- |bright| |wholePart| |c05adf| |initTable!| |complexNumericIfCan|
- |paraboloidal| |iiatanh| |partition| |nthRoot| |addPointLast|
- |listOfMonoms| |tanIfCan| |factorsOfCyclicGroupSize| |orbit| |/\\|
- |subset?| |declare| |mapmult| |GospersMethod| |pmintegrate|
- |OMconnInDevice| |bracket| |rightCharacteristicPolynomial|
- |movedPoints| |units| |OMunhandledSymbol| |uniform01| |digit|
- |stFunc1| |iiacosh| |\\/| |associatedEquations| |minset|
- |removeRoughlyRedundantFactorsInPols| |source| |rootPoly| |laplacian|
- |integrate| |quoted?| |LowTriBddDenomInv| |tracePowMod|
- |pmComplexintegrate| |plenaryPower| |exquo| |red| |localAbs| |s15adf|
- |toScale| |e02zaf| |createNormalPrimitivePoly| |processTemplate|
- |firstNumer| ~= |squareFreePart| |zeroDimPrime?| |div|
- |bivariatePolynomials| |bounds| |write!| |c05pbf| |outputAsTex|
- |algintegrate| |SturmHabicht| |doubleRank| |LazardQuotient2| |d02raf|
- |coerce| |quo| |totalDegree| |pastel| |mirror| |curryLeft| |divisor|
- |difference| |ldf2lst| |resultantReduit| |dihedral| |delete|
- |getPickedPoints| |prepareDecompose| |construct| |bernoulliB|
- |mightHaveRoots| |iiacoth| |groebgen| |cAcos| |solveInField|
- |isobaric?| |varList| |rightZero| |code| |every?| |rename!|
- |changeWeightLevel| |integers| NOT |infieldint| |generators| |ref|
- |target| |numerator| |returnType!| |oneDimensionalArray| |iisec|
- |increment| |logpart| |setMinPoints3D| |vspace| |suchThat| OR |ode1|
- |shufflein| |removeRoughlyRedundantFactorsInPol| |leadingTerm|
- |monicRightDivide| |blue| |call| |notOperand| |s21baf| |cotIfCan|
- |eulerPhi| |less?| AND |exteriorDifferential| |OMgetEndAttr|
- |monicDecomposeIfCan| |compiledFunction| |algebraicVariables|
- |leastAffineMultiple| |octon| |OMreceive| |trim| |genericRightNorm|
- |removeSquaresIfCan| |leadingSupport| |ellipticCylindrical|
- |printingInfo?| |sumSquares| |monic?| |rationalPoint?| |addPoint2|
- |curry| |simplify| |f04arf| |OMputEndBVar| |universe| |isTimes|
- |nextSubsetGray| |e04dgf| |numeric| |viewDeltaYDefault|
- |leftCharacteristicPolynomial| |makeFR| |symmetricSquare| |check|
- |tab1| |floor| |pointColorPalette| |FormatArabic| |c06eaf|
- |nextSublist| |radical| |countRealRoots| |traceMatrix| |hessian|
- |d03edf| |normal01| |constantKernel| |permutationGroup| |deriv|
- |s15aef| |intersect| |sdf2lst| |palgintegrate| |multiset| |inR?|
- |LazardQuotient| |branchIfCan| |prefix| |mainValue| |stFunc2|
- |arrayStack| |iiasech| |abs| |cAsin| |resultantReduitEuclidean|
- |irreducible?| |firstDenom| |leftZero| |BumInSepFFE| |hspace|
- |quotedOperators| |test| |iifact| |useNagFunctions| |extendedint|
- |wronskianMatrix| |quadraticForm| |weakBiRank| |colorDef|
- |zeroDimPrimary?| |ratpart| |userOrdered?| |characteristicSerie|
- |read!| |totolex| |OMgetEndBind| |leftDivide| |argumentList!| |cap|
- |weights| |iicsc| |log10| |secIfCan| |genericRightTrace|
- |minimumDegree| |constantRight| |interReduce| |radicalEigenvectors|
- |writable?| |zeroSetSplitIntoTriangularSystems| |bitand| |sort| |any?|
- |charpol| |fibonacci| |OMsend| |f04asf| |eulerE| * |refine|
- |sequences| |makingStats?| |euclideanNormalForm| |corrPoly| |bitior|
- |plus| |oddintegers| |variable?| |minPoints3D| |htrigs|
- |unprotectedRemoveRedundantFactors| |lprop| |bivariateSLPEBR|
- |complement| |monicCompleteDecompose| |e04fdf| |deepestInitial|
- |associatedSystem| |musserTrials| |mappingAst| |ODESolve| |s21bbf|
- |setelt| |iiacos| |OMputEndError| |ode2| |prolateSpheroidal| |c06ebf|
- |SturmHabichtMultiple| |viewDeltaXDefault| |green| |d03eef| |addPoint|
- |split| |rectangularMatrix| |constantIfCan| |tab| |totalDifferential|
- |eq| |firstSubsetGray| |part?| |curveColorPalette| |getlo|
- |absolutelyIrreducible?| |replace| |reducedQPowers| |rightNorm|
- |startTableGcd!| |copy| |randomLC| |mainDefiningPolynomial|
- |shrinkable| |iter| |iiacsch| |overset?| |palginfieldint| |cCsc|
- |times| |random| |swap| |bandedHessian| |factor1| |diag|
- |mergeDifference| |superHeight| |isExpt| |limitedint| |s17acf|
- |semiResultantReduitEuclidean| |back| |mkAnswer| |ceiling|
- |compactFraction| |optimize| |exponential1| |rur| |largest| |subst|
- |ScanArabic| |OMgetEndBVar| |Beta| |match?| |variationOfParameters|
- |rightDivide| |genericRightMinimalPolynomial| |isList|
- |subResultantChain| |cscIfCan| |autoCoerce| |wordsForStrongGenerators|
- |characteristicSet| |rationalPoints| |gderiv| |width| |roughBasicSet|
- |endSubProgram| |zeroSetSplit| |iiasin| |openBinaryFile| |intensity|
- |OMserve| |multiplyExponents| |f04atf| |stFuncN| |setButtonValue|
- |minPol| |extractIfCan| |readable?| |euclideanGroebner| |monom|
- |ratPoly| |solve1| |decimal| |simplifyExp| |harmonic| |llprop|
- |iibinom| |cardinality| |radicalEigenvector| |lifting| |e04gcf|
- |biRank| |term| |iiatan| |stopMusserTrials| |primaryDecomp|
- |removeRedundantFactors| |expr| |iomode| |exp| |c06ecf| |permutations|
- |iteratedInitials| |countRealRootsMultiple| |identityMatrix| |cup|
- |constDsolve| |kovacic| |d03faf| |monomials| |OMputEndObject|
- |constantLeft| |latex| |divideIfCan| |gethi| |viewZoomDefault|
- |diagonal?| |common| |host| |merge| |numericIfCan| |stopTableGcd!|
- |mainForm| |lex| |middle| |oblateSpheroidal| |specialTrigs|
- |var1Steps| |cSec| |leftNorm| |minPoly| |tValues| |minimize|
- |subHeight| |cond| |objects| |clipPointsDefault|
- |solveLinearPolynomialEquationByRecursion| |bitLength| |integerIfCan|
- |optional| |front| |jacobian| |perfectNthPower?| |s21bcf|
- |squareFreePrim| |more?| |base| |variable| |ode| |OMgetEndError|
- |ParCond| |hermiteH| |divide| |halfExtendedSubResultantGcd2|
- |asinIfCan| |upperCase!| |rightRankPolynomial| |create| |directory|
- |iterators| |homogeneous?| |s17adf| |crushedSet| |factors|
- |reduceByQuasiMonic| |partialFraction| |genus| |makeop| |f04axf|
- |medialSet| |physicalLength!| |digamma| |insert!|
- |factorGroebnerBasis| |currentSubProgram| |lighting|
- |symmetricProduct| |simplifyLog| |jacobi| |lllp| |stop| |flatten|
- |isPower| |nonSingularModel| |internalIntegrate0| |exists?| |e04jaf|
- |summation| |next| |numberOfFactors| |chiSquare1| |iiacot|
- |certainlySubVariety?| |FormatRoman| |computeBasis| |c06ekf|
- |lifting1| |signatureAst| |subResultantsChain| |innerEigenvectors|
- |e01baf| |isOp| |name| |laplace| |OMputInteger| |compose|
- |radicalEigenvalues| |member?| |outputMeasure| |deepestTail|
- |repeating?| |body| |term?| |startTableInvSet!| |laurentIfCan|
- |rischDE| |slex| |setAttributeButtonStep| |atoms| |quasiRegular|
- |cCot| |viewPhiDefault| |showTheIFTable| |rootPower| |freeOf?|
- |module| |messagePrint| |iiperm| |localReal?| |noKaratsuba|
- |var2Steps| |rotate!| |deepCopy| |basisOfCommutingElements|
- |perfectNthRoot| |compdegd| |setVariableOrder| |close!| |tree|
- |bipolar| |internalIntegrate| |bitCoef| |laguerreL| |cn| |rightTrace|
- |wreath| |acosIfCan| |f04faf| |enterInCache| |drawToScale| |nil|
- |twist| |systemCommand| |rewriteSetByReducingWithParticularGenerators|
- |Lazard| |collectQuasiMonic| |leader| |bandedJacobian| |trueEqual|
- |opeval| |lllip| |Hausdorff| |roman| |OMgetEndObject| |redmat|
- |groebnerFactorize| |nthFactor| |localUnquote|
- |halfExtendedSubResultantGcd1| |tRange| |expandPower| |skewSFunction|
- |iiasec| |previous| |factorByRecursion| |s17aef| |interpretString|
- |e04mbf| |newSubProgram| |unary?| |gcdPrimitive| |modularFactor|
- |s21bdf| |moebiusMu| |trailingCoefficient| |extension| |makeCos|
- |approximate| |mpsode| |polygamma| Y |normal| |pop!| |clipSurface|
- |e01bef| |upperCase| |possiblyNewVariety?| |rischDEsys| |outerProduct|
- |algSplitSimple| |c06fpf| |balancedBinaryTree| |exprex| |factorials|
- |getZechTable| |stopTableInvSet!| |OMputFloat| |padecf|
- |wordInStrongGenerators| |coord| |enumerate| |measure2Result| |head|
- |close| |parseString| |operators| |symmetricPower| |inverse|
- |getVariableOrder| |quoByVar| |cTan| |eigenMatrix| |quasiRegular?|
- |viewThetaDefault| |top| |equiv| |approxNthRoot| |exponential|
- |rightRegularRepresentation| |rightTraceMatrix| |rischNormalize|
- |makeResult| |space| |dequeue!| |display| |satisfy?| |atanIfCan|
- |univcase| |f04jgf| |makeRecord| |infieldIntegrate| |insert|
- |karatsubaOnce| |bitTruth| |legendreP| |sayLength| |evaluateInverse|
- |laurentRep| |currentCategoryFrame| |mesh?| |bipolarCylindrical|
- |rewriteIdealWithQuasiMonicGenerators| |Lazard2| |removeZero| |expPot|
- |basisOfLeftAnnihilator| |expandLog| |iiacsc| |Frobenius| |adaptive|
- |OMgetInteger| |credPol| |nthExpon| |datalist| |formula| |equiv?|
- |SFunction| |useSingleFactorBound?| |cyclotomicDecomposition|
- |normalizeIfCan| |e04naf| |clearTheSymbolTable| |simpsono|
- |factorList| |e01bff| |numberOfDivisors| |monomRDE| |ParCondList|
- |dec| |shallowExpand| |push!| |input| |extractIndex| |plot|
- |stosePrepareSubResAlgo| |pade| |probablyZeroDim?| |s13aaf|
- |sylvesterMatrix| |coerceL| |library| |rightAlternative?| |mainKernel|
- |fortranCompilerName| |OMputVariable| |resetVariableOrder| |t|
- |composites| |att2Result| |mdeg| |leftScalarTimes!| |nrows|
- |leftTraceMatrix| |maxrow| |zeroVector| |entry| |cCos|
- |pointColorDefault| |rank| |routines| |ncols| |OMread| |subNodeOf?|
- |leftRegularRepresentation| |f04maf| |squareFreeLexTriangular|
- |tubePoints| |enqueue!| BY |ramified?| |doubleDisc| |ideal| |cyclic?|
- |consnewpol| |mesh| |realZeros| |contains?| |writeBytes!| |set|
- |fortranDouble| |putGraph| |rightMult| |hdmpToP| |iisinh|
- |currentScope| |getSyntaxFormsFromFile| |doubleResultant| |setnext!|
- |d02bbf| |expt| |polCase| |transcendenceDegree| |commonDenominator|
- |rowEchLocal| |numberOfImproperPartitions| |zeroDim?| |qPot|
- |predicates| |internalSubPolSet?| |cyclotomicFactorization| |baseRDE|
- |polar| |dflist| |supRittWu?| |impliesOperands| |setright!|
- |vectorise| |sumOfDivisors| |root| |completeHensel| |colorFunction|
- |cTanh| |lists| |trapezoidalo| |rootProduct| |eigenvector| |rule|
- |submod| |redpps| |idealSimplify| |reset| |clipParametric|
- |extractPoint| |coerceP| |expintfldpoly| |normalDenom| |setvalue!|
- |showSummary| |ravel| |s13acf| |rightLcm|
- |semiSubResultantGcdEuclidean2| |nextNormalPoly| |leftAlternative?|
- |gcdprim| |shade| |over| |prepareSubResAlgo| |reshape|
- |indicialEquationAtInfinity| |components| |removeCoshSq| |write|
- |rightScalarTimes!| |s19abf| |OMreadFile| |cosSinInfo| |weierstrass|
- |showAttributes| |save| |zeroSquareMatrix| |pascalTriangle| |resetNew|
- |polyred| |adaptive3D?| |complexNormalize| |iiexp| |makeCrit|
- |belong?| |log2| |e02daf| |mainSquareFreePart| |fortranReal| |nodeOf?|
- |palgextint0| |f02axf| |mainCharacterization| |rowEchelonLocal|
- |subSet| |show| |ramifiedAtInfinity?| |graphs| |precision| |d02bhf|
- |trivialIdeal?| |radicalSolve| |surface| |df2mf| |RittWuCompare|
- |setprevious!| |makeUnit| |internalInfRittWu?| |ran| |OMputError|
- |curveColor| |clearDenominator| |cCosh| |update| |trace| |lookup|
- |setleft!| |showArrayValues| |entry?| |bumprow| |constant|
- |cylindrical| |addmod| |definingInequation| |implies?|
- |generalizedEigenvector| |hasPredicate?| |primeFactor| |setchildren!|
- |multMonom| |leftExtendedGcd| |semiSubResultantGcdEuclidean1| |sup|
- |monomialIntegrate| |extend| |totalfract| |zag| |B1solve| |reduceLODE|
- |removeSinhSq| |traverse| |rootSimp| |nthRootIfCan|
- |internalLastSubResultant| |loopPoints| |s13adf| |rangePascalTriangle|
- |symFunc| |antiAssociative?| |powerSum| |OMreadStr| |virtualDegree|
- |qqq| |numberOfComposites| |bfKeys| |e02dcf| |times!| |gcdcofact|
- |complexElementary| |iilog| |f02bbf| |brillhartIrreducible?|
- |rationalApproximation| |unrankImproperPartitions0| |position|
- |mainPrimitivePart| |external?| |setScreenResolution3D| |palglimint0|
- |radicalRoots| |identitySquareMatrix| |ldf2vmf| |normalizedDivide|
- |padicFraction| |d02cjf| |s19acf| |highCommonTerms| |collectUpper| =
- |Ci| |cSinh| |mainMonomials| |isOpen?| |fortran| |graphStates|
- |internalSubQuasiComponent?| |updateStatus!| |indices| |OMputObject|
- |algebraicOf| |definingEquations| |move| |shanksDiscLogAlgorithm|
- |generalizedEigenvectors| |singular?| |node?| |bumptab| < |coordinate|
- |pointColor| |leftGcd| |eof?| |normal?| |monomialIntPoly| |reverse!|
- |nthFlag| |postfix| > |splitDenominator| |symmetricRemainder|
- |expandTrigProducts| |orOperands| |expIfCan| |showScalarValues|
- |pushdterm| |generalTwoFactor| <= |spherical|
- |generalizedContinuumHypothesisAssumed?| |discriminantEuclidean|
- |imagE| |OMlistCDs| |optional?| |conditionsForIdempotents|
- |integralLastSubResultant| >= |build| |sizePascalTriangle| |singRicDE|
- |f02bjf| |defineProperty| |trigs| |truncate| |loadNativeModule|
- |integralBasis| |factorset| |e02ddf| |symbolTableOf| |associative?|
- |rootKerSimp| |scalarTypeOf| |iisin| |contractSolve| |s14aaf| |vector|
- |relerror| |unrankImproperPartitions1| |power!| |elementary| |d02ejf|
- |mapCoef| |palgRDE0| |characteristic| + |numberOfComponents|
- |differentiate| |edf2ef| |maxint| |gcdcofactprim| |mainContent|
- |plusInfinity| |subQuasiComponent?| |index?| |collect|
- |wordInGenerators| - |brillhartTrials| |cAcsc| |mainCoefficients|
- |lift| |eigenvectors| |padicallyExpand| |minusInfinity|
- |screenResolution3D| |OMputEndApp| |child?| / |lSpaceBasis|
- |setStatus| |modifyPointData| |status| |reduce| |graphState|
- |inverseLaplace| |s19adf| |infix| |bumptab1| |Si| |clip|
- |leftExactQuotient| |reflect| |logIfCan| |extractSplittingLeaf|
- |nthExponent| |generalSqFr| |partitions| |positiveRemainder|
- |fintegrate| |script| |basis| |singularAtInfinity?| |OMlistSymbols|
- |genericRightDiscriminant| |pushucoef| |ReduceOrder|
- |fillPascalTriangle| |semiDiscriminantEuclidean| |or?| |makeMulti|
- |real?| |f02fjf| |toseLastSubResultant| |monicRightFactorIfCan|
- |e02def| |polyRicDE| |imagk| |fortranCarriageReturn| |solveRetract|
- |decomposeFunc| |localIntegralBasis| |matrix| |parabolic|
- |subresultantSequence| |argumentListOf| |tex| |type| |closeComponent|
- |d02gaf| |multiple?| |iicos| |nthCoef| |level| |leadingIndex|
- |vedf2vef| |complexSolve| |antiCommutative?|
- |removeSuperfluousQuasiComponents| |order| |palgLODE0| |entries|
- |error| |maxrank| |cAsec| |binaryFunction| |trace2PowMod| |gradient|
- |leftRank| |factorAndSplit| |collectUnder| |distance| |s14abf|
- |assert| |quasiAlgebraicSet| |leastMonomial| |element?| |double|
- |primitivePart!| |alternating| |iprint| |OMputEndAtp| |vconcat|
- |create3Space| |leftRemainder| |subspace| |numberOfFractionalTerms|
- |content| |lintgcd| |sinIfCan| |untab| |twoFactor| |finiteBasis|
- |clipBoolean| |coefficient| |lazyPseudoRemainder| |makeViewport2D|
- |leaves| |OMsupportsCD?| |setMaxPoints3D| |irreducibleFactor|
- |genericRightTraceForm| |Ei| |safeCeiling| |bit?| |reify| |s20acf|
- |complexForm| |pushuconst| |f02wef| |setref| |e02dff|
- |chainSubResultants| |normalElement| |fortranLiteral| |squareMatrix|
- |toseInvertible?| |unvectorise| |conjugates| |ricDsolve|
- |SturmHabichtSequence| |andOperands| |branchPoint?| |d02gbf|
- |binomThmExpt| |qualifier| |rightFactorIfCan| |df2st| |returnTypeOf|
- |makeTerm| |imagj| |orbits| |subCase?| |iitan| |key?| |id|
- |parabolicCylindrical| |complexRoots| |cAcot| |modifyPoint| |declare!|
- |rightOne| |mainVariable| |chineseRemainder| |nodes| |leadingExponent|
- |makeFloatFunction| |radicalSimplify| |commutative?| |elem?|
- |generic?| |hconcat| |mainVariable?| |currentEnv| |table| |s14baf|
- |leftQuotient| |mainMonomial| |cosIfCan| |terms| |OMputEndAttr|
- |setOrder| |new| |minrank| |coHeight| |makeViewport3D|
- |subresultantVector| |rightRank| |zero| |OMsupportsSymbol?|
- |genericLeftDiscriminant| |bat1| |outputAsScript| |style| |safeFloor|
- |jordanAdmissible?| |cyclic| |UpTriBddDenomInv| |nilFactor| |f02xef|
- |principal?| |algint| |e02gaf| |elColumn2!| |fortranLiteralLine| |hex|
- |And| |numberOfMonomials| |bubbleSort!| |null| |schema|
- |SturmHabichtCoefficients| |characteristicPolynomial|
- |selectSumOfSquaresRoutines| |d02kef| |Or| |maxPoints3D| |pomopo!|
- |toseInvertibleSet| |case| |LyndonCoordinates| |f2st| |triangulate|
- |gcdPolynomial| |oddInfiniteProduct| |s20adf| |Not|
- |removeSuperfluousCases| |symbolIfCan| |mainExpression| |Zero|
- |baseRDEsys| |cAtan| |printHeader| |drawCurves| |iicot| |leftOne|
- |transpose| |li| |rename| |One| |rubiksGroup| |realRoots|
- |denominator| |identity| |divisors| |rspace| |controlPanel| |point|
- |unaryFunction| |monicLeftDivide| |setFieldInfo| |schwerpunkt|
- |d01apf| |mainVariables| |getOrder| |partialDenominators|
- |quasiMonic?| |extendIfCan| |primes| |genericPosition| |startTable!|
- |genericLeftTraceForm| |implies| |OMputEndBind| |constructorName|
- |leftUnits| |safetyMargin| |viewport3D| |atrapezoidal| |minPoints|
- |solveLinearlyOverQ| |f04adf| |bat| |bsolve| |left| |series| |mr|
- |primitivePart| |categoryFrame| |s18adf| |regularRepresentation| |xor|
- |insertionSort!| |elt| |droot| |right| |modularGcdPrimitive|
- |numberOfCycles| |lieAdmissible?| |primextendedint| |setCondition!|
- |mapExponents| |members| |goto| |semiIndiceSubResultantEuclidean|
- |invmultisect| |fractionFreeGauss!| |normalizeAtInfinity|
- |OMReadError?| |argument| |toseSquareFreePart| |LyndonBasis|
- |quadraticNorm| |rightGcd| |selectFiniteRoutines| |duplicates?|
- |yCoord| |normInvertible?| |numer| |weighted| |min| |float| |cot2tan|
- |torsion?| |standardBasisOfCyclicSubmodule| |direction| |radix| |nil?|
- |denom| |youngGroup| |rules| |heapSort| |explicitlyFinite?| |scale|
- |anfactor| |topPredicate| |decreasePrecision| |presuper| |viewpoint|
- |retract| |bezoutMatrix| |drawComplexVectorField| |dictionary|
- |d01aqf| |karatsubaDivide| |leftRecip| |getCurve| |pi| |iroot|
- |edf2fi| |modularGcd| |complex| |pol| |setErrorBound| |stopTable!|
- |lepol| |invertible?| |infinity| |partialNumerators| |cAtanh|
- |degreeSubResultant| |systemSizeIF| |boundOfCauchy| |selectsecond|
- |setProperties!| |lfunc| |f02adf| |tubeRadiusDefault| |compBound|
- |rightExactQuotient| |acothIfCan| |groebner?| |extendedResultant|
- |expextendedint| |romberg| |parametric?| |key| |changeNameToObjf|
- |quadratic| |dmp2rfi| |cyclePartition| |coth2tanh| |hdmpToDmp|
- |constantToUnaryFunction| |pointData| |s18aef| |zCoord| |BasicMethod|
- |depth| |kernel| |f07aef| |shellSort| |multisect| |npcoef|
- |jacobiIdentity?| |filename| |OMUnknownSymbol?| |setValue!| F2FG
- |remainder| |draw| |infinityNorm| |curve?| |symbol| |meshPar1Var| GE
- |infiniteProduct| |complementaryBasis| |invertIfCan| |not?|
- |createThreeSpace| |OMsetEncoding| |randnum| |basisOfLeftNucloid|
- |repeatUntilLoop| |expression| |lazyPremWithDefault| GT
- |numberOfNormalPoly| |fortranCharacter| |selectODEIVPRoutines|
- |mapGen| |parse| |presub| |buildSyntax| |setRealSteps|
- |zeroDimensional?| |normFactors| |integer| LE |condition|
- |explicitEntries?| |torsionIfCan| |d01asf| |areEquivalent?|
- |increasePrecision| |listLoops| |reduction| |rdHack1| |nextItem| LT
- |maxRowIndex| |label| |connect| |setTopPredicate| |supDimElseRittWu?|
- |prinshINFO| |leftPower| |makeObject| |bezoutResultant| |lexGroebner|
- |signature| |degreeSubResultantEuclidean| |noLinearFactor?| |dioSolve|
- |getProperties| |monicDivide| |f02aef| |invertibleElseSplit?|
- |dimensions| |edf2df| |rightRemainder| |escape| |xn| |rootSplit|
- |primlimitedint| |cubic| |dimension| |coef| |reducedContinuedFraction|
- |cAcosh| |removeCosSq| |trunc| |interpret| |startPolynomial|
- |selectfirst| |rCoord| |lhs| |optAttributes| |tubePlot| |tablePow|
- |outputSpacing| |asechIfCan| |expenseOfEvaluationIF| |inHallBasis?|
- |simpson| |OMUnknownCD?| |rhs| |PollardSmallFactor| |explogs2trigs|
- |se2rfi| |ptFunc| |coerceListOfPairs| |groebnerIdeal| |parent|
- |plotPolar| |cyclicParents| |headRemainder| |reseed| |f07fdf|
- |lazyPquo| |revert| |pToHdmp| |powerAssociative?|
- |fortranDoubleComplex| |s18aff| |OMputApp| |super| |curve| |nand|
- |scaleRoots| |listexp| |arguments| |copy!| |d01bbf| |empty?| |solve|
- |closed?| |basisOfRightNucloid| |whileLoop| |setImagSteps| |search|
- |evenInfiniteProduct| |selectPDERoutines| |integral?| |algebraicSort|
- |bits| |prindINFO| |fglmIfCan| |expenseOfEvaluation| |signAround|
- |createIrreduciblePoly| |setProperty!| |getGoodPrime| |mapExpon|
- |index| |rightPower| |f02aff| |node| |operator| |cAsinh|
- |semiDegreeSubResultantEuclidean| |matrixDimensions| |region|
- |explimitedint| |isAbsolutelyIrreducible?|
- |purelyAlgebraicLeadingMonomial?| |quartic| |totalGroebner|
- |rightQuotient| |acschIfCan| |minRowIndex| |newLine| |option|
- |exponentialOrder| |patternVariable| |thetaCoord| |erf| |crest|
- |resize| |coercePreimagesImages| |removeSinSq| |insertRoot!|
- |dAndcExp| |OMParseError?| |pair| |divideExponents| |Nul|
- |trigs2explogs| |push| |outputGeneral| |log| |compile|
- |generalLambert| |ord| |makeprod| |ratDenom| |cyclicEqual?|
- |showTheFTable| |seed| |solveid| |Aleph| |minimumExponent| |degree|
- |cycleElt| |trapezoidal| |fortranComplex| |dilog| |sub|
- |roughUnitIdeal?| |pr2dmp| |shiftRoots| |lazyPrem| |reorder|
- |extractProperty| |d01fcf| |OMputAtp| |sin| |open?| |setClipValue|
- |f07fef| |function| |e02bbf| |alternative?| |fprindINFO| |debug3D|
- |moreAlgebraic?| |triangularSystems| |cos| |invmod| |point?|
- |nextColeman| |rightTrim| |comparison| |plus!| |unitNormalize|
- |s18dcf| |f02agf| |tan| |unknown| |numberOfOperations| |forLoop|
- |lastSubResultantEuclidean| |leftTrim| |getProperty|
- |selectOptimizationRoutines| |derivationCoordinates| |splitNodeOf!|
- |aLinear| |cot| |groebner| |outputFixed| |cCsch| |completeEval|
- |badNum| |integralAtInfinity?| |primextintfrac|
- |algebraicCoefficients?| |sec| |midpoint| |maximumExponent| |pushdown|
- |swap!| |points| |commutativeEquality| |phiCoord| |csc| |cfirst|
- |derivative| |listRepresentation| |pquo| |copies| |exponents|
- |OMwrite| |meatAxe| |rational| |asin| |bindings| |binaryTournament|
- |evenlambert| |repSq| |clearTheFTable| |withPredicates|
- |cyclicEntries| |rarrow| |acos| |testModulus| |unravel| |option?|
- |fortranLogical| |equivOperands| |unmakeSUP| |roughEqualIdeals?|
- |atan| |setClosed| |degreePartition| |hasoln| |powmod| |equation|
- |computeCycleLength| |rombergo| |pattern| |prinpolINFO| |d01gaf|
- |OMputAttr| |acot| |s01eaf| |e02bcf| |semiLastSubResultantEuclidean|
- |destruct| |headAst| |extractClosed| |f02ajf| |subTriSet?| |asec|
- |rootDirectory| |initial| |enterPointData| |changeVar|
- |nextLatticePermutation| |equality| |isQuotient| |flexible?| |unit|
- |s18def| |clearCache| |aQuadratic| |acsc| |sin?| |edf2efi| |subscript|
- |scopes| |minus!| |lowerPolynomial| |numFunEvals3D| |one?| |sinh|
- |byte| |lexTriangular| |lcm| |cSech| |primlimintfrac| |message|
- |selectIntegrationRoutines| |fill!| |remove!| |purelyTranscendental?|
- |cosh| |midpoints| |binding| |pushup| |monomial|
- |integralBasisAtInfinity| |mix| |color| |rational?| |tanh| |sts2stst|
- |outputFloating| |dark| |append| |permanent| |multivariate| |iisqrt2|
- |getGraph| |leftMult| |po| |assign| |coth| |rowEch| |remove| |fmecg|
- |gcd| |oddlambert| |variables| |height| |fTable| |scanOneDimSubspaces|
- |cyclicCopy| |sech| |tube| |constantOperator| |leviCivitaSymbol|
- |false| |prem| |vertConcat| |fortranInteger| |prinb| |setPredicates|
- |roughSubIdeal?| |csch| |cartesian| |last| |binaryTree|
- |factorOfDegree| |getMeasure| |d01gbf| |f02akf| |makeSUP| |OMputBind|
- |asinh| |assoc| |HenselLift| |range| |e02bdf| |conditionP|
- |computeCycleEntry| |subPolSet?| |aCubic| |acosh| |hostPlatform|
- |mulmod| |comp| |nextPartition| |qelt| |magnitude| |eigenvalues|
- |raisePolynomial| |heap| |flagFactor| |atanh| |expressIdealMember|
- |dfRange| |subResultantGcdEuclidean| |#| |taylor| |logGamma|
- |primintfldpoly| |minIndex| |s19aaf| |splitSquarefree| |acoth|
- |denomLODE| |cCoth| |ratDsolve| |xRange| |laurent| |imports|
- |setAdaptive3D| |hue| |rationalIfCan| |purelyAlgebraic?| |asech|
- |root?| |reducedDiscriminant| |scripted?| |yRange| |puiseux|
- |firstUncouplingMatrix| |slash| |clikeUniv| |setLabelValue|
- |subtractIfCan| |kroneckerDelta| |zRange| |say| |tower| |getMatch|
- |rk4a| |endOfFile?| |concat| |iisqrt3| |multiple| |unitVector|
- |meshPar2Var| |position!| |factorsOfDegree| |map!| |inv| |character?|
- |lazyGintegrate| |subResultantGcd| ~ |applyQuote| |critpOrder|
- |palgint0| |reverse| |monicModulo| |qsetelt!| |exp1| |e02bef|
- |ground?| |balancedFactorisation| |divisorCascade| |c06gsf| |f02awf|
- |roughBase?| |mathieu12| |multinomial| |ground| |open| |pointLists|
- |symbol?| F |OMputBVar| |aQuartic| |basisOfCenter| |rotate|
- |extractTop!| |categories| |leadingMonomial| |associatorDependence|
- |setScreenResolution| |univariateSolve| |normalDeriv| |ruleset|
- |nativeModuleExtension| |numerators| |has?|
- |irreducibleRepresentation| |leadingCoefficient| |horizConcat|
- |complexNumeric| |getConstant| |s17def| |sqfrFactor| |maxIndex|
- |genericLeftTrace| |idealiserMatrix| |sechIfCan| |primitiveMonomials|
- |changeMeasure| |removeConstantTerm| |airyBi| |principalIdeal|
- |commutator| |infinite?| |acsch| |reductum| |kernels|
- |solveLinearPolynomialEquation| |inverseIntegralMatrixAtInfinity|
- |lazyIrreducibleFactors| |parametersOf| |stronglyReduced?|
- |indicialEquations| |bernoulli| |sech2cosh| |cross| |univariate|
- |limit| |OMencodingSGML| |setLegalFortranSourceExtensions| |critMonD1|
- |nary?| |leaf?| |e02adf| |internalDecompose| |multiplyCoefficients|
- |hypergeometric0F1| |tensorProduct| |readIfCan!| |Vectorise| |f01qdf|
- |find| |getCode| |singularitiesOf| |stoseInvertible?| |distdfact|
- |sequence| |doubleComplex?| |failed?| |negative?| |completeHermite|
- |meshFun2Var| |knownInfBasis| |lyndonIfCan| |exprHasAlgebraicWeight|
- |center| |integral| |hash| |factor| |d01ajf| |resultant|
- |basisOfCentroid| |viewDefaults| |graeffe| |insertBottom!|
- |lazyPseudoDivide| |ridHack1| |symbolTable| |mapUnivariateIfCan| |rem|
- |count| |fixedPoint| |rk4qc| |sqrt| |splitLinear| |string?|
- |multiEuclidean| |mantissa| |mathieu22| |checkRur|
- |rightFactorCandidate| |cycle| |cyclotomic| |power| |round| |real|
- |makeGraphImage| |realSolve| |unitNormal| |taylorQuoByVar|
- |pushFortranOutputStack| |drawStyle| |cschIfCan| |setfirst!|
- |lagrange| |OMgetBVar| |mapDown!| |imag| |select!| |screenResolution|
- |complete| |fractRadix| |convergents| |popFortranOutputStack|
- |moduleSum| |finite?| |central?| |printInfo!| |permutation|
- |directProduct| |mkPrim| |s17dgf| |OMconnOutDevice| |prod|
- |genericLeftMinimalPolynomial| |associator| |sin2csc|
- |outputAsFortran| |sizeMultiplication| |generalPosition| |lieAlgebra?|
- |removeIrreducibleRedundantFactors| |subNode?| |fortranTypeOf|
- |reduced?| |LagrangeInterpolation| |someBasis| |chebyshevT|
- |charClass| |sylvesterSequence| |squareTop| |integralMatrixAtInfinity|
- |OMencodingXML| |fracPart| |redPo| |indicialEquation| |e02aef|
- |decompose| |c02aff| |halfExtendedResultant2| |changeThreshhold|
- |linearlyDependent?| |readLineIfCan!| |setPoly| |f01qef| |outputForm|
- |polynomialZeros| |stoseInvertibleSet| |showAllElements| |high|
- |factorSquareFreePolynomial| |complex?| |permutationRepresentation|
- |zero?| |smith| |printCode| |insertTop!| |lyndon| |objectOf|
- |monomial?| |dot| |d01akf| |optpair| |radicalOfLeftTraceForm|
- |viewWriteDefault| |goodPoint| |mathieu23| |cAcsch| |interpolate|
- |exprHasLogarithmicWeights| |parts| |rotatez| |list?| |discriminant|
- |simpleBounds?| |extendedEuclidean| |operation|
- |createPrimitiveNormalPoly| |outlineRender| |measure| |asinhIfCan|
- |mapMatrixIfCan| |not| |inc| |iterationVar| |pleskenSplit|
- |positiveSolve| |lfextendedint| |iExquo| |approximants| |continue|
- |pureLex| |cycleSplit!| |zeroMatrix| |euler| |rk4f| |delete!|
- |graphImage| |pole?| |wholeRadix| |leftRankPolynomial|
- |complexEigenvalues| |sinh2csch| |square?| |OMgetError|
- |primitiveElement| |intPatternMatch| |setMaxPoints| |OMconnectTCP|
- |overlabel| |psolve| |sort!| |upDateBranches|
- |initializeGroupForWordProblem| |startStats!| |sincos| |s17dhf|
- |normalForm| |empty| |normalized?| |denomRicDE| |f2df| |e02agf|
- |getMultiplicationMatrix| |univariatePolynomial| |stack| |mapUp!|
- |OMencodingUnknown| |infLex?| |polyPart| |hMonic| |coefficients|
- |alphanumeric?| |sample| |lyndon?| |stoseSquareFreePart| |elliptic?|
- |failed| |stirling1| |inverseIntegralMatrix| |readLine!| |exponent|
- |f01rcf| |printStatement| |bottom!| |nullSpace| |quotient| |rquo|
- |jordanAlgebra?| |double?| |linearDependence| |keys| |augment|
- |completeSmith| |distFact| |bothWays| |coerceImages|
- |combineFeatureCompatibility| |sturmSequence| |elRow1!| |d01alf|
- |completeEchelonBasis| |euclideanSize| |viewWriteAvailable| |nothing|
- |polyRDE| |cAsech| |concat!| |mapBivariate| |halfExtendedResultant1|
- |selectMultiDimensionalRoutines| |getBadValues| |pair?| |linearMatrix|
- |getStream| |nullary?| |beauzamyBound| |delay| |acoshIfCan|
- |fixedDivisor| |lp| |predicate| |factorPolynomial| |pseudoRemainder|
- |squareFree| |lflimitedint| |cycleRagits| |mathieu24|
- |complexEigenvectors| |totalLex| |domainOf| |OMgetObject| |scan|
- |constantOpIfCan| |sn| |overbar| |listBranches| |properties| |brace|
- |diagonals| |preprocess| |tan2trig| |chvar| |printStats!| |any|
- |rotatey| |reciprocalPolynomial| |primintegrate| |OMbindTCP|
- |quasiComponent| |ptree| |reducedForm| |ef2edf| |copyInto!|
- |translate| |getMultiplicationTable| |nextIrreduciblePoly| |updatF|
- |readBytes!| |groebSolve| |omError| |sum| |compound?| |generic|
- |numberOfComputedEntries| |e02ahf| |frst| |aromberg| |maxPoints|
- |changeBase| |fullPartialFraction| |f01rdf| |wrregime| |nullity|
- |coleman| |column| |arg1| |nextPrime| |s17dlf| |writeLine!| |exQuo|
- |diophantineSystem| |makeSketch| |top!| |fixedPoints| |value|
- |lowerCase?| |arg2| |sinhcosh| |ffactor| |setEmpty!| |sizeLess?|
- |lastSubResultant| |leadingCoefficientRicDE| |reverseLex| |cycleTail|
- |lquo| |setleaves!| |inspect| |d01amf| |getRef| |var1StepsDefault|
- |argscript| |bombieriNorm| |tanh2trigh| |sparsityIF| |parameters|
- |stirling2| |conditions| |integralMatrix| |atom?| |linearPart|
- |prefixRagits| |block| |sorted?| |normalizedAssociate| |fullDisplay|
- |noncommutativeJordanAlgebra?| |match| |solveLinear|
- |linearlyDependentOverZ?| |lfinfieldint| |prime| |identification|
- |e02ajf| |internalZeroSetSplit| |laguerre| |elRow2!| |dn|
- |createRandomElement| |triangular?| |initials| |repeating| |ocf2ocdf|
- |monomRDEsys| |or| |inverseColeman| |OMgetEndApp| |expintegrate|
- |selectNonFiniteRoutines| |resetBadValues| |outputList| |sPol|
- |OMopenFile| |arity| |bag| |dequeue| |clearTable!|
- |squareFreePolynomial| |errorInfo| |shiftLeft| |f01ref| |getOperands|
- |setColumn!| |janko2| |innerSolve| |rst| |primitive?| |clipWithRanges|
- |graphCurves| |integerBound| |companionBlocks| |setPosition| |csubst|
- |binarySearchTree| |axes| |indiceSubResultant| |rowEchelon|
- |lazyEvaluate| |nextNormalPrimitivePoly| |rotatex| |rootRadius| |sign|
- |simplifyPower| |primeFrobenius| |partialQuotients| |box| |leftLcm|
- |odd?| |row| |readByteIfCan!| |qfactor| |testDim| |makeSeries|
- |moebius| |substring?| |rightUnits| |tan2cot| |cycleLength|
- |upperCase?| |void| |asimpson| |d01anf| |setMinPoints| |fractRagits|
- |lastSubResultantElseSplit| |rdregime| |LiePoly| |rootBound|
- |mindegTerm| |prevPrime| |s18acf| |null?| |quote| |var2StepsDefault|
- |suffix?| |inrootof| |e02akf| |normalize|
- |stiffnessAndStabilityFactor| |setStatus!| |linearDependenceOverZ|
- |nonLinearPart| |basicSet| |delta| |constantCoefficientRicDE|
- |listYoungTableaus| |internalAugment| |relationsIdeal|
- |leadingBasisTerm| |extract!| |sncndn| |updatD| |lfintegrate|
- |prefix?| |superscript| |recolor| |socf2socdf| |legendre|
- |physicalLength| |reduceBasisAtInfinity| |tanintegrate| |length|
- |f02aaf| |rewriteIdealWithRemainder| |returns| |makeEq| |even?|
- |OMgetEndAtp| |ScanRoman| |reducedSystem| |errorKind| |scripts|
- |OMopenString| |particularSolution| |indiceSubResultantEuclidean|
- |cycleEntry| |usingTable?| |rroot| |xCoord| |cyclicSubmodule|
- |number?| |getOperator| |clearTheIFTable| |obj| |singleFactorBound|
- |rightExtendedGcd| |numberOfIrreduciblePoly| |addiag|
- |hasTopPredicate?| |nonQsign| |generalizedContinuumHypothesisAssumed|
- GF2FG |shallowCopy| |cache| |outputArgs| |tanh2coth| |lazy?|
- |resetAttributeButtons| |UP2ifCan| |shiftRight| |discreteLog|
- |wholeRagits| |leftTrace| |quickSort| |possiblyInfinite?|
- |maxColIndex| |iipow| |rightRecip| |supersub| |lambda| |duplicates|
- |infix?| |df2fi| |e02baf| |alphabetic?| |reopen!| |shift| |regime|
- |stripCommentsAndBlanks| |invertibleSet| |infRittWu?| ** |mask|
- |extendedSubResultantGcd| |char| |cAcoth| |makeYoungTableau| |product|
- |setsubMatrix!| |makeSin| |s17aff| |printInfo| |minGbasis|
- |tubePointsDefault| |symmetricGroup| |drawComplex| |atanhIfCan|
- |stiffnessAndStabilityOfODEIF| |recoverAfterFail| |c06fqf| |Gamma|
- |quadratic?| |f02abf| |showClipRegion| |saturate| EQ
- |factorSquareFreeByRecursion| |hyperelliptic| |setOfMinN|
- |lfextlimint| |mapSolve| |init| |mkcomm| |perfectSquare?| |lowerCase!|
- |eval| |dmpToHdmp| UP2UTS |anticoord| |constant?| |seriesSolve|
- |rewriteIdealWithHeadRemainder| |dim| |unparse| |createZechTable|
- |acotIfCan| |numberOfPrimitivePoly| |ignore?| |realElementary|
- |retractIfCan| |normalise| FG2F |OMclose| |merge!| |directSum|
- |evaluate| |explicitlyEmpty?| |flexibleArray| |limitedIntegrate| |is?|
- |kind| |iFTable| |chiSquare| |cos2sec| |minColIndex|
- |ScanFloatIgnoreSpaces| |squareFreeFactors| |karatsuba|
- |nextsousResultant2| |initiallyReduce| |useSingleFactorBound|
- |numberOfChildren| |op| |addBadValue| |hexDigit?| |toroidal| |qroot|
- |accuracyIF| |OMgetFloat| |redPol| |overlap| |removeDuplicates!|
- |e01bgf| |rationalPower| |LiePolyIfCan| |lazyIntegrate| |figureUnits|
- |setPrologue!| |e04ucf| |showTheSymbolTable| |exactQuotient!|
- |basisOfRightAnnihilator| |stoseInternalLastSubResultant|
- |getButtonValue| |iiGamma| |sqfree| |deepExpand| |minordet|
- |alternatingGroup| |distribute| |listConjugateBases|
- |selectPolynomials| |prime?| |iidsum| |generator| |recur| |c06frf|
- |s17agf| |segment| |iflist2Result| |coerceS| |showRegion|
- |perfectSqrt| |pointPlot| |rightDiscriminant| |OMputString|
- |rightUnit| |fractionPart| |elements| |besselJ| |cSin| |mvar|
- |polarCoordinates| |fortranLinkerArgs| |asecIfCan| |f04mbf| |tableau|
- |subMatrix| |elliptic| |mindeg| |quatern| |lineColorDefault| |binary|
- |conjug| |union| |lowerCase| |nsqfree| |polygon?| |validExponential|
- |showTheRoutinesTable| |intcompBasis| |map| |tubeRadius|
- |writeByteIfCan!| |resultantEuclidean| |createMultiplicationTable|
- |cosh2sech| |iicosh| |pushNewContour| |randomR| |extendedIntegrate|
- |gramschmidt| |inf| |headReduce| |second| |showIntensityFunctions|
- |countable?| |solveLinearPolynomialEquationByFractions| |quotientByP|
- |extensionDegree| UTS2UP |Is| |univariatePolynomialsGcds| |gbasis|
- |resultantnaif| |third| |children| |useEisensteinCriterion?|
- |factorFraction| |rangeIsFinite| |rationalFunction| |computeInt|
- |options| |OMgetVariable| |separate| |e04ycf| |hcrf|
- |linearAssociatedLog| |comment| |e01bhf| |badValues|
- |leftDiscriminant| |sumOfKthPowerDivisors| |elseBranch| |conical|
- |setTex!| |determinant| |printTypes| |linears|
- |stoseIntegralLastSubResultant| |dominantTerm| |f04mcf|
- |selectOrPolynomials| |lo| |iiabs| |ScanFloatIgnoreSpacesIfCan|
- |putColorInfo| |convert| |pdf2ef| |clearFortranOutputStack|
- |exactQuotient| |basisOfLeftNucleus| |functionIsFracPolynomial?|
- |OMputSymbol| |polygon| |incr| |froot| |string| |c06fuf|
- |inconsistent?| |cLog| |frobenius| |dom| |abelianGroup| |matrixGcd|
- |approxSqrt| |size?| |listOfLists| |hi| |nlde| |s17ahf|
- |replaceKthElement| |imagK| |relativeApprox| |hitherPlane|
- |calcRanges| |acscIfCan| |iitanh| |createLowComplexityNormalBasis|
- |decrease| |besselY| |maxdeg| |blankSeparate| |axesColorDefault|
- |imaginary| |aspFilename| |adjoint| |reindex| |palgextint| |iidprod|
- |rootNormalize| |integralDerivationMatrix| |weight| |stronglyReduce|
- |packageCall| |KrullNumber| |cot2trig| |intChoose| |univariate?|
- |leftUnit| |varselect| |choosemon| |critT| |qinterval|
- |semiResultantEuclidean2| |createMultiplicationMatrix|
- |useEisensteinCriterion| |moduloP| |findBinding| |swapColumns!|
- |OMgetString| |orthonormalBasis| |f01brf| |resultantEuclideannaif|
- |hasSolution?| |expint| |e01daf| |title| |taylorIfCan|
- |inGroundField?| |deleteRoutine!| |addMatchRestricted|
- |removeRoughlyRedundantFactorsInContents| |hclf| |diagonalProduct|
- |child| |uniform| |stoseLastSubResultant|
- |functionIsContinuousAtEndPoints| |represents| |factorSFBRlcUnit|
- |setEpilogue!| |pseudoDivide| |pdf2df| |newTypeLists|
- |linearAssociatedOrder| |problemPoints| |retractable?|
- |HermiteIntegrate| |f04qaf| LODO2FUN |zeroOf| |modTree|
- |showFortranOutputStack| |cExp| |e| |ddFact| |generateIrredPoly|
- |limitPlus| |selectAndPolynomials| |closedCurve?| |checkForZero|
- |bringDown| |appendPoint| |computePowers| |imagJ|
- |primPartElseUnitCanonical!| |basisOfRightNucleus| |sinhIfCan| |eq?|
- |OMgetApp| |thenBranch| |c06gbf| |numFunEvals| |semicolonSeparate|
- |rootOf| |divideIfCan!| |cyclicGroup| |getDatabase| |result| |iicoth|
- |tanSum| |nthr| |s17ajf| |incrementKthElement|
- |rewriteSetWithReduction| |unitsColorDefault| |eyeDistance|
- |dimensionsOf| |coth2trigh| |representationType| |palglimint|
- |numericalIntegration| |max| |besselI| |RemainderList| |makeVariable|
- |critM| |debug| |solid| |eisensteinIrreducible?| |fixPredicate|
- |findCycle| |alphanumeric| |univariatePolynomials| |generate| |tanQ|
- |powern| |integralRepresents| |tail| |interval| |f01bsf| D
- |applyRules| |innerSolve1| |e01saf| |numberOfVariables| |coefChoose|
- |modulus| |output| |increase| |kmax| |transform|
- |semiResultantEuclideannaif| |diagonal| |semiResultantEuclidean1|
- |createLowComplexityTable| |stoseInvertible?sqfreg| |contours|
- |removeZeroes| |incrementBy| |ipow| |OMgetSymbol|
- |antisymmetricTensors| |df2ef| |lexico| |nextPrimitivePoly| |diff|
- |complexExpand| |linSolve| |mergeFactors| |transcendent?|
- |createPrimitivePoly| |expand| |rightMinimalPolynomial| |insertMatch|
- |removeRedundantFactorsInContents| |list| |cRationalPower| |typeLists|
- |nullary| |birth| |coshIfCan| |binomial| |functionIsOscillatory|
- |f07adf| |topFortranOutputStack| |filterWhile| |swapRows!| |car|
- |prologue| |pseudoQuotient| |matrixConcat3D| |imagI|
- |linearAssociatedExp| |numericalOptimization| |ListOfTerms| |palgint|
- |closedCurve| |filterUntil| |rootsOf| |charthRoot|
- |multiEuclideanTree| |cdr| |pow| |commaSeparate| |separateFactors|
- |csc2sin| |split!| |bezoutDiscriminant| |quasiMonicPolynomials|
- |intermediateResultsIF| |select| |newReduc| |getExplanations|
- |component| |setDifference| |allRootsOf| |autoReduced?|
- |primPartElseUnitCanonical| |basisOfMiddleNucleus|
- |tryFunctionalDecomposition?| |iisech| |OMgetAtp| |critB|
- |setIntersection| RF2UTS |c06gcf| |setAdaptive| |leadingIdeal|
- |pointSizeDefault| |digit?| |dihedralGroup| |leastPower| |e01sbf|
- |palgRDE| |tanAn| |doubleFloatFormat| |finiteBound| |setUnion|
- |s17akf| |float?| |f01maf| |dmpToP| |perspective| |restorePrecision|
- |stoseInvertibleSetsqfreg| |createPrimitiveElement| |linear?|
- |generalizedInverse| |unit?| |apply| |besselK| |unexpand|
- |realEigenvalues| |diagonalMatrix| |print| |solid?|
- |differentialVariables| |algebraicDecompose| |alphabetic| |digits|
- |callForm?| |rk4| |fi2df| |integralCoordinates|
- |generalInfiniteProduct| |pdct| |complexIntegrate| |algDsolve| |true|
- |patternMatch| |myDegree| |taylorRep| |radPoly| |ksec| |port| |pack!|
- |size| |cPower| |OMmakeConn| |separateDegrees| |nil| |infinite|
+ |Record| |Union| |fracPart| |traverse| |prindINFO|
+ |selectOrPolynomials| |drawToScale| |partialQuotients|
+ |outputAsScript| |rootSimp| |redPo| |low| |iiabs| |fglmIfCan| |style|
+ |twist| |suchThat| |leftLcm| |symbolTable| |currentEnv| |divisor|
+ |indicialEquation| |nthRootIfCan| |expenseOfEvaluation|
+ |ScanFloatIgnoreSpacesIfCan|
+ |rewriteSetByReducingWithParticularGenerators| |safeFloor| |odd?|
+ |difference| |putColorInfo| |e02aef| |internalLastSubResultant|
+ |signAround| |true| |height| |jordanAdmissible?| |Lazard|
+ |pushFortranOutputStack| |row| |ldf2lst| |brace| |pdf2ef| |decompose|
+ |loopPoints| |createIrreduciblePoly| |and| |cyclic|
+ |popFortranOutputStack| |readByteIfCan!| |resultantReduit| |eq|
+ |c02aff| |s13adf| |setProperty!| |clearFortranOutputStack| |cSec|
+ |qfactor| |outputAsFortran| |UpTriBddDenomInv| |dihedral| |iter|
+ |rangePascalTriangle| |halfExtendedResultant2| |getGoodPrime|
+ |exactQuotient| |leftNorm| |nilFactor| |testDim| |getPickedPoints|
+ |tree| |changeThreshhold| |symFunc| |basisOfLeftNucleus| |mapExpon|
+ |minPoly| |makeSeries| |f02xef| |prepareDecompose| |value|
+ |functionIsFracPolynomial?| |rightPower| |previous| |tValues|
+ |principal?| |moebius| |bernoulliB| |qPot| |principalIdeal| |f02aff|
+ |OMputSymbol| |minimize| |rightUnits| |algint| |mightHaveRoots|
+ |commutator| |predicates| |operator| |polygon| |subHeight| |e02gaf|
+ |tan2cot| |level| |iiacoth| |infinite?| |internalSubPolSet?| |cAsinh|
+ |froot| |cothIfCan| |clipPointsDefault| |groebgen|
+ |cyclotomicFactorization| |solveLinearPolynomialEquation| |c06fuf|
+ |semiDegreeSubResultantEuclidean| |normDeriv2|
+ |solveLinearPolynomialEquationByRecursion| |entries| |frst| |unknown|
+ |cAcos| |inverseIntegralMatrixAtInfinity| |baseRDE| |matrixDimensions|
+ |inconsistent?| |bitLength| |aromberg| |maxrank| |solveInField|
+ |polar| |lazyIrreducibleFactors| |cLog| |region| |constructorName|
+ |integerIfCan| |cAsec| |maxPoints| |isobaric?| |dflist| |parametersOf|
+ |front| |binaryFunction| |changeBase| |rightZero| |repeatUntilLoop|
+ |supRittWu?| |stronglyReduced?| |setPrologue!| |real| |jacobian|
+ |trace2PowMod| |fullPartialFraction| |every?| |e04ucf|
+ |indicialEquations| |impliesOperands| |lazyPremWithDefault| |imag|
+ |perfectNthPower?| |gradient| |f01rdf| |setright!| |rename!| |rules|
+ |directProduct| |bernoulli| |numberOfNormalPoly| |showTheSymbolTable|
+ |s21bcf| |leftRank| |wrregime| |changeWeightLevel| |sech2cosh|
+ |vectorise| |fortranCharacter| |exactQuotient!| |squareFreePrim|
+ |factorAndSplit| |nullity| |binomial| |basisOfRightAnnihilator|
+ |sumOfDivisors| |integers| |bright| |cross| |selectODEIVPRoutines|
+ |destruct| |more?| |collectUnder| |coleman| |functionIsOscillatory|
+ |infieldint| |limit| |root| |poisson| |mapGen|
+ |stoseInternalLastSubResultant| |ode| |distance| |column| |f07adf|
+ |getButtonValue| |bfEntry| |generators| |completeHensel|
+ |OMencodingSGML| |presub| |paren| |OMgetEndError| |s14abf| |nextPrime|
+ |topFortranOutputStack| |colorFunction| |ref|
+ |setLegalFortranSourceExtensions| |iiGamma| |buildSyntax| |typeList|
+ |insert| NOT |ParCond| |s17dlf| |quasiAlgebraicSet| |swapRows!|
+ |setRealSteps| |critMonD1| |numerator| |cTanh| |lazyPseudoQuotient|
+ |sqfree| |monomial| OR |hermiteH| |leastMonomial| |writeLine!| |obj|
+ |prologue| |nary?| |deepExpand| |inRadical?| |returnType!|
+ |zeroDimensional?| |trapezoidalo| |multivariate| |nextsubResultant2|
+ AND |rootProduct| |divide| |element?| |exQuo| |oneDimensionalArray|
+ |pseudoQuotient| |zerosOf| |cache| |delete| |s17dcf| |normFactors|
+ |leaf?| |variables| |minordet| |halfExtendedSubResultantGcd2|
+ |primitivePart!| |diophantineSystem| |matrixConcat3D| |iisec|
+ |eigenvector| |explicitEntries?| |e02adf| |alternatingGroup| |sec2cos|
+ |asinIfCan| |makeSketch| |alternating| |imagI| |distribute|
+ |increment| |submod| |internalDecompose| |torsionIfCan| |recip|
+ |shift| |upperCase!| |top!| |iprint| |linearAssociatedExp|
+ |setProperty| |logpart| |redpps| |multiplyCoefficients|
+ |listConjugateBases| |d01asf| |rightRankPolynomial| |OMputEndAtp|
+ |fixedPoints| |numericalOptimization| |eval| |hypergeometric0F1|
+ |setMinPoints3D| |iiasinh| |idealSimplify| |selectPolynomials|
+ |areEquivalent?| |suffix?| |create| |lowerCase?| |vconcat|
+ |ListOfTerms| |clipParametric| |increasePrecision| |vspace| |prime?|
+ |tensorProduct| |taylor| |norm| |homogeneous?| |create3Space|
+ |sinhcosh| |palgint| |showTypeInOutput| |iidsum| |precision| |ode1|
+ |extractPoint| |readIfCan!| |listLoops| |laurent| |prefix?| |s17adf|
+ |ffactor| |leftRemainder| |closedCurve| |coerceP| |seriesToOutputForm|
+ |reduction| |shufflein| |recur| |Vectorise| |puiseux|
+ |OMencodingBinary| |crushedSet| |setEmpty!| |subspace| |rootsOf|
+ |sturmVariationsOf| |expintfldpoly|
+ |removeRoughlyRedundantFactorsInPol| |c06frf| |f01qdf| |rdHack1|
+ |symmetricTensors| |tower| * |factors| |sizeLess?|
+ |numberOfFractionalTerms| |charthRoot| |find| |leadingTerm|
+ |linkToFortran| |normalDenom| |s17agf| |inv| |nextItem|
+ |reduceByQuasiMonic| |content| |lastSubResultant| |multiEuclideanTree|
+ |iflist2Result| |getCode| |monicRightDivide| |ground?| |setvalue!|
+ |maxRowIndex| |headReduced?| |partialFraction| |lintgcd|
+ |leadingCoefficientRicDE| |pow| |blue| |singularitiesOf| |log10|
+ |ground| |coerceS| |s13acf| |connect| |nthFractionalTerm| |exp|
+ |setRow!| |genus| |reverseLex| |sinIfCan| |bitand| |commaSeparate|
+ |operation| |declare| |notOperand| |setTopPredicate| |rightLcm|
+ |stoseInvertible?| |leadingMonomial| |showRegion| |infix?| |makeop|
+ |untab| |cycleTail| |separateFactors| |bitior| |distdfact| |btwFact|
+ |s21baf| |perfectSqrt| |semiSubResultantGcdEuclidean2|
+ |leadingCoefficient| |supDimElseRittWu?| |complexNumeric| |mask|
+ |f04axf| |twoFactor| |lquo| |csc2sin| |nextNormalPoly| |cotIfCan|
+ |prinshINFO| |sequence| |pointPlot| |primitiveMonomials| |medialSet|
+ |setleaves!| |finiteBasis| |split!| |leftAlternative?| |eulerPhi|
+ |rightDiscriminant| |doubleComplex?| |leftPower| |reductum| |kernels|
+ |physicalLength!| |inspect| |clipBoolean| |bezoutDiscriminant|
+ |replace| |less?| |gcdprim| |failed?| |bezoutResultant| |OMputString|
+ |univariate| |digamma| |d01amf| |coefficient| |quasiMonicPolynomials|
+ |exteriorDifferential| |shade| |negative?| |rightUnit| |lexGroebner|
+ |insert!| |getRef| |lazyPseudoRemainder| |intermediateResultsIF|
+ |OMgetEndAttr| |degreeSubResultantEuclidean| |over| |completeHermite|
+ |condition| |fractionPart| |options| |factorGroebnerBasis|
+ |makeViewport2D| |var1StepsDefault| |newReduc| |monicDecomposeIfCan|
+ |meshFun2Var| |prepareSubResAlgo| |noLinearFactor?| |elements|
+ |factor| |currentSubProgram| |OMsupportsCD?| |argscript|
+ |getExplanations| |compiledFunction| |knownInfBasis|
+ |indicialEquationAtInfinity| |dioSolve| |besselJ| |sqrt| |lighting|
+ |bombieriNorm| |setMaxPoints3D| |component| |getProperties|
+ |algebraicVariables| |lyndonIfCan| |components| |cSin| |string|
+ |symmetricProduct| |irreducibleFactor| |tanh2trigh| |allRootsOf| |dom|
+ |exprHasAlgebraicWeight| |leastAffineMultiple| |expression|
+ |removeCoshSq| |mvar| |monicDivide| |simplifyLog| |sparsityIF|
+ |genericRightTraceForm| |autoReduced?| |polarCoordinates| |octon|
+ |rightScalarTimes!| |integral| |f02aef| |integer| |jacobi| |stirling2|
+ |Ei| |primPartElseUnitCanonical| |OMreceive| |d01ajf| |s19abf|
+ |fortranLinkerArgs| |invertibleElseSplit?| |lllp| |integralMatrix|
+ |safeCeiling| |basisOfMiddleNucleus| |trim| |OMreadFile| |resultant|
+ |asecIfCan| |dimensions| |isPower| |bit?| |atom?|
+ |tryFunctionalDecomposition?| |genericRightNorm| |basisOfCentroid|
+ |cosSinInfo| |edf2df| |f04mbf| |nonSingularModel| |reify| |linearPart|
+ |iisech| |center| |title| |rightRemainder| |removeSquaresIfCan|
+ |viewDefaults| |weierstrass| |sort| |tableau| |internalIntegrate0|
+ |s20acf| |prefixRagits| |associates?| |OMgetAtp| |leadingSupport|
+ |graeffe| |zeroSquareMatrix| |escape| |subMatrix| |exists?| |block|
+ |complexForm| |critB| |genericLeftNorm| |ellipticCylindrical|
+ |insertBottom!| |pascalTriangle| |elliptic| |xn| |e04jaf| |sorted?|
+ |pushuconst| RF2UTS |e| |printingInfo?| |lazyPseudoDivide| |resetNew|
+ |rootSplit| |mindeg| |summation| |f02wef| |normalizedAssociate|
+ |c06gcf| |airyAi| |sumSquares| |primlimitedint| |polyred| |ridHack1|
+ |quatern| |name| |numberOfFactors| |fullDisplay| |setref|
+ |setAdaptive| |mapUnivariateIfCan| |pToDmp| |compile| |random| |body|
+ |adaptive3D?| |cubic| |lineColorDefault| |chiSquare1|
+ |noncommutativeJordanAlgebra?| |e02dff| |leadingIdeal| |iiatanh|
+ |fixedPoint| |complexNormalize| |binary| |dimension| |iiacot|
+ |solveLinear| |chainSubResultants| |pointSizeDefault| |partition| |lo|
+ |iiexp| |rk4qc| |reducedContinuedFraction| |conjug| |normalElement|
+ |certainlySubVariety?| |debug| |linearlyDependentOverZ?|
+ |dihedralGroup| |nthRoot| |incr| |splitLinear| |makeCrit| |cAcosh|
+ |lowerCase| |fortranLiteral| |lfinfieldint| D |leastPower| |hi|
+ |addPointLast| |belong?| |string?| |nsqfree| |removeCosSq| |iiasin|
+ |prime| |squareMatrix| |e01sbf| |listOfMonoms| |powers|
+ |multiEuclidean| |log2| |polygon?| |trunc| |intensity|
+ |identification| |toseInvertible?| |palgRDE| |antiCommutator|
+ |tanIfCan| |e02daf| |mathieu22| |startPolynomial| |validExponential|
+ |OMserve| |e02ajf| |unvectorise| Y |tanAn| |factorsOfCyclicGroupSize|
+ |selectfirst| |showTheRoutinesTable| |multiplyExponents| |conjugates|
+ |internalZeroSetSplit| |delta| |doubleFloatFormat| |directory| |orbit|
+ |extractIndex| |scripted?| |intcompBasis| |rCoord| |f04atf|
+ |ricDsolve| |laguerre| |finiteBound| |subset?| |close| |plot|
+ |firstUncouplingMatrix| |tubeRadius| |optAttributes| |stFuncN|
+ |elRow2!| |SturmHabichtSequence| |s17akf| |mapmult| |slash|
+ |stosePrepareSubResAlgo| |tubePlot| |writeByteIfCan!| |setButtonValue|
+ |float?| |GospersMethod| |display| |pade| |clikeUniv| |status|
+ |tablePow| |resultantEuclidean| |minPol| |child?|
+ |completeEchelonBasis| |remove| |f01maf| |pmintegrate| |setLabelValue|
+ |probablyZeroDim?| |createMultiplicationTable| |outputSpacing| |arg1|
+ |extractIfCan| |euclideanSize| |lSpaceBasis| |print| |dmpToP|
+ |OMconnInDevice| |subtractIfCan| |s13aaf| |asechIfCan| |cosh2sech|
+ |readable?| |arg2| |reverse| |setStatus| |last| |viewWriteAvailable|
+ |perspective| |formula| |bracket| |sylvesterMatrix| |kroneckerDelta|
+ |assoc| |euclideanGroebner| |polyRDE| |modifyPointData| |lambda|
+ |restorePrecision| |setProperties| |rightCharacteristicPolynomial|
+ |coerceL| |getMatch| |iroot| |saturate| |conditions| |ratPoly|
+ |cAsech| |graphState| |morphism| |input| BY |stoseInvertibleSetsqfreg|
+ |movedPoints| |generate| |rightAlternative?| |rk4a| |edf2fi|
+ |factorSquareFreeByRecursion| |match| |solve1| |inverseLaplace|
+ |concat!| |createPrimitiveElement| |library| |OMunhandledSymbol|
+ |mainKernel| |endOfFile?| |hyperelliptic| |modularGcd| |decimal|
+ |mapBivariate| |s19adf| |incrementBy| |uniform01| |nrows| SEGMENT
+ |iisqrt3| |fortranCompilerName| |pol| |setOfMinN| |simplifyExp|
+ |halfExtendedResultant1| |infix| |degreePartition| |dimensionsOf|
+ |digit| |expand| |ncols| |OMputVariable| |unitVector| |setErrorBound|
+ |lfextlimint| |harmonic| |selectMultiDimensionalRoutines| |bumptab1|
+ |hasoln| |coth2trigh| |filterWhile| |stFunc1| |meshPar2Var|
+ |resetVariableOrder| |stopTable!| |mapSolve| |llprop| |Si|
+ |getBadValues| |representationType| |powmod| |iiacosh| |set|
+ |filterUntil| |position!| |composites| |mkcomm| |lepol| |iibinom|
+ |clip| |pair?| |computeCycleLength| |palglimint| |associatedEquations|
+ |select| |att2Result| |factorsOfDegree| |perfectSquare?| |invertible?|
+ |cardinality| |linearMatrix| |leftExactQuotient|
+ |numericalIntegration| |rombergo| |minset| |character?| |mdeg|
+ |partialNumerators| |lowerCase!| |radicalEigenvector| |reflect|
+ |getStream| |prinpolINFO| |besselI|
+ |removeRoughlyRedundantFactorsInPols| |leftScalarTimes!|
+ |lazyGintegrate| |cAtanh| |dmpToHdmp| |lifting| |nullary?| |logIfCan|
+ |d01gaf| |RemainderList| |rootPoly| |leftTraceMatrix|
+ |subResultantGcd| |degreeSubResultant| UP2UTS |cons| |e04gcf|
+ |beauzamyBound| |extractSplittingLeaf| |makeVariable| |OMputAttr|
+ |laplacian| |critpOrder| |maxrow| |systemSizeIF| |anticoord|
+ |inputBinaryFile| |biRank| |nthExponent| |delay| |critM| |s01eaf|
+ |integrate| |zeroVector| |palgint0| |boundOfCauchy| |constant?|
+ |approximate| |term| |acoshIfCan| |generalSqFr| |solid| |e02bcf|
+ |cCos| |makeRecord| |quoted?| |double| |monicModulo| |seriesSolve|
+ |selectsecond| |complex| |iiatan| |partitions| |fixedDivisor|
+ |eisensteinIrreducible?| |semiLastSubResultantEuclidean| |max|
+ |LowTriBddDenomInv| |exp1| |pointColorDefault| |setProperties!|
+ |rewriteIdealWithHeadRemainder| |stopMusserTrials| |headAst|
+ |positiveRemainder| |factorPolynomial| |fixPredicate| |property|
+ |tracePowMod| |e02bef| |routines| |lfunc| |unparse| |yellow|
+ |primaryDecomp| |fintegrate| |pseudoRemainder| |findCycle|
+ |extractClosed| |balancedFactorisation| |pmComplexintegrate| |show|
+ |createZechTable| |OMread| |f02adf| |retract| |source| |getIdentifier|
+ |removeRedundantFactors| |basis| |squareFree| |alphanumeric| |f02ajf|
+ |plenaryPower| |divisorCascade| |subNodeOf?| |acotIfCan|
+ |tubeRadiusDefault| |singularAtInfinity?| |iomode| |lflimitedint|
+ |univariatePolynomials| |subTriSet?| |units| ~= |red| |trace|
+ |leftRegularRepresentation| |c06gsf| |numberOfPrimitivePoly|
+ |compBound| |c06ecf| |OMlistSymbols| |cycleRagits| |tanQ|
+ |rootDirectory| |coerce| |localAbs| |f02awf| |f04maf| |ignore?|
+ |rightExactQuotient| |stack| |permutations| |genericRightDiscriminant|
+ |mathieu24| |enterPointData| |powern| |construct|
+ |squareFreeLexTriangular| |s15adf| |roughBase?| |declare!|
+ |realElementary| |acothIfCan| |integralRepresents| |iteratedInitials|
+ |pushucoef| |complexEigenvectors| |generator| |changeVar| |toScale|
+ |tubePoints| |mathieu12| |groebner?| |normalise| |target| =
+ |countRealRootsMultiple| |totalLex| |ReduceOrder| |interval|
+ |nextLatticePermutation| |e02zaf| |multinomial| |enqueue!| FG2F
+ |extendedResultant| |domainOf| |equality| |identityMatrix| |code|
+ |fillPascalTriangle| |f01bsf| |dim| |createNormalPrimitivePoly|
+ |ramified?| |pointLists| |expextendedint| |OMclose| |/\\|
+ |retractIfCan| |cup| < |OMgetObject| |semiDiscriminantEuclidean|
+ |applyRules| |flexible?| |processTemplate| |doubleDisc| |symbol?|
+ |romberg| |merge!| |\\/| |constDsolve| > |or?| |scan| |unit|
+ |innerSolve1| |firstNumer| |ideal| |OMputBVar| |directSum|
+ |parametric?| |kovacic| <= |constantOpIfCan| |makeMulti| |e01saf|
+ |s18def| |squareFreePart| |aQuartic| |cyclic?| |changeNameToObjf|
+ |evaluate| |d03faf| >= |sn| |real?| |aQuadratic| |numberOfVariables|
+ |basisOfCenter| |zeroDimPrime?| |consnewpol| |segment|
+ |explicitlyEmpty?| |quadratic| |loadNativeModule| |monomials| |f02fjf|
+ |overbar| |sin?| |coefChoose| |bivariatePolynomials| |mesh| |rotate|
+ |flexibleArray| |dmp2rfi| |output| |OMputEndObject| |listBranches|
+ |toseLastSubResultant| |edf2efi| |modulus| |bounds| |extractTop!|
+ |realZeros| |limitedIntegrate| |cyclePartition| |constantLeft| +
+ |monicRightFactorIfCan| |diagonals| |increase| |subscript| |write!|
+ |associatorDependence| |contains?| |is?| |coth2tanh| |scopes| |latex|
+ - |e02def| |preprocess| |kmax| |lhs| |c05pbf| |writeBytes!|
+ |setScreenResolution| |iFTable| |hdmpToDmp| |transform| |divideIfCan|
+ / |polyRicDE| |tan2trig| |minus!| |rhs| |outputAsTex| |fortranDouble|
+ |univariateSolve| |constantToUnaryFunction| |chiSquare| |map| |gethi|
+ |chvar| |imagk| |lowerPolynomial| |semiResultantEuclideannaif|
+ |algintegrate| |normalDeriv| |putGraph| |pointData| |cos2sec|
+ |fortranCarriageReturn| |viewZoomDefault| |printStats!|
+ |numFunEvals3D| |diagonal| |second| |setelt| |rightMult|
+ |SturmHabicht| |s18aef| |nativeModuleExtension| |plusInfinity|
+ |minColIndex| |rotatey| |dec| |diagonal?| |one?| |solveRetract|
+ |semiResultantEuclidean1| |third| |doubleRank| |numerators| |hdmpToP|
+ |ScanFloatIgnoreSpaces| |minusInfinity| |zCoord| |node| |host|
+ |reciprocalPolynomial| |decomposeFunc| |byte|
+ |createLowComplexityTable| |copy| |LazardQuotient2| |has?| |iisinh|
+ |BasicMethod| |squareFreeFactors| |merge| |primintegrate|
+ |localIntegralBasis| |lexTriangular| |stoseInvertible?sqfreg| |d02raf|
+ |irreducibleRepresentation| |currentScope| |f07aef| |karatsuba|
+ |convert| |numericIfCan| |parabolic| |OMbindTCP| |cSech| |contours|
+ |totalDegree| |horizConcat| |getSyntaxFormsFromFile| |shellSort|
+ |nextsousResultant2| |match?| |init| |stopTableGcd!|
+ |subresultantSequence| |quasiComponent| |primlimintfrac|
+ |removeZeroes| |autoCoerce| |tail| |pastel| |doubleResultant|
+ |getConstant| |initiallyReduce| |multisect| |mainForm| |reducedForm|
+ |argumentListOf| |ipow| |selectIntegrationRoutines| |mirror|
+ |setnext!| |s17def| |useSingleFactorBound| |npcoef| |inc| |void| |lex|
+ |ef2edf| |closeComponent| |fill!| |OMgetSymbol| |type| |stop|
+ |curryLeft| |sqfrFactor| |d02bbf| |jacobiIdentity?| |numberOfChildren|
+ |width| |middle| |copyInto!| |d02gaf| |antisymmetricTensors| |remove!|
+ |maxIndex| |expt| |OMUnknownSymbol?| |addBadValue| |oblateSpheroidal|
+ |error| |getMultiplicationTable| |multiple?| |df2ef|
+ |purelyTranscendental?| |LyndonWordsList1| |genericLeftTrace|
+ |polCase| |curryRight| |expr| |hexDigit?| |setValue!| |iicos|
+ |specialTrigs| |nextIrreduciblePoly| |lexico| |assert| |midpoints|
+ |splitConstant| |idealiserMatrix| |complexLimit| |transcendenceDegree|
+ |toroidal| F2FG |var1Steps| |nthCoef| |updatF| |binding|
+ |nextPrimitivePoly| |sh| |irreducibleFactors| |sechIfCan|
+ |commonDenominator| |qroot| |remainder| |leadingIndex| |readBytes!|
+ |diff| |pushup| |strongGenerators| |rowEchLocal| |changeMeasure|
+ |showAll?| |accuracyIF| |infinityNorm| |cond| |green| |vedf2vef|
+ |groebSolve| |integralBasisAtInfinity| |complexExpand| |critMTonD1|
+ |removeConstantTerm| |variable| |numberOfImproperPartitions|
+ |OMgetFloat| |curve?| |d03eef| |optional| |complexSolve| |omError|
+ |linSolve| |mix| |UnVectorise| |zeroDim?| |iterators| |airyBi|
+ |redPol| |meshPar1Var| |continue| |addPoint| |antiCommutative?|
+ |compound?| |mergeFactors| |color| |viewport2D| |overlap|
+ |infiniteProduct| |equation| |split| |generic|
+ |removeSuperfluousQuasiComponents| |rational?| |transcendent?| |nor|
+ |rowEch| |getVariableOrder| |complementaryBasis| |removeDuplicates!|
+ |rectangularMatrix| |next| |numberOfComputedEntries| |order|
+ |createPrimitivePoly| |sts2stst| |e01sff| |fmecg| |quoByVar|
+ |invertIfCan| |e01bgf| |constantIfCan| |hexDigit|
+ |rightMinimalPolynomial| |palgLODE0| |e02ahf| |outputFloating|
+ |clearCache| |geometric| |cTan| |oddlambert| |createThreeSpace|
+ |rationalPower| |tab| |exprToXXP| |dark| |insertMatch|
+ |exprHasWeightCosWXorSinWX| |fTable| |eigenMatrix| |OMsetEncoding|
+ |LiePolyIfCan| |totalDifferential| |symmetricRemainder| |sinh2csch|
+ |permanent| |removeRedundantFactorsInContents| |bivariate?|
+ |scanOneDimSubspaces| |quasiRegular?| |randnum| |lazyIntegrate|
+ |arguments| |firstSubsetGray| |square?| |expandTrigProducts| |linear|
+ |iisqrt2| |cRationalPower| |linGenPos| |cyclicCopy| |viewThetaDefault|
+ |basisOfLeftNucloid| |figureUnits| |part?| |OMgetError| |orOperands|
+ |typeLists| |getGraph| |fixedPointExquo| |equiv| |tube|
+ |curveColorPalette| |null| |primitiveElement| |expIfCan| |polynomial|
+ |leftMult| |nullary| |hasHi| |constantOperator| |approxNthRoot|
+ |minPoints| |cyclicSubmodule| |getlo| |intPatternMatch| |case|
+ |systemCommand| |showScalarValues| |po| |birth| |leviCivitaSymbol|
+ |f01qcf| |lazyVariations| |exponential| |number?| |solveLinearlyOverQ|
+ |absolutelyIrreducible?| |Zero| |pushdterm| |setMaxPoints| |assign|
+ |coshIfCan| |rightRegularRepresentation| |positive?| |divergence|
+ |prem| |f04adf| |getOperator| |reducedQPowers| |One| |OMconnectTCP|
+ |generalTwoFactor| |separant| |rightTraceMatrix| |vertConcat|
+ |clearTheIFTable| |bat| |removeDuplicates| |spherical| |rightNorm|
+ |invmod| |point| |overlabel| |normal| |message| |deleteRoutine!|
+ |numberOfHues| |rischNormalize| |fortranInteger| |singleFactorBound|
+ |bsolve| |startTableGcd!| |generalizedContinuumHypothesisAssumed?|
+ |psolve| |addMatchRestricted| |point?| |leftFactor| |prinb|
+ |makeResult| |rightExtendedGcd| |primitivePart| |char| |randomLC|
+ |sort!| |discriminantEuclidean|
+ |removeRoughlyRedundantFactorsInContents| |nextColeman|
+ |stoseInvertibleSetreg| |space| |setPredicates| |categoryFrame|
+ |numberOfIrreduciblePoly| |erf| |series| |mainDefiningPolynomial|
+ |imagE| |upDateBranches| |comparison| |hclf| |mapUnivariate|
+ |roughSubIdeal?| |dequeue!| |s18adf| |addiag| |outerProduct|
+ |shrinkable| |elt| |OMlistCDs| |initializeGroupForWordProblem| |plus!|
+ |diagonalProduct| |light| |substring?| |cartesian| |satisfy?|
+ |regularRepresentation| |hasTopPredicate?| |iiacsch| |optional?|
+ |startStats!| |unitNormalize| |child| |innerint| |binaryTree|
+ |atanIfCan| |insertionSort!| |nonQsign| |conditionsForIdempotents|
+ |dilog| |overset?| |s18dcf| |sincos| |uniform| |vector| |exprToGenUPS|
+ |factorOfDegree| |univcase| |droot|
+ |generalizedContinuumHypothesisAssumed| |palginfieldint| |f02agf|
+ |s17dhf| |min| |integralLastSubResultant| |float| |sin|
+ |stoseLastSubResultant| |differentiate| |deref| |f04jgf| |getMeasure|
+ |modularGcdPrimitive| GF2FG |build| |cCsc| |normalForm| |cos|
+ |functionIsContinuousAtEndPoints| |numberOfOperations| |hermite|
+ |infieldIntegrate| |d01gbf| |numberOfCycles| |shallowCopy| |t| |swap|
+ |forLoop| |sizePascalTriangle| |empty| |tan| |represents|
+ |dimensionOfIrreducibleRepresentation| |viewSizeDefault| |f02akf|
+ |karatsubaOnce| |lieAdmissible?| |outputArgs| |bandedHessian|
+ |patternMatchTimes| |singRicDE| |normalized?| |cot| |factorSFBRlcUnit|
+ |lastSubResultantEuclidean| |minimalPolynomial| |nil| |bitTruth|
+ |makeSUP| |primextendedint| |tanh2coth| |factor1| |f02bjf|
+ |denomRicDE| |sec| |getProperty| |setEpilogue!| |doublyTransitive?|
+ |OMputBind| |legendreP| |lazy?| |setCondition!| |f2df| |diag|
+ |numeric| |defineProperty| |csc| |selectOptimizationRoutines|
+ |pseudoDivide| |nextPrimitiveNormalPoly| |sayLength| |HenselLift|
+ |resetAttributeButtons| |mapExponents| |radical| |mergeDifference|
+ |e02agf| |checkPrecision| |trigs| |asin| |pdf2df|
+ |derivationCoordinates| |setrest!| |range| |evaluateInverse|
+ |UP2ifCan| |members| |getMultiplicationMatrix| |superHeight|
+ |truncate| |acos| |splitNodeOf!| |newTypeLists| |chebyshevU| |e02bdf|
+ |laurentRep| |goto| |shiftRight| |linearAssociatedOrder| |mr|
+ |univariatePolynomial| |isExpt| |integralBasis| |atan| |aLinear| GE
+ |henselFact| |conditionP| |currentCategoryFrame| |discreteLog|
+ |semiIndiceSubResultantEuclidean| |mapUp!| |problemPoints|
+ |limitedint| |factorset| |acot| |groebner| GT |computeCycleEntry|
+ |contract| |lift| |mesh?| |wholeRagits| |invmultisect| |outputFixed|
+ |s17acf| |e02ddf| |OMencodingUnknown| |retractable?| LE
+ |bipolarCylindrical| |c05nbf| |tanhIfCan| |subPolSet?| |reduce|
+ |leftTrace| |fractionFreeGauss!| |HermiteIntegrate|
+ |semiResultantReduitEuclidean| |infLex?| |symbolTableOf| |cCsch| LT
+ |showSummary| |isMult| |shuffle|
+ |rewriteIdealWithQuasiMonicGenerators| |aCubic| |normalizeAtInfinity|
+ |quickSort| |back| |associative?| |polyPart| |completeEval| |f04qaf|
+ |sumOfSquares| |structuralConstants| |Lazard2| |hostPlatform|
+ |OMReadError?| |possiblyInfinite?| |leaves| |ravel| |mkAnswer|
+ |rootKerSimp| |hMonic| |badNum| LODO2FUN |neglist| |createNormalPoly|
+ |mulmod| |showAttributes| |removeZero| |argument| |maxColIndex|
+ |reshape| |zeroOf| |ceiling| |scalarTypeOf| |coefficients|
+ |integralAtInfinity?| |parts| |and?| |mapdiv| |expPot| |nextPartition|
+ |iipow| |toseSquareFreePart| |compactFraction| |alphanumeric?| |iisin|
+ |modTree| |primextintfrac| |const| |OMgetType|
+ |basisOfLeftAnnihilator| |magnitude| |LyndonBasis| |rightRecip|
+ |exponential1| |contractSolve| |sample| |showFortranOutputStack|
+ |algebraicCoefficients?| |exprToUPS| |eigenvalues| |expandLog|
+ |quadraticNorm| |supersub| |coordinates| |rur| |lyndon?| |s14aaf|
+ |cExp| |midpoint| |OMgetBind| |createGenericMatrix| |iiacsc|
+ |raisePolynomial| |duplicates| |rightGcd| |relerror| |largest|
+ |ddFact| |stoseSquareFreePart| |maximumExponent| |varList| |isPlus|
+ |conjugate| |heap| |Frobenius| |df2fi| |selectFiniteRoutines| |update|
+ |ScanArabic| |elliptic?| |unrankImproperPartitions1|
+ |generateIrredPoly| |pushdown| |symmetricDifference| |flagFactor|
+ |adaptive| |duplicates?| |e02baf| |OMgetEndBVar| |stirling1| |power!|
+ |swap!| |limitPlus| |leftFactorIfCan| |OMgetInteger|
+ |expressIdealMember| |alphabetic?| |yCoord| |Beta| |elementary|
+ |inverseIntegralMatrix| |selectAndPolynomials| |points| |dfRange|
+ |unitCanonical| |credPol| |f01mcf| |reopen!| |normInvertible?|
+ |variationOfParameters| |d02ejf| |readLine!| |commutativeEquality|
+ |closedCurve?| |iCompose| |lambert| |nthExpon|
+ |subResultantGcdEuclidean| |regime| |weighted| |rightDivide| |mapCoef|
+ |exponent| |checkForZero| |phiCoord| |branchPointAtInfinity?| |depth|
+ |logGamma| |equiv?| |stripCommentsAndBlanks| |cot2tan|
+ |genericRightMinimalPolynomial| |palgRDE0| |f01rcf| |log| |bringDown|
+ |cfirst| |imagi| |SFunction| |primintfldpoly| |torsion?|
+ |invertibleSet| |position| |isList| |printStatement| |characteristic|
+ |derivative| |appendPoint| |notelem| |useSingleFactorBound?|
+ |minIndex| |standardBasisOfCyclicSubmodule| |infRittWu?|
+ |subResultantChain| |bottom!| |numberOfComponents| |computePowers|
+ |listRepresentation| |wholePart| |cyclotomicDecomposition| |s19aaf|
+ |extendedSubResultantGcd| |direction| |uncouplingMatrices| |edf2ef|
+ |cscIfCan| |function| |nullSpace| |imagJ| |pquo| |c05adf|
+ |normalizeIfCan| |splitSquarefree| |cAcoth| |radix| |mat|
+ |wordsForStrongGenerators| |quotient| |maxint| |copies|
+ |primPartElseUnitCanonical!| |initTable!| |e04naf| |denomLODE|
+ |makeYoungTableau| |nil?| |characteristicSet| |gcdcofactprim| |rquo|
+ |basisOfRightNucleus| |exponents| |complexNumericIfCan| |cCoth|
+ |clearTheSymbolTable| |youngGroup| |product| |rationalPoints|
+ |jordanAlgebra?| |plus| |OMwrite| |mainContent| |sinhIfCan| |pile|
+ |paraboloidal| |fortran| |simpsono| |ratDsolve| |heapSort|
+ |setsubMatrix!| |eq?| |gderiv| |double?| |subQuasiComponent?|
+ |exptMod| |meatAxe| |factorList| |imports| |makeSin|
+ |explicitlyFinite?| |roughBasicSet| |index?| |linearDependence|
+ |OMgetApp| |rational| |e01bff| |setAdaptive3D| |s17aff| |scale|
+ |endSubProgram| |collect| |augment| |bindings| |thenBranch|
+ |triangSolve| |numberOfDivisors| |hue| |anfactor| |minGbasis|
+ |binaryTournament| |c06gbf| |zeroSetSplit| |wordInGenerators|
+ |completeSmith| |times| |ptree| |backOldPos| |rationalIfCan|
+ |monomRDE| |topPredicate| |tubePointsDefault| |brillhartTrials|
+ |distFact| |numFunEvals| |evenlambert| |ParCondList|
+ |purelyAlgebraic?| |decreasePrecision| |symmetricGroup| |weakBiRank|
+ |bothWays| |cAcsc| |repSq| |semicolonSeparate| |shallowExpand| |root?|
+ |drawComplex| |presuper| |colorDef| |coerceImages| |mainCoefficients|
+ |clearTheFTable| |rootOf| |reducedDiscriminant| |push!| |atanhIfCan|
+ |viewpoint| |zeroDimPrimary?| |combineFeatureCompatibility|
+ |eigenvectors| |divideIfCan!| |withPredicates| |monom| |bezoutMatrix|
+ |stiffnessAndStabilityOfODEIF| |ratpart| |lcm| |padicallyExpand|
+ |sturmSequence| |cyclicGroup| |cyclicEntries| |collectQuasiMonic|
+ |drawComplexVectorField| |recoverAfterFail| |userOrdered?| |elRow1!|
+ |screenResolution3D| |getDatabase| |rarrow| |bandedJacobian| |result|
+ |dictionary| |c06fqf| |characteristicSerie| |iicoth| |common| |d01alf|
+ |OMputEndApp| |testModulus| |append| |trueEqual| |d01aqf| |Gamma|
+ |read!| |unravel| |gcd| |tanSum| |opeval| |qelt| |script| |quadratic?|
+ |karatsubaDivide| |totolex| |antiAssociative?| |linearlyDependent?|
+ |option?| |false| |nthr| |lllip| |leftRecip| |f02abf| |OMgetEndBind|
+ |powerSum| |readLineIfCan!| |fortranLogical| |s17ajf| |Hausdorff|
+ |xRange| |getCurve| |showClipRegion| |leftDivide| |setPoly|
+ |OMreadStr| |equivOperands| |incrementKthElement| |roman| |yRange|
+ |tex| |argumentList!| |virtualDegree| |f01qef|
+ |rewriteSetWithReduction| |unmakeSUP| |elColumn2!| |OMgetEndObject|
+ |cycleLength| |zRange| |cap| |outputForm| |qqq| |roughEqualIdeals?|
+ |unitsColorDefault| |#| |upperCase?| |redmat| |fortranLiteralLine|
+ |map!| |weights| |polynomialZeros| |numberOfComposites| |setClosed|
+ |eyeDistance| |qsetelt!| |groebnerFactorize| |hex| |asimpson| |iicsc|
+ |bfKeys| |stoseInvertibleSet| |numberOfMonomials| |nthFactor| |d01anf|
+ F |secIfCan| |e02dcf| |showAllElements| |explimitedint| |frobenius|
+ |localUnquote| |setMinPoints| |bubbleSort!| |genericRightTrace|
+ |times!| |high| |abelianGroup| |isAbsolutelyIrreducible?| |cn|
+ |halfExtendedSubResultantGcd1| |schema| |fractRagits| |id|
+ |minimumDegree| |gcdcofact| |factorSquareFreePolynomial| |matrixGcd|
+ |purelyAlgebraicLeadingMonomial?| |tRange| |lastSubResultantElseSplit|
+ |SturmHabichtCoefficients| |constantRight| |complex?|
+ |complexElementary| |approxSqrt| |quartic| |characteristicPolynomial|
+ |expandPower| |rdregime| |outputList| |acsch| |table| |interReduce|
+ |iilog| |permutationRepresentation| |size?| |totalGroebner| |zero|
+ |skewSFunction| |LiePoly| |selectSumOfSquaresRoutines| |lp| |new|
+ |radicalEigenvectors| |f02bbf| |zero?| |rightQuotient| |listOfLists|
+ |iiasec| |rootBound| |d02kef| |writable?| |brillhartIrreducible?|
+ |smith| |acschIfCan| |nlde| |And| |factorByRecursion| |maxPoints3D|
+ |mindegTerm| |zeroSetSplitIntoTriangularSystems| |printCode|
+ |rationalApproximation| |s17ahf| |minRowIndex| |rank| |Or| |s17aef|
+ |pomopo!| |prevPrime| |insertTop!| |any?| |sum|
+ |unrankImproperPartitions0| |newLine| |replaceKthElement| |exquo|
+ |Not| |interpretString| |s18acf| |toseInvertibleSet| |charpol|
+ |lyndon| |mainPrimitivePart| |exponentialOrder| |imagK| |div|
+ |LyndonCoordinates| |e04mbf| |null?| |viewPosDefault| |fibonacci|
+ |objectOf| |external?| |patternVariable| |relativeApprox| |quo| |f2st|
+ |li| |newSubProgram| |quote| |zoom| |tableForDiscreteLogarithm|
+ |OMsend| |setScreenResolution3D| |monomial?| |thetaCoord|
+ |hitherPlane| |extractBottom!| |deleteProperty!| |unary?| |categories|
+ |hash| |triangulate| |var2StepsDefault| |palglimint0| |f04asf|
+ |calcRanges| |dot| |factorSquareFree| |crest| |idealiser| |rem|
+ |inrootof| |count| |gcdPrimitive| |gcdPolynomial|
+ |stoseInvertible?reg| |eulerE| |d01akf| |radicalRoots| |acscIfCan|
+ |resize| |lists| |modularFactor| |e02akf| |oddInfiniteProduct|
+ |continuedFraction| |refine| |identitySquareMatrix| |optpair| |iitanh|
+ |coercePreimagesImages| |s20adf| |s21bdf| |normalize| |tanNa| |left|
+ |sequences| |radicalOfLeftTraceForm| |ldf2vmf|
+ |createLowComplexityNormalBasis| |removeSinSq|
+ |stiffnessAndStabilityFactor| |moebiusMu| |removeSuperfluousCases|
+ |int| |right| |makingStats?| |normalizedDivide| |viewWriteDefault|
+ |decrease| |insertRoot!| |subscriptedVariables| |trailingCoefficient|
+ |symbolIfCan| |setStatus!| |euclideanNormalForm| |goodPoint|
+ |padicFraction| |dAndcExp| |besselY| |extension| |mainExpression|
+ |linearDependenceOverZ| |adaptive?| |corrPoly| |d02cjf| |mathieu23|
+ |OMParseError?| |maxdeg| |nonLinearPart| |makeCos| |baseRDEsys|
+ |integer?| |oddintegers| |cAcsch| |s19acf| |blankSeparate|
+ |divideExponents| |sortConstraints| |mpsode| |cAtan| |basicSet|
+ |variable?| |highCommonTerms| |interpolate| |Nul| |axesColorDefault|
+ |polygamma| |constantCoefficientRicDE| |printHeader| |minPoints3D|
+ |exprHasLogarithmicWeights| |collectUpper| |imaginary| |trigs2explogs|
+ |pop!| |listYoungTableaus| |drawCurves| |htrigs| |rotatez| |Ci| |push|
+ |aspFilename| |not| |key| |clipSurface| |iicot| |internalAugment|
+ |unprotectedRemoveRedundantFactors| |cSinh| |list?| |outputGeneral|
+ |adjoint| |e01bef| |leftOne| |relationsIdeal| |lprop| |mainMonomials|
+ |discriminant| |reindex| |generalLambert| |filename| |upperCase|
+ |leadingBasisTerm| |transpose| |bivariateSLPEBR| |simpleBounds?|
+ |isOpen?| |ord| |palgextint| |not?| |extract!| |possiblyNewVariety?|
+ |prefix| |rename| |complement| |extendedEuclidean| |graphStates|
+ |iidprod| |makeprod| |failed| |parse| |rischDEsys| |sncndn|
+ |rubiksGroup| |symbol| |test| |monicCompleteDecompose|
+ |createPrimitiveNormalPoly| |internalSubQuasiComponent?| |ratDenom|
+ |rootNormalize| |algSplitSimple| |realRoots| |updatD| |e04fdf|
+ |updateStatus!| |outlineRender| |integralDerivationMatrix|
+ |cyclicEqual?| |lfintegrate| |c06fpf| |PDESolve| |denominator|
+ |weight| |deepestInitial| |indices| |measure| |showTheFTable| |label|
+ |balancedBinaryTree| |identity| |csch2sinh| |superscript| |signature|
+ |associatedSystem| |OMputObject| |asinhIfCan| |seed| |stronglyReduce|
+ |recolor| |exprex| |iicsch| |divisors| |musserTrials| |mapMatrixIfCan|
+ |algebraicOf| |solveid| |packageCall| |factorials| |socf2socdf|
+ |algebraic?| |rspace| |mappingAst| |iterationVar| |definingEquations|
+ |Aleph| |KrullNumber| |factorial| |getZechTable| |legendre|
+ |controlPanel| |ODESolve| |pleskenSplit| |move| |minimumExponent|
+ |cot2trig| |any| |physicalLength| |stopTableInvSet!| |unaryFunction|
+ |An| |s21bbf| |shanksDiscLogAlgorithm| |positiveSolve| |intChoose|
+ |degree| |reduceBasisAtInfinity| |OMputFloat| |epilogue|
+ |monicLeftDivide| |iiacos| |generalizedEigenvectors| |lfextendedint|
+ |cycleElt| |univariate?| |setFieldInfo| |padecf| |tanintegrate|
+ |composite| |OMputEndError| |singular?| |iExquo| |leftUnit|
+ |trapezoidal| |schwerpunkt| |setFormula!| |wordInStrongGenerators|
+ |f02aaf| |symmetric?| |ode2| |approximants| |node?| |fortranComplex|
+ |varselect| |index| |coord| |d01apf| |addMatch|
+ |rewriteIdealWithRemainder| |antisymmetric?| |search|
+ |prolateSpheroidal| |pureLex| |bumptab| |choosemon| |sub| |returns|
+ |enumerate| |mainVariables| |initiallyReduced?| |option| |c06ebf|
+ |coordinate| |cycleSplit!| |critT| |roughUnitIdeal?| |measure2Result|
+ |tryFunctionalDecomposition| |makeEq| |getOrder|
+ |SturmHabichtMultiple| |pointColor| |zeroMatrix| |qinterval| |pr2dmp|
+ |pair| |properties| |partialDenominators| |head| |even?|
+ |lazyResidueClass| |viewDeltaXDefault| |leftGcd| |euler| |shiftRoots|
+ |semiResultantEuclidean2| |parseString| |nothing| |translate|
+ |OMgetEndAtp| |quasiMonic?| |setlast!| |createMultiplicationMatrix|
+ |eof?| |rk4f| |or| |lazyPrem| |list| |changeName| |operators|
+ |ScanRoman| |extendIfCan| |monic?| |delete!| |useEisensteinCriterion|
+ |normal?| |reorder| |car| |palgLODE| |symmetricPower| |reducedSystem|
+ |primes| |rationalPoint?| |graphImage| |monomialIntPoly| |moduloP|
+ |cdr| |extractProperty| |mkIntegral| |inverse| |genericPosition|
+ |errorKind| |addPoint2| |setDifference| |reverse!| |pole?| |d01fcf|
+ |findBinding| |complexZeros| |OMopenString| |startTable!| |curry|
+ |nthFlag| |setIntersection| |wholeRadix| |swapColumns!| |OMputAtp|
+ |FormatRoman| |leftMinimalPolynomial| |genericLeftTraceForm|
+ |particularSolution| |rightTrim| |simplify| |leftRankPolynomial| |box|
+ |setUnion| |postfix| |OMgetString| |open?| |computeBasis| |logical?|
+ |OMputEndBind| |indiceSubResultantEuclidean|
+ |removeRedundantFactorsInPols| |c02agf| |f04arf| |leftTrim|
+ |setClipValue| |complexEigenvalues| |splitDenominator| |apply|
+ |orthonormalBasis| |comment| |c06ekf| |critBonD| |leftUnits| |setelt!|
+ |cycleEntry| |rootOfIrreduciblePoly| |OMputEndBVar| |f01brf| |f07fef|
+ |lifting1| |safetyMargin| |usingTable?| |cycles| |flatten| |universe|
+ |checkRur| |mainSquareFreePart| |e02bbf| |resultantEuclideannaif|
+ |size| |signatureAst| |rroot| |viewport3D| |definingPolynomial|
+ |isTimes| |fortranReal| |rightFactorCandidate| |alternative?|
+ |hasSolution?| |subResultantsChain| |length| |atrapezoidal| |xCoord|
+ |mathieu11| |nextSubsetGray| |cycle| |nodeOf?| |fprindINFO| |expint|
+ |pattern| |innerEigenvectors| |scripts| |basisOfNucleus| |implies|
+ |e04dgf| |palgextint0| |cyclotomic| |e01daf| |debug3D| |first| |entry|
+ |e01baf| |dn| |andOperands| |e01sef| ** |viewDeltaYDefault| |f02axf|
+ |power| |moreAlgebraic?| |taylorIfCan| |rest| |isOp| |branchPoint?|
+ |createRandomElement| |OMgetAttr| |xor| |leftCharacteristicPolynomial|
+ |mainCharacterization| |round| |substitute| |triangularSystems|
+ |inGroundField?| |outputBinaryFile| |laplace| |d02gbf| |triangular?|
+ |linearPolynomials| |datalist| |initial| |makeFR| |makeGraphImage|
+ |LyndonWordsList| |rowEchelonLocal| EQ |OMputInteger| |binomThmExpt|
+ |initials| |yCoordinates| |symmetricSquare| |subSet| |realSolve|
+ |internal?| |expenseOfEvaluationIF| |iicosh| |compose| |repeating|
+ |qualifier| |vark| |rule| |check| |ramifiedAtInfinity?| |unitNormal|
+ |inHallBasis?| |pushNewContour| |radicalEigenvalues| |ocf2ocdf|
+ |rightFactorIfCan| |tab1| |taylorQuoByVar| |graphs| |simpson|
+ |randomR| |member?| |df2st| |monomRDEsys| |floor| |d02bhf| |drawStyle|
+ |extendedIntegrate| |OMUnknownCD?| |outputMeasure| |inverseColeman|
+ |returnTypeOf| |linear?| |pointColorPalette| |trivialIdeal?|
+ |cschIfCan| |PollardSmallFactor| |gramschmidt| |deepestTail| |top|
+ |makeTerm| |OMgetEndApp| |generalizedInverse| |FormatArabic|
+ |radicalSolve| |setfirst!| |inf| |explogs2trigs| |expintegrate|
+ |repeating?| |externalList| |imagj| |unit?| |c06eaf| |scalarMatrix|
+ |surface| |lagrange| |se2rfi| |headReduce| |kind| |in?| |term?|
+ |orbits| |selectNonFiniteRoutines| |ranges| |besselK| |denominators|
+ |leader| |comp| |nextSublist| |df2mf| |OMgetBVar| |ptFunc|
+ |showIntensityFunctions| |createNormalElement| |startTableInvSet!|
+ |resetBadValues| |subCase?| |c06gqf| |unexpand| |mapDown!|
+ |countRealRoots| |countable?| |RittWuCompare| |op| |coerceListOfPairs|
+ |iitan| |laurentIfCan| |sPol| |goodnessOfFit| |realEigenvalues|
+ |traceMatrix| |setprevious!| |select!| |groebnerIdeal|
+ |solveLinearPolynomialEquationByFractions| |rischDE| |key?|
+ |OMopenFile| |diagonalMatrix| |hessian| |makeUnit| |screenResolution|
+ |quotientByP| |parent| |concat| |slex| |arity| |parabolicCylindrical|
+ |solid?| |d03edf| |complete| |internalInfRittWu?| |plotPolar|
+ |extensionDegree| |setAttributeButtonStep| |bag| |complexRoots|
+ |differentialVariables| |say| |normal01| |ran| |fractRadix|
+ |cyclicParents| UTS2UP ~ |atoms| |dequeue| |cAcot|
+ |algebraicDecompose| |constantKernel| |convergents| |OMputError| |Is|
+ |headRemainder| |quasiRegular| |modifyPoint| |clearTable!|
+ |alphabetic| |curveColor| |permutationGroup| |moduleSum|
+ |univariatePolynomialsGcds| |reseed| |union| |open| |digit?| |cCot|
+ |rightOne| |squareFreePolynomial| |digits| |deriv| |finite?|
+ |clearDenominator| |gbasis| |f07fdf| |viewPhiDefault| |errorInfo|
+ |mainVariable| |callForm?| |s15aef| |central?| |cCosh| |resultantnaif|
+ |lazyPquo| |showTheIFTable| |predicate| |chineseRemainder| |shiftLeft|
+ |call| |rk4| |intersect| |lookup| |printInfo!| |children| |revert|
+ |rootPower| |f01ref| |nodes| |fi2df| |setleft!| |sdf2lst|
+ |permutation| |reset| |useEisensteinCriterion?| |pToHdmp| |freeOf?|
+ |leadingExponent| |getOperands| |integralCoordinates| |palgintegrate|
+ |mkPrim| |showArrayValues| |powerAssociative?| |factorFraction|
+ |module| |setColumn!| |makeFloatFunction| |generalInfiniteProduct|
+ |entry?| |multiset| |s17dgf| |write| |rangeIsFinite|
+ |fortranDoubleComplex| |messagePrint| |janko2| |radicalSimplify|
+ |pdct| |save| |inR?| |OMconnOutDevice| |bumprow| |s18aff|
+ |rationalFunction| |iiperm| |asec| |commutative?| |innerSolve|
+ |complexIntegrate| |LazardQuotient| |cylindrical| |prod| |computeInt|
+ |OMputApp| |localReal?| |acsc| |elem?| |rst| |algDsolve| |branchIfCan|
+ |genericLeftMinimalPolynomial| |addmod| |OMgetVariable| |super|
+ |mantissa| |sinh| |noKaratsuba| |primitive?| |generic?| |patternMatch|
+ |mainValue| |associator| |definingInequation| |curve| |separate|
+ |var2Steps| |parameters| |cosh| |clipWithRanges| |hconcat| |myDegree|
+ |numer| |stFunc2| |implies?| |sin2csc| |nand| |e04ycf| |mainVariable?|
+ |tanh| |rotate!| |graphCurves| |denom| |taylorRep| |constant|
+ |arrayStack| |generalizedEigenvector| |sizeMultiplication|
+ |scaleRoots| |hcrf| |coth| |deepCopy| |integerBound| |s14baf|
+ |radPoly| |iiasech| |generalPosition| |realEigenvectors|
+ |hasPredicate?| |linearAssociatedLog| |listexp|
+ |basisOfCommutingElements| |sech| |leftQuotient| |companionBlocks|
+ |ksec| |pi| |abs| |lieAlgebra?| |primeFactor| |copy!| |e01bhf|
+ |perfectNthRoot| |csch| |setPosition| |mainMonomial| |infinity| |port|
+ |cAsin| |OMcloseConn| |removeIrreducibleRedundantFactors|
+ |setchildren!| |d01bbf| |badValues| |compdegd| |asinh| |whatInfinity|
+ |cosIfCan| |csubst| |pack!| |multMonom| |keys|
+ |resultantReduitEuclidean| |queue| |subNode?| |leftDiscriminant|
+ |empty?| |acosh| |transcendentalDecompose| |setVariableOrder|
+ |binarySearchTree| |terms| |cPower| |matrix| |irreducible?|
+ |leftExtendedGcd| |fortranTypeOf| |sumOfKthPowerDivisors| |solve|
+ |subst| |close!| |kernel| |atanh| |OMputEndAttr| |axes| |OMmakeConn|
+ |optimize| |firstDenom| |semiSubResultantGcdEuclidean1| |reduced?|
+ |elseBranch| |closed?| |bipolar| |acoth| |indiceSubResultant|
+ |setOrder| |separateDegrees| |draw| |leftZero| |sup|
+ |LagrangeInterpolation| |basisOfRightNucloid| |conical|
+ |internalIntegrate| |asech| |minrank| |rowEchelon| |BumInSepFFE|
+ |someBasis| |monomialIntegrate| |whileLoop| |setTex!| |bitCoef|
+ |lazyEvaluate| |coHeight| |hspace| |chebyshevT| |extend|
+ |setImagSteps| |determinant| |multiple| |laguerreL|
+ |nextNormalPrimitivePoly| |makeViewport3D| |printInfo|
+ |quotedOperators| |charClass| |totalfract| |evenInfiniteProduct|
+ |printTypes| |rightTrace| |applyQuote| |rotatex| |subresultantVector|
+ |makeObject| |iifact| |zag| |sylvesterSequence| |linears|
+ |selectPDERoutines| |objects| |wreath| |rightRank| |rootRadius|
+ |useNagFunctions| |squareTop| |B1solve| |integral?|
+ |stoseIntegralLastSubResultant| |base| |acosIfCan| |OMsupportsSymbol?|
+ |sign| |coef| |integralMatrixAtInfinity| |extendedint| |interpret|
+ |reduceLODE| |algebraicSort| |dominantTerm| |isQuotient| |f04faf|
+ |ruleset| |simplifyPower| |genericLeftDiscriminant| |wronskianMatrix|
+ |OMencodingXML| |removeSinhSq| |bits| |f04mcf| |enterInCache|
+ |primeFrobenius| |bat1| |quadraticForm| |nil| |infinite|
|arbitraryExponent| |approximate| |complex| |shallowMutable|
|canonical| |noetherian| |central| |partiallyOrderedSet|
|arbitraryPrecision| |canonicalsClosed| |noZeroDivisors|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 6a430ca2..14c18906 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5160 +1,5164 @@
-(3175158 . 3431822580)
-((-3654 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-3491 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-1705 ((|#2| $ (-550) |#2|) NIL) ((|#2| $ (-1194 (-550)) |#2|) 34)) (-2342 (($ $) 59)) (-2419 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-2302 (((-550) (-1 (-112) |#2|) $) 22) (((-550) |#2| $) NIL) (((-550) |#2| $ (-550)) 73)) (-3450 (((-623 |#2|) $) 13)) (-1832 (($ (-1 (-112) |#2| |#2|) $ $) 48) (($ $ $) NIL)) (-3234 (($ (-1 |#2| |#2|) $) 29)) (-3972 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-2055 (($ |#2| $ (-550)) NIL) (($ $ $ (-550)) 50)) (-3321 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 24)) (-1543 (((-112) (-1 (-112) |#2|) $) 21)) (-2680 ((|#2| $ (-550) |#2|) NIL) ((|#2| $ (-550)) NIL) (($ $ (-1194 (-550))) 49)) (-1529 (($ $ (-550)) 56) (($ $ (-1194 (-550))) 55)) (-3350 (((-749) (-1 (-112) |#2|) $) 26) (((-749) |#2| $) NIL)) (-3593 (($ $ $ (-550)) 52)) (-1731 (($ $) 51)) (-1532 (($ (-623 |#2|)) 53)) (-3227 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-623 $)) 62)) (-1518 (((-836) $) 69)) (-1675 (((-112) (-1 (-112) |#2|) $) 20)) (-2316 (((-112) $ $) 72)) (-2335 (((-112) $ $) 75)))
-(((-18 |#1| |#2|) (-10 -8 (-15 -2316 ((-112) |#1| |#1|)) (-15 -1518 ((-836) |#1|)) (-15 -2335 ((-112) |#1| |#1|)) (-15 -3491 (|#1| |#1|)) (-15 -3491 (|#1| (-1 (-112) |#2| |#2|) |#1|)) (-15 -2342 (|#1| |#1|)) (-15 -3593 (|#1| |#1| |#1| (-550))) (-15 -3654 ((-112) |#1|)) (-15 -1832 (|#1| |#1| |#1|)) (-15 -2302 ((-550) |#2| |#1| (-550))) (-15 -2302 ((-550) |#2| |#1|)) (-15 -2302 ((-550) (-1 (-112) |#2|) |#1|)) (-15 -3654 ((-112) (-1 (-112) |#2| |#2|) |#1|)) (-15 -1832 (|#1| (-1 (-112) |#2| |#2|) |#1| |#1|)) (-15 -1705 (|#2| |#1| (-1194 (-550)) |#2|)) (-15 -2055 (|#1| |#1| |#1| (-550))) (-15 -2055 (|#1| |#2| |#1| (-550))) (-15 -1529 (|#1| |#1| (-1194 (-550)))) (-15 -1529 (|#1| |#1| (-550))) (-15 -2680 (|#1| |#1| (-1194 (-550)))) (-15 -3972 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3227 (|#1| (-623 |#1|))) (-15 -3227 (|#1| |#1| |#1|)) (-15 -3227 (|#1| |#2| |#1|)) (-15 -3227 (|#1| |#1| |#2|)) (-15 -1532 (|#1| (-623 |#2|))) (-15 -3321 ((-3 |#2| "failed") (-1 (-112) |#2|) |#1|)) (-15 -2419 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -2419 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -2419 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -2680 (|#2| |#1| (-550))) (-15 -2680 (|#2| |#1| (-550) |#2|)) (-15 -1705 (|#2| |#1| (-550) |#2|)) (-15 -3350 ((-749) |#2| |#1|)) (-15 -3450 ((-623 |#2|) |#1|)) (-15 -3350 ((-749) (-1 (-112) |#2|) |#1|)) (-15 -1543 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -1675 ((-112) (-1 (-112) |#2|) |#1|)) (-15 -3234 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3972 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -1731 (|#1| |#1|))) (-19 |#2|) (-1181)) (T -18))
+(3175758 . 3431897926)
+((-1837 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-2734 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-2409 ((|#2| $ (-550) |#2|) NIL) ((|#2| $ (-1195 (-550)) |#2|) 34)) (-3770 (($ $) 59)) (-2924 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-3088 (((-550) (-1 (-112) |#2|) $) 22) (((-550) |#2| $) NIL) (((-550) |#2| $ (-550)) 73)) (-2971 (((-623 |#2|) $) 13)) (-2441 (($ (-1 (-112) |#2| |#2|) $ $) 48) (($ $ $) NIL)) (-3311 (($ (-1 |#2| |#2|) $) 29)) (-2392 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-1476 (($ |#2| $ (-550)) NIL) (($ $ $ (-550)) 50)) (-1614 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 24)) (-1410 (((-112) (-1 (-112) |#2|) $) 21)) (-2757 ((|#2| $ (-550) |#2|) NIL) ((|#2| $ (-550)) NIL) (($ $ (-1195 (-550))) 49)) (-1512 (($ $ (-550)) 56) (($ $ (-1195 (-550))) 55)) (-3457 (((-749) (-1 (-112) |#2|) $) 26) (((-749) |#2| $) NIL)) (-2502 (($ $ $ (-550)) 52)) (-2435 (($ $) 51)) (-2245 (($ (-623 |#2|)) 53)) (-4006 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-623 $)) 62)) (-2233 (((-837) $) 69)) (-3404 (((-112) (-1 (-112) |#2|) $) 20)) (-2264 (((-112) $ $) 72)) (-2290 (((-112) $ $) 75)))
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NIL
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-(((-19 |#1|) (-138) (-1181)) (T -19))
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NIL
-(-13 (-366 |t#1|) (-10 -7 (-6 -4343)))
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-((-3219 (((-3 $ "failed") $ $) 12)) (-2403 (($ $) NIL) (($ $ $) 9)) (* (($ (-894) $) NIL) (($ (-749) $) 16) (($ (-550) $) 21)))
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+(-13 (-366 |t#1|) (-10 -7 (-6 -4345)))
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NIL
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NIL
(((-97) (-138)) (T -97))
NIL
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-NIL
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+NIL
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(((-101) (-138)) (T -101))
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-((-3685 (($ (-623 |#2|)) 11)))
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NIL
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(((-188) (-765)) (T -188))
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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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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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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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
(-56 |#1| |#4| |#5|)
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-(((-511 |#1| |#2|) (-644 |#1|) (-1181) (-550)) (T -511))
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NIL
(-644 |#1|)
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NIL
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(((-171) . T))
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(((-522 |#1|) (-13 (-771) (-500 (-749) |#1|)) (-825)) (T -522))
NIL
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(((-819) (-138)) (T -819))
NIL
(-13 (-825) (-361))
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(((-821) (-138)) (T -821))
NIL
(-13 (-832) (-705))
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NIL
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(((-823) (-138)) (T -823))
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-NIL
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+NIL
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(((-825) (-138)) (T -825))
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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
-NIL
-NIL
-NIL
-NIL
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T) -8 NIL NIL) (-1172 2870209 2871055 2871997 "TRMANIP" 2875082 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1171 2869650 2869713 2869876 "TRIMAT" 2870141 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1170 2867446 2867683 2868047 "TRIGMNIP" 2869399 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1169 2866966 2867079 2867109 "TRIGCAT" 2867322 T TRIGCAT (NIL) -9 NIL NIL) (-1168 2866635 2866714 2866855 "TRIGCAT-" 2866860 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1167 2863534 2865495 2865775 "TREE" 2866390 NIL TREE (NIL T) -8 NIL NIL) (-1166 2862808 2863336 2863366 "TRANFUN" 2863401 T TRANFUN (NIL) -9 NIL 2863467) (-1165 2862087 2862278 2862558 "TRANFUN-" 2862563 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1164 2861891 2861923 2861984 "TOPSP" 2862048 T TOPSP (NIL) -7 NIL NIL) (-1163 2861239 2861354 2861508 "TOOLSIGN" 2861772 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1162 2859900 2860416 2860655 "TEXTFILE" 2861022 T TEXTFILE (NIL) -8 NIL NIL) (-1161 2857765 2858279 2858717 "TEX" 2859484 T TEX (NIL) -8 NIL NIL) (-1160 2857546 2857577 2857649 "TEX1" 2857728 NIL TEX1 (NIL T) -7 NIL NIL) (-1159 2857194 2857257 2857347 "TEMUTL" 2857478 T TEMUTL (NIL) -7 NIL NIL) (-1158 2855348 2855628 2855953 "TBCMPPK" 2856917 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1157 2847236 2853508 2853564 "TBAGG" 2853964 NIL TBAGG (NIL T T) -9 NIL 2854175) (-1156 2842306 2843794 2845548 "TBAGG-" 2845553 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1155 2841690 2841797 2841942 "TANEXP" 2842195 NIL TANEXP (NIL T) -7 NIL NIL) (-1154 2835191 2841547 2841640 "TABLE" 2841645 NIL TABLE (NIL T T) -8 NIL NIL) (-1153 2834603 2834702 2834840 "TABLEAU" 2835088 NIL TABLEAU (NIL T) -8 NIL NIL) (-1152 2829211 2830431 2831679 "TABLBUMP" 2833389 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1151 2828639 2828739 2828867 "SYSTEM" 2829105 T SYSTEM (NIL) -7 NIL NIL) (-1150 2825102 2825797 2826580 "SYSSOLP" 2827890 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1149 2821394 2822101 2822835 "SYNTAX" 2824390 T SYNTAX (NIL) -8 NIL NIL) (-1148 2818552 2819154 2819786 "SYMTAB" 2820784 T SYMTAB (NIL) -8 NIL NIL) (-1147 2813801 2814703 2815686 "SYMS" 2817591 T SYMS (NIL) -8 NIL NIL) (-1146 2811073 2813259 2813489 "SYMPOLY" 2813606 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1145 2810590 2810665 2810788 "SYMFUNC" 2810985 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1144 2806567 2807827 2808649 "SYMBOL" 2809790 T SYMBOL (NIL) -8 NIL NIL) (-1143 2800106 2801795 2803515 "SWITCH" 2804869 T SWITCH (NIL) -8 NIL NIL) (-1142 2793376 2798927 2799230 "SUTS" 2799861 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1141 2785345 2792491 2792773 "SUPXS" 2793152 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1140 2776874 2784963 2785089 "SUP" 2785254 NIL SUP (NIL T) -8 NIL NIL) (-1139 2776033 2776160 2776377 "SUPFRACF" 2776742 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1138 2775654 2775713 2775826 "SUP2" 2775968 NIL SUP2 (NIL T T) -7 NIL NIL) (-1137 2774067 2774341 2774704 "SUMRF" 2775353 NIL SUMRF (NIL T) -7 NIL NIL) (-1136 2773381 2773447 2773646 "SUMFS" 2773988 NIL SUMFS (NIL T T) -7 NIL NIL) (-1135 2757390 2772558 2772809 "SULS" 2773188 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1134 2757019 2757212 2757282 "SUCHTAST" 2757342 T SUCHTAST (NIL) -8 NIL NIL) (-1133 2756341 2756544 2756684 "SUCH" 2756927 NIL SUCH (NIL T T) -8 NIL NIL) (-1132 2750235 2751247 2752206 "SUBSPACE" 2755429 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1131 2749665 2749755 2749919 "SUBRESP" 2750123 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1130 2743034 2744330 2745641 "STTF" 2748401 NIL STTF (NIL T) -7 NIL NIL) (-1129 2737207 2738327 2739474 "STTFNC" 2741934 NIL STTFNC (NIL T) -7 NIL NIL) (-1128 2728522 2730389 2732183 "STTAYLOR" 2735448 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1127 2721766 2728386 2728469 "STRTBL" 2728474 NIL STRTBL (NIL T) -8 NIL NIL) (-1126 2717157 2721721 2721752 "STRING" 2721757 T STRING (NIL) -8 NIL NIL) (-1125 2712045 2716530 2716560 "STRICAT" 2716619 T STRICAT (NIL) -9 NIL 2716681) (-1124 2704758 2709568 2710188 "STREAM" 2711460 NIL STREAM (NIL T) -8 NIL NIL) (-1123 2704268 2704345 2704489 "STREAM3" 2704675 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1122 2703250 2703433 2703668 "STREAM2" 2704081 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1121 2702938 2702990 2703083 "STREAM1" 2703192 NIL STREAM1 (NIL T) -7 NIL NIL) (-1120 2701954 2702135 2702366 "STINPROD" 2702754 NIL STINPROD (NIL T) -7 NIL NIL) (-1119 2701532 2701716 2701746 "STEP" 2701826 T STEP (NIL) -9 NIL 2701904) (-1118 2695075 2701431 2701508 "STBL" 2701513 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1117 2690250 2694297 2694340 "STAGG" 2694493 NIL STAGG (NIL T) -9 NIL 2694582) (-1116 2687952 2688554 2689426 "STAGG-" 2689431 NIL STAGG- (NIL T T) -8 NIL NIL) (-1115 2686147 2687722 2687814 "STACK" 2687895 NIL STACK (NIL T) -8 NIL NIL) (-1114 2678872 2684288 2684744 "SREGSET" 2685777 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1113 2671298 2672666 2674179 "SRDCMPK" 2677478 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1112 2664265 2668738 2668768 "SRAGG" 2670071 T SRAGG (NIL) -9 NIL 2670679) (-1111 2663282 2663537 2663916 "SRAGG-" 2663921 NIL SRAGG- (NIL T) -8 NIL NIL) (-1110 2657777 2662229 2662650 "SQMATRIX" 2662908 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1109 2651529 2654497 2655223 "SPLTREE" 2657123 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1108 2647519 2648185 2648831 "SPLNODE" 2650955 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1107 2646566 2646799 2646829 "SPFCAT" 2647273 T SPFCAT (NIL) -9 NIL NIL) (-1106 2645303 2645513 2645777 "SPECOUT" 2646324 T SPECOUT (NIL) -7 NIL NIL) (-1105 2636992 2638736 2638766 "SPADXPT" 2643158 T SPADXPT (NIL) -9 NIL 2645192) (-1104 2636753 2636793 2636862 "SPADPRSR" 2636945 T SPADPRSR (NIL) -7 NIL NIL) (-1103 2634936 2636708 2636739 "SPADAST" 2636744 T SPADAST (NIL) -8 NIL NIL) (-1102 2626907 2628654 2628697 "SPACEC" 2633070 NIL SPACEC (NIL T) -9 NIL 2634886) (-1101 2625078 2626839 2626888 "SPACE3" 2626893 NIL SPACE3 (NIL T) -8 NIL NIL) (-1100 2623830 2624001 2624292 "SORTPAK" 2624883 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1099 2621880 2622183 2622602 "SOLVETRA" 2623494 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1098 2620891 2621113 2621387 "SOLVESER" 2621653 NIL SOLVESER (NIL T) -7 NIL NIL) (-1097 2616111 2616992 2617994 "SOLVERAD" 2619943 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1096 2611926 2612535 2613264 "SOLVEFOR" 2615478 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1095 2606223 2611275 2611372 "SNTSCAT" 2611377 NIL SNTSCAT (NIL T T T T) -9 NIL 2611447) (-1094 2600366 2604546 2604937 "SMTS" 2605913 NIL SMTS (NIL T T T) -8 NIL NIL) (-1093 2594816 2600254 2600331 "SMP" 2600336 NIL SMP (NIL T T) -8 NIL NIL) (-1092 2592975 2593276 2593674 "SMITH" 2594513 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1091 2585958 2590113 2590216 "SMATCAT" 2591567 NIL SMATCAT (NIL NIL T T T) -9 NIL 2592117) (-1090 2582898 2583721 2584899 "SMATCAT-" 2584904 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1089 2580611 2582134 2582177 "SKAGG" 2582438 NIL SKAGG (NIL T) -9 NIL 2582573) (-1088 2576727 2579715 2579993 "SINT" 2580355 T SINT (NIL) -8 NIL NIL) (-1087 2576499 2576537 2576603 "SIMPAN" 2576683 T SIMPAN (NIL) -7 NIL NIL) (-1086 2575806 2576034 2576174 "SIG" 2576381 T SIG (NIL) -8 NIL NIL) (-1085 2574644 2574865 2575140 "SIGNRF" 2575565 NIL SIGNRF (NIL T) -7 NIL NIL) (-1084 2573449 2573600 2573891 "SIGNEF" 2574473 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1083 2572782 2573032 2573156 "SIGAST" 2573347 T SIGAST (NIL) -8 NIL NIL) (-1082 2570472 2570926 2571432 "SHP" 2572323 NIL SHP (NIL T NIL) -7 NIL NIL) (-1081 2564378 2570373 2570449 "SHDP" 2570454 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1080 2563977 2564143 2564173 "SGROUP" 2564266 T SGROUP (NIL) -9 NIL 2564328) (-1079 2563835 2563861 2563934 "SGROUP-" 2563939 NIL SGROUP- (NIL T) -8 NIL NIL) (-1078 2560671 2561368 2562091 "SGCF" 2563134 T SGCF (NIL) -7 NIL NIL) (-1077 2555066 2560118 2560215 "SFRTCAT" 2560220 NIL SFRTCAT (NIL T T T T) -9 NIL 2560259) (-1076 2548490 2549505 2550641 "SFRGCD" 2554049 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1075 2541618 2542689 2543875 "SFQCMPK" 2547423 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1074 2541240 2541329 2541439 "SFORT" 2541559 NIL SFORT (NIL T T) -8 NIL NIL) (-1073 2540385 2541080 2541201 "SEXOF" 2541206 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1072 2539519 2540266 2540334 "SEX" 2540339 T SEX (NIL) -8 NIL NIL) (-1071 2534295 2534984 2535079 "SEXCAT" 2538850 NIL SEXCAT (NIL T T T T T) -9 NIL 2539469) (-1070 2531475 2534229 2534277 "SET" 2534282 NIL SET (NIL T) -8 NIL NIL) (-1069 2529726 2530188 2530493 "SETMN" 2531216 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1068 2529332 2529458 2529488 "SETCAT" 2529605 T SETCAT (NIL) -9 NIL 2529690) (-1067 2529112 2529164 2529263 "SETCAT-" 2529268 NIL SETCAT- (NIL T) -8 NIL NIL) (-1066 2525499 2527573 2527616 "SETAGG" 2528486 NIL SETAGG (NIL T) -9 NIL 2528826) (-1065 2524957 2525073 2525310 "SETAGG-" 2525315 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1064 2524427 2524653 2524754 "SEQAST" 2524878 T SEQAST (NIL) -8 NIL NIL) (-1063 2523631 2523924 2523985 "SEGXCAT" 2524271 NIL SEGXCAT (NIL T T) -9 NIL 2524391) (-1062 2522687 2523297 2523479 "SEG" 2523484 NIL SEG (NIL T) -8 NIL NIL) (-1061 2521594 2521807 2521850 "SEGCAT" 2522432 NIL SEGCAT (NIL T) -9 NIL 2522670) (-1060 2520643 2520973 2521173 "SEGBIND" 2521429 NIL SEGBIND (NIL T) -8 NIL NIL) (-1059 2520264 2520323 2520436 "SEGBIND2" 2520578 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1058 2519865 2520065 2520142 "SEGAST" 2520209 T SEGAST (NIL) -8 NIL NIL) (-1057 2519084 2519210 2519414 "SEG2" 2519709 NIL SEG2 (NIL T T) -7 NIL NIL) (-1056 2518521 2519019 2519066 "SDVAR" 2519071 NIL SDVAR (NIL T) -8 NIL NIL) (-1055 2510811 2518291 2518421 "SDPOL" 2518426 NIL SDPOL (NIL T) -8 NIL NIL) (-1054 2509404 2509670 2509989 "SCPKG" 2510526 NIL SCPKG (NIL T) -7 NIL NIL) (-1053 2508540 2508720 2508920 "SCOPE" 2509226 T SCOPE (NIL) -8 NIL NIL) (-1052 2507761 2507894 2508073 "SCACHE" 2508395 NIL SCACHE (NIL T) -7 NIL NIL) (-1051 2507470 2507630 2507660 "SASTCAT" 2507665 T SASTCAT (NIL) -9 NIL 2507678) (-1050 2506909 2507230 2507315 "SAOS" 2507407 T SAOS (NIL) -8 NIL NIL) (-1049 2506474 2506509 2506682 "SAERFFC" 2506868 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1048 2500448 2506371 2506451 "SAE" 2506456 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1047 2500041 2500076 2500235 "SAEFACT" 2500407 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1046 2498362 2498676 2499077 "RURPK" 2499707 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1045 2496998 2497277 2497589 "RULESET" 2498196 NIL RULESET (NIL T T T) -8 NIL NIL) (-1044 2494185 2494688 2495153 "RULE" 2496679 NIL RULE (NIL T T T) -8 NIL NIL) (-1043 2493824 2493979 2494062 "RULECOLD" 2494137 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1042 2493322 2493541 2493635 "RSTRCAST" 2493752 T RSTRCAST (NIL) -8 NIL NIL) (-1041 2488171 2488965 2489885 "RSETGCD" 2492521 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1040 2477428 2482480 2482577 "RSETCAT" 2486696 NIL RSETCAT (NIL T T T T) -9 NIL 2487793) (-1039 2475355 2475894 2476718 "RSETCAT-" 2476723 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1038 2467742 2469117 2470637 "RSDCMPK" 2473954 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1037 2465747 2466188 2466262 "RRCC" 2467348 NIL RRCC (NIL T T) -9 NIL 2467692) (-1036 2465098 2465272 2465551 "RRCC-" 2465556 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1035 2464568 2464794 2464895 "RPTAST" 2465019 T RPTAST (NIL) -8 NIL NIL) (-1034 2438796 2448381 2448448 "RPOLCAT" 2459112 NIL RPOLCAT (NIL T T T) -9 NIL 2462271) (-1033 2430296 2432634 2435756 "RPOLCAT-" 2435761 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1032 2421343 2428507 2428989 "ROUTINE" 2429836 T ROUTINE (NIL) -8 NIL NIL) (-1031 2418101 2420894 2421043 "ROMAN" 2421216 T ROMAN (NIL) -8 NIL NIL) (-1030 2416376 2416961 2417221 "ROIRC" 2417906 NIL ROIRC (NIL T T) -8 NIL NIL) (-1029 2412827 2415066 2415096 "RNS" 2415400 T RNS (NIL) -9 NIL 2415672) (-1028 2411336 2411719 2412253 "RNS-" 2412328 NIL RNS- (NIL T) -8 NIL NIL) (-1027 2410785 2411167 2411197 "RNG" 2411202 T RNG (NIL) -9 NIL 2411223) (-1026 2410177 2410539 2410582 "RMODULE" 2410644 NIL RMODULE (NIL T) -9 NIL 2410686) (-1025 2409013 2409107 2409443 "RMCAT2" 2410078 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1024 2405718 2408187 2408512 "RMATRIX" 2408747 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1023 2398660 2400894 2401009 "RMATCAT" 2404368 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2405350) (-1022 2398035 2398182 2398489 "RMATCAT-" 2398494 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1021 2397602 2397677 2397805 "RINTERP" 2397954 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1020 2396690 2397210 2397240 "RING" 2397352 T RING (NIL) -9 NIL 2397447) (-1019 2396482 2396526 2396623 "RING-" 2396628 NIL RING- (NIL T) -8 NIL NIL) (-1018 2395323 2395560 2395818 "RIDIST" 2396246 T RIDIST (NIL) -7 NIL NIL) (-1017 2386639 2394791 2394997 "RGCHAIN" 2395171 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1016 2383633 2384247 2384917 "RF" 2386003 NIL RF (NIL T) -7 NIL NIL) (-1015 2383279 2383342 2383445 "RFFACTOR" 2383564 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1014 2383004 2383039 2383136 "RFFACT" 2383238 NIL RFFACT (NIL T) -7 NIL NIL) (-1013 2381121 2381485 2381867 "RFDIST" 2382644 T RFDIST (NIL) -7 NIL NIL) (-1012 2380574 2380666 2380829 "RETSOL" 2381023 NIL RETSOL (NIL T T) -7 NIL NIL) (-1011 2380162 2380242 2380285 "RETRACT" 2380478 NIL RETRACT (NIL T) -9 NIL NIL) (-1010 2380011 2380036 2380123 "RETRACT-" 2380128 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1009 2379640 2379833 2379903 "RETAST" 2379963 T RETAST (NIL) -8 NIL NIL) (-1008 2372494 2379293 2379420 "RESULT" 2379535 T RESULT (NIL) -8 NIL NIL) (-1007 2371120 2371763 2371962 "RESRING" 2372397 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1006 2370756 2370805 2370903 "RESLATC" 2371057 NIL RESLATC (NIL T) -7 NIL NIL) (-1005 2370462 2370496 2370603 "REPSQ" 2370715 NIL REPSQ (NIL T) -7 NIL NIL) (-1004 2367884 2368464 2369066 "REP" 2369882 T REP (NIL) -7 NIL NIL) (-1003 2367582 2367616 2367727 "REPDB" 2367843 NIL REPDB (NIL T) -7 NIL NIL) (-1002 2361492 2362871 2364094 "REP2" 2366394 NIL REP2 (NIL T) -7 NIL NIL) (-1001 2357869 2358550 2359358 "REP1" 2360719 NIL REP1 (NIL T) -7 NIL NIL) (-1000 2350595 2356010 2356466 "REGSET" 2357499 NIL REGSET (NIL T T T T) -8 NIL NIL) (-999 2349416 2349751 2349999 "REF" 2350380 NIL REF (NIL T) -8 NIL NIL) (-998 2348797 2348900 2349065 "REDORDER" 2349300 NIL REDORDER (NIL T T) -7 NIL NIL) (-997 2344817 2348025 2348248 "RECLOS" 2348626 NIL RECLOS (NIL T) -8 NIL NIL) (-996 2343874 2344055 2344268 "REALSOLV" 2344624 T REALSOLV (NIL) -7 NIL NIL) (-995 2343722 2343763 2343791 "REAL" 2343796 T REAL (NIL) -9 NIL 2343831) (-994 2340213 2341015 2341897 "REAL0Q" 2342887 NIL REAL0Q (NIL T) -7 NIL NIL) (-993 2335824 2336812 2337871 "REAL0" 2339194 NIL REAL0 (NIL T) -7 NIL NIL) (-992 2335326 2335545 2335637 "RDUCEAST" 2335752 T RDUCEAST (NIL) -8 NIL NIL) (-991 2334734 2334806 2335011 "RDIV" 2335248 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-990 2333807 2333981 2334192 "RDIST" 2334556 NIL RDIST (NIL T) -7 NIL NIL) (-989 2332408 2332695 2333065 "RDETRS" 2333515 NIL RDETRS (NIL T T) -7 NIL NIL) (-988 2330225 2330679 2331215 "RDETR" 2331950 NIL RDETR (NIL T T) -7 NIL NIL) (-987 2328839 2329117 2329519 "RDEEFS" 2329941 NIL RDEEFS (NIL T T) -7 NIL NIL) (-986 2327337 2327643 2328073 "RDEEF" 2328527 NIL RDEEF (NIL T T) -7 NIL NIL) (-985 2321674 2324545 2324573 "RCFIELD" 2325850 T RCFIELD (NIL) -9 NIL 2326580) (-984 2319743 2320247 2320940 "RCFIELD-" 2321013 NIL RCFIELD- (NIL T) -8 NIL NIL) (-983 2316074 2317859 2317900 "RCAGG" 2318971 NIL RCAGG (NIL T) -9 NIL 2319436) (-982 2315705 2315799 2315959 "RCAGG-" 2315964 NIL RCAGG- (NIL T T) -8 NIL NIL) (-981 2315045 2315157 2315320 "RATRET" 2315589 NIL RATRET (NIL T) -7 NIL NIL) (-980 2314602 2314669 2314788 "RATFACT" 2314973 NIL RATFACT (NIL T) -7 NIL NIL) (-979 2313917 2314037 2314187 "RANDSRC" 2314472 T RANDSRC (NIL) -7 NIL NIL) (-978 2313654 2313698 2313769 "RADUTIL" 2313866 T RADUTIL (NIL) -7 NIL NIL) (-977 2306719 2312397 2312714 "RADIX" 2313369 NIL RADIX (NIL NIL) -8 NIL NIL) (-976 2298375 2306563 2306691 "RADFF" 2306696 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-975 2298027 2298102 2298130 "RADCAT" 2298287 T RADCAT (NIL) -9 NIL NIL) (-974 2297812 2297860 2297957 "RADCAT-" 2297962 NIL RADCAT- (NIL T) -8 NIL NIL) (-973 2295963 2297587 2297676 "QUEUE" 2297756 NIL QUEUE (NIL T) -8 NIL NIL) (-972 2292539 2295900 2295945 "QUAT" 2295950 NIL QUAT (NIL T) -8 NIL NIL) (-971 2292177 2292220 2292347 "QUATCT2" 2292490 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-970 2286037 2289338 2289378 "QUATCAT" 2290158 NIL QUATCAT (NIL T) -9 NIL 2290924) (-969 2282181 2283218 2284605 "QUATCAT-" 2284699 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-968 2279701 2281265 2281306 "QUAGG" 2281681 NIL QUAGG (NIL T) -9 NIL 2281856) (-967 2279333 2279526 2279594 "QQUTAST" 2279653 T QQUTAST (NIL) -8 NIL NIL) (-966 2278258 2278731 2278903 "QFORM" 2279205 NIL QFORM (NIL NIL T) -8 NIL NIL) (-965 2269591 2274794 2274834 "QFCAT" 2275492 NIL QFCAT (NIL T) -9 NIL 2276491) (-964 2265163 2266364 2267955 "QFCAT-" 2268049 NIL QFCAT- (NIL T T) -8 NIL NIL) (-963 2264801 2264844 2264971 "QFCAT2" 2265114 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-962 2264261 2264371 2264501 "QEQUAT" 2264691 T QEQUAT (NIL) -8 NIL NIL) (-961 2257409 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(-786 1867925 1868494 1869003 "ODEPROB" 1869567 T ODEPROB (NIL) -8 NIL NIL) (-785 1864447 1864930 1865577 "ODEPRIM" 1867404 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-784 1863696 1863798 1864058 "ODEPAL" 1864339 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-783 1859858 1860649 1861513 "ODEPACK" 1862852 T ODEPACK (NIL) -7 NIL NIL) (-782 1858891 1858998 1859227 "ODEINT" 1859747 NIL ODEINT (NIL T T) -7 NIL NIL) (-781 1852992 1854417 1855864 "ODEIFTBL" 1857464 T ODEIFTBL (NIL) -8 NIL NIL) (-780 1848327 1849113 1850072 "ODEEF" 1852151 NIL ODEEF (NIL T T) -7 NIL NIL) (-779 1847662 1847751 1847981 "ODECONST" 1848232 NIL ODECONST (NIL T T T) -7 NIL NIL) (-778 1845813 1846448 1846476 "ODECAT" 1847081 T ODECAT (NIL) -9 NIL 1847612) (-777 1842720 1845525 1845644 "OCT" 1845726 NIL OCT (NIL T) -8 NIL NIL) (-776 1842358 1842401 1842528 "OCTCT2" 1842671 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-775 1837219 1839619 1839659 "OC" 1840756 NIL OC (NIL T) -9 NIL 1841614) (-774 1834446 1835194 1836184 "OC-" 1836278 NIL OC- (NIL T T) -8 NIL NIL) (-773 1833824 1834266 1834294 "OCAMON" 1834299 T OCAMON (NIL) -9 NIL 1834320) (-772 1833381 1833696 1833724 "OASGP" 1833729 T OASGP (NIL) -9 NIL 1833749) (-771 1832668 1833131 1833159 "OAMONS" 1833199 T OAMONS (NIL) -9 NIL 1833242) (-770 1832108 1832515 1832543 "OAMON" 1832548 T OAMON (NIL) -9 NIL 1832568) (-769 1831412 1831904 1831932 "OAGROUP" 1831937 T OAGROUP (NIL) -9 NIL 1831957) (-768 1831102 1831152 1831240 "NUMTUBE" 1831356 NIL NUMTUBE (NIL T) -7 NIL NIL) (-767 1824675 1826193 1827729 "NUMQUAD" 1829586 T NUMQUAD (NIL) -7 NIL NIL) (-766 1820431 1821419 1822444 "NUMODE" 1823670 T NUMODE (NIL) -7 NIL NIL) (-765 1817812 1818666 1818694 "NUMINT" 1819617 T NUMINT (NIL) -9 NIL 1820381) (-764 1816760 1816957 1817175 "NUMFMT" 1817614 T NUMFMT (NIL) -7 NIL NIL) (-763 1803119 1806064 1808596 "NUMERIC" 1814267 NIL NUMERIC (NIL T) -7 NIL NIL) (-762 1797516 1802568 1802663 "NTSCAT" 1802668 NIL NTSCAT (NIL T T T T) -9 NIL 1802707) (-761 1796710 1796875 1797068 "NTPOLFN" 1797355 NIL NTPOLFN (NIL T) -7 NIL NIL) (-760 1784550 1793535 1794347 "NSUP" 1795931 NIL NSUP (NIL T) -8 NIL NIL) (-759 1784182 1784239 1784348 "NSUP2" 1784487 NIL NSUP2 (NIL T T) -7 NIL NIL) (-758 1774179 1783956 1784089 "NSMP" 1784094 NIL NSMP (NIL T T) -8 NIL NIL) (-757 1772611 1772912 1773269 "NREP" 1773867 NIL NREP (NIL T) -7 NIL NIL) (-756 1771202 1771454 1771812 "NPCOEF" 1772354 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-755 1770268 1770383 1770599 "NORMRETR" 1771083 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-754 1768309 1768599 1769008 "NORMPK" 1769976 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-753 1767994 1768022 1768146 "NORMMA" 1768275 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-752 1767821 1767951 1767980 "NONE" 1767985 T NONE (NIL) -8 NIL NIL) (-751 1767610 1767639 1767708 "NONE1" 1767785 NIL NONE1 (NIL T) -7 NIL NIL) (-750 1767093 1767155 1767341 "NODE1" 1767542 NIL NODE1 (NIL T T) -7 NIL NIL) (-749 1765433 1766256 1766511 "NNI" 1766858 T NNI (NIL) -8 NIL NIL) (-748 1763853 1764166 1764530 "NLINSOL" 1765101 NIL NLINSOL (NIL T) -7 NIL NIL) (-747 1760020 1760988 1761910 "NIPROB" 1762951 T NIPROB (NIL) -8 NIL NIL) (-746 1758777 1759011 1759313 "NFINTBAS" 1759782 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-745 1757485 1757716 1757997 "NCODIV" 1758545 NIL NCODIV (NIL T T) -7 NIL NIL) (-744 1757247 1757284 1757359 "NCNTFRAC" 1757442 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-743 1755427 1755791 1756211 "NCEP" 1756872 NIL NCEP (NIL T) -7 NIL NIL) (-742 1754338 1755077 1755105 "NASRING" 1755215 T NASRING (NIL) -9 NIL 1755289) (-741 1754133 1754177 1754271 "NASRING-" 1754276 NIL NASRING- (NIL T) -8 NIL NIL) (-740 1753286 1753785 1753813 "NARNG" 1753930 T NARNG (NIL) -9 NIL 1754021) (-739 1752978 1753045 1753179 "NARNG-" 1753184 NIL NARNG- (NIL T) -8 NIL NIL) (-738 1751857 1752064 1752299 "NAGSP" 1752763 T NAGSP (NIL) -7 NIL NIL) (-737 1743129 1744813 1746486 "NAGS" 1750204 T NAGS (NIL) -7 NIL NIL) (-736 1741677 1741985 1742316 "NAGF07" 1742818 T NAGF07 (NIL) -7 NIL NIL) (-735 1736215 1737506 1738813 "NAGF04" 1740390 T NAGF04 (NIL) -7 NIL NIL) (-734 1729183 1730797 1732430 "NAGF02" 1734602 T NAGF02 (NIL) -7 NIL NIL) (-733 1724407 1725507 1726624 "NAGF01" 1728086 T NAGF01 (NIL) -7 NIL NIL) (-732 1718035 1719601 1721186 "NAGE04" 1722842 T NAGE04 (NIL) -7 NIL NIL) (-731 1709204 1711325 1713455 "NAGE02" 1715925 T NAGE02 (NIL) -7 NIL NIL) (-730 1705157 1706104 1707068 "NAGE01" 1708260 T NAGE01 (NIL) -7 NIL NIL) (-729 1702952 1703486 1704044 "NAGD03" 1704619 T NAGD03 (NIL) -7 NIL NIL) (-728 1694702 1696630 1698584 "NAGD02" 1701018 T NAGD02 (NIL) -7 NIL NIL) (-727 1688513 1689938 1691378 "NAGD01" 1693282 T NAGD01 (NIL) -7 NIL NIL) (-726 1684722 1685544 1686381 "NAGC06" 1687696 T NAGC06 (NIL) -7 NIL NIL) (-725 1683187 1683519 1683875 "NAGC05" 1684386 T NAGC05 (NIL) -7 NIL NIL) (-724 1682563 1682682 1682826 "NAGC02" 1683063 T NAGC02 (NIL) -7 NIL NIL) (-723 1681623 1682180 1682220 "NAALG" 1682299 NIL NAALG (NIL T) -9 NIL 1682360) (-722 1681458 1681487 1681577 "NAALG-" 1681582 NIL NAALG- (NIL T T) -8 NIL NIL) (-721 1675408 1676516 1677703 "MULTSQFR" 1680354 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-720 1674727 1674802 1674986 "MULTFACT" 1675320 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-719 1667950 1671815 1671868 "MTSCAT" 1672938 NIL MTSCAT (NIL T T) -9 NIL 1673452) (-718 1667662 1667716 1667808 "MTHING" 1667890 NIL MTHING (NIL T) -7 NIL NIL) (-717 1667454 1667487 1667547 "MSYSCMD" 1667622 T MSYSCMD (NIL) -7 NIL NIL) (-716 1663566 1666209 1666529 "MSET" 1667167 NIL MSET (NIL T) -8 NIL NIL) (-715 1660661 1663127 1663168 "MSETAGG" 1663173 NIL MSETAGG (NIL T) -9 NIL 1663207) (-714 1656544 1658040 1658785 "MRING" 1659961 NIL MRING (NIL T T) -8 NIL NIL) (-713 1656110 1656177 1656308 "MRF2" 1656471 NIL MRF2 (NIL T T T) -7 NIL NIL) (-712 1655728 1655763 1655907 "MRATFAC" 1656069 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-711 1653340 1653635 1654066 "MPRFF" 1655433 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-710 1647400 1653194 1653291 "MPOLY" 1653296 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-709 1646890 1646925 1647133 "MPCPF" 1647359 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-708 1646404 1646447 1646631 "MPC3" 1646841 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-707 1645599 1645680 1645901 "MPC2" 1646319 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-706 1643900 1644237 1644627 "MONOTOOL" 1645259 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-705 1643151 1643442 1643470 "MONOID" 1643689 T MONOID (NIL) -9 NIL 1643836) (-704 1642697 1642816 1642997 "MONOID-" 1643002 NIL MONOID- (NIL T) -8 NIL NIL) (-703 1633747 1639653 1639712 "MONOGEN" 1640386 NIL MONOGEN (NIL T T) -9 NIL 1640842) (-702 1630965 1631700 1632700 "MONOGEN-" 1632819 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-701 1629824 1630244 1630272 "MONADWU" 1630664 T MONADWU (NIL) -9 NIL 1630902) (-700 1629196 1629355 1629603 "MONADWU-" 1629608 NIL MONADWU- (NIL T) -8 NIL NIL) (-699 1628581 1628799 1628827 "MONAD" 1629034 T MONAD (NIL) -9 NIL 1629146) (-698 1628266 1628344 1628476 "MONAD-" 1628481 NIL MONAD- (NIL T) -8 NIL NIL) (-697 1626582 1627179 1627458 "MOEBIUS" 1628019 NIL MOEBIUS (NIL T) -8 NIL NIL) (-696 1625974 1626352 1626392 "MODULE" 1626397 NIL MODULE (NIL T) -9 NIL 1626423) (-695 1625542 1625638 1625828 "MODULE-" 1625833 NIL MODULE- (NIL T T) -8 NIL NIL) (-694 1623257 1623906 1624233 "MODRING" 1625366 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-693 1620243 1621362 1621883 "MODOP" 1622786 NIL MODOP (NIL T T) -8 NIL NIL) (-692 1618430 1618882 1619223 "MODMONOM" 1620042 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-691 1608138 1616622 1617045 "MODMON" 1618058 NIL MODMON (NIL T T) -8 NIL NIL) (-690 1605329 1606982 1607258 "MODFIELD" 1608013 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1604333 1604610 1604800 "MMLFORM" 1605159 T MMLFORM (NIL) -8 NIL NIL) (-688 1603859 1603902 1604081 "MMAP" 1604284 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-687 1602128 1602861 1602902 "MLO" 1603325 NIL MLO (NIL T) -9 NIL 1603567) (-686 1599495 1600010 1600612 "MLIFT" 1601609 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-685 1598886 1598970 1599124 "MKUCFUNC" 1599406 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-684 1598485 1598555 1598678 "MKRECORD" 1598809 NIL MKRECORD (NIL T T) -7 NIL NIL) (-683 1597533 1597694 1597922 "MKFUNC" 1598296 NIL MKFUNC (NIL T) -7 NIL NIL) (-682 1596921 1597025 1597181 "MKFLCFN" 1597416 NIL MKFLCFN (NIL T) -7 NIL NIL) (-681 1596347 1596714 1596803 "MKCHSET" 1596865 NIL MKCHSET (NIL T) -8 NIL NIL) (-680 1595624 1595726 1595911 "MKBCFUNC" 1596240 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-679 1592366 1595178 1595314 "MINT" 1595508 T MINT (NIL) -8 NIL NIL) (-678 1591178 1591421 1591698 "MHROWRED" 1592121 NIL MHROWRED (NIL T) -7 NIL NIL) (-677 1586604 1589713 1590118 "MFLOAT" 1590793 T MFLOAT (NIL) -8 NIL NIL) (-676 1585961 1586037 1586208 "MFINFACT" 1586516 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-675 1582276 1583124 1584008 "MESH" 1585097 T MESH (NIL) -7 NIL NIL) (-674 1580666 1580978 1581331 "MDDFACT" 1581963 NIL MDDFACT (NIL T) -7 NIL NIL) (-673 1577508 1579825 1579866 "MDAGG" 1580121 NIL MDAGG (NIL T) -9 NIL 1580264) (-672 1567288 1576801 1577008 "MCMPLX" 1577321 T MCMPLX (NIL) -8 NIL NIL) (-671 1566429 1566575 1566775 "MCDEN" 1567137 NIL MCDEN (NIL T T) -7 NIL NIL) (-670 1564319 1564589 1564969 "MCALCFN" 1566159 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-669 1563230 1563403 1563644 "MAYBE" 1564117 NIL MAYBE (NIL T) -8 NIL NIL) (-668 1560842 1561365 1561927 "MATSTOR" 1562701 NIL MATSTOR (NIL T) -7 NIL NIL) (-667 1556848 1560214 1560462 "MATRIX" 1560627 NIL MATRIX (NIL T) -8 NIL NIL) (-666 1552617 1553321 1554057 "MATLIN" 1556205 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-665 1542771 1545909 1545986 "MATCAT" 1550866 NIL MATCAT (NIL T T T) -9 NIL 1552283) (-664 1539135 1540148 1541504 "MATCAT-" 1541509 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-663 1537729 1537882 1538215 "MATCAT2" 1538970 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-662 1535841 1536165 1536549 "MAPPKG3" 1537404 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-661 1534822 1534995 1535217 "MAPPKG2" 1535665 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-660 1533321 1533605 1533932 "MAPPKG1" 1534528 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-659 1532427 1532727 1532904 "MAPPAST" 1533164 T MAPPAST (NIL) -8 NIL NIL) (-658 1532038 1532096 1532219 "MAPHACK3" 1532363 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-657 1531630 1531691 1531805 "MAPHACK2" 1531970 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-656 1531068 1531171 1531313 "MAPHACK1" 1531521 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-655 1529174 1529768 1530072 "MAGMA" 1530796 NIL MAGMA (NIL T) -8 NIL NIL) (-654 1528680 1528898 1528989 "MACROAST" 1529103 T MACROAST (NIL) -8 NIL NIL) (-653 1525147 1526919 1527380 "M3D" 1528252 NIL M3D (NIL T) -8 NIL NIL) (-652 1519302 1523517 1523558 "LZSTAGG" 1524340 NIL LZSTAGG (NIL T) -9 NIL 1524635) (-651 1515275 1516433 1517890 "LZSTAGG-" 1517895 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-650 1512389 1513166 1513653 "LWORD" 1514820 NIL LWORD (NIL T) -8 NIL NIL) (-649 1511992 1512193 1512268 "LSTAST" 1512334 T LSTAST (NIL) -8 NIL NIL) (-648 1505193 1511763 1511897 "LSQM" 1511902 NIL LSQM (NIL NIL T) -8 NIL NIL) (-647 1504417 1504556 1504784 "LSPP" 1505048 NIL LSPP (NIL T T T T) -7 NIL NIL) (-646 1502229 1502530 1502986 "LSMP" 1504106 NIL LSMP (NIL T T T T) -7 NIL NIL) (-645 1499008 1499682 1500412 "LSMP1" 1501531 NIL LSMP1 (NIL T) -7 NIL NIL) (-644 1492934 1498176 1498217 "LSAGG" 1498279 NIL LSAGG (NIL T) -9 NIL 1498357) (-643 1489629 1490553 1491766 "LSAGG-" 1491771 NIL LSAGG- (NIL T T) -8 NIL NIL) (-642 1487255 1488773 1489022 "LPOLY" 1489424 NIL LPOLY (NIL T T) -8 NIL NIL) (-641 1486837 1486922 1487045 "LPEFRAC" 1487164 NIL LPEFRAC (NIL T) -7 NIL NIL) (-640 1485184 1485931 1486184 "LO" 1486669 NIL LO (NIL T T T) -8 NIL NIL) (-639 1484836 1484948 1484976 "LOGIC" 1485087 T LOGIC (NIL) -9 NIL 1485168) (-638 1484698 1484721 1484792 "LOGIC-" 1484797 NIL LOGIC- (NIL T) -8 NIL NIL) (-637 1483891 1484031 1484224 "LODOOPS" 1484554 NIL LODOOPS (NIL T T) -7 NIL NIL) (-636 1481349 1483807 1483873 "LODO" 1483878 NIL LODO (NIL T NIL) -8 NIL NIL) (-635 1479887 1480122 1480475 "LODOF" 1481096 NIL LODOF (NIL T T) -7 NIL NIL) (-634 1476330 1478727 1478768 "LODOCAT" 1479206 NIL LODOCAT (NIL T) -9 NIL 1479417) (-633 1476063 1476121 1476248 "LODOCAT-" 1476253 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-632 1473418 1475904 1476022 "LODO2" 1476027 NIL LODO2 (NIL T T) -8 NIL NIL) (-631 1470888 1473355 1473400 "LODO1" 1473405 NIL LODO1 (NIL T) -8 NIL NIL) (-630 1469748 1469913 1470225 "LODEEF" 1470711 NIL LODEEF (NIL T T T) -7 NIL NIL) (-629 1465034 1467878 1467919 "LNAGG" 1468866 NIL LNAGG (NIL T) -9 NIL 1469310) (-628 1464181 1464395 1464737 "LNAGG-" 1464742 NIL LNAGG- (NIL T T) -8 NIL NIL) (-627 1460344 1461106 1461745 "LMOPS" 1463596 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-626 1459739 1460101 1460142 "LMODULE" 1460203 NIL LMODULE (NIL T) -9 NIL 1460245) (-625 1456985 1459384 1459507 "LMDICT" 1459649 NIL LMDICT (NIL T) -8 NIL NIL) (-624 1456711 1456893 1456953 "LITERAL" 1456958 NIL LITERAL (NIL T) -8 NIL NIL) (-623 1449938 1455657 1455955 "LIST" 1456446 NIL LIST (NIL T) -8 NIL NIL) (-622 1449463 1449537 1449676 "LIST3" 1449858 NIL LIST3 (NIL T T T) -7 NIL NIL) (-621 1448470 1448648 1448876 "LIST2" 1449281 NIL LIST2 (NIL T T) -7 NIL NIL) (-620 1446604 1446916 1447315 "LIST2MAP" 1448117 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-619 1445354 1445990 1446031 "LINEXP" 1446286 NIL LINEXP (NIL T) -9 NIL 1446435) (-618 1444001 1444261 1444558 "LINDEP" 1445106 NIL LINDEP (NIL T T) -7 NIL NIL) (-617 1440768 1441487 1442264 "LIMITRF" 1443256 NIL LIMITRF (NIL T) -7 NIL NIL) (-616 1439044 1439339 1439755 "LIMITPS" 1440463 NIL LIMITPS (NIL T T) -7 NIL NIL) (-615 1433499 1438555 1438783 "LIE" 1438865 NIL LIE (NIL T T) -8 NIL NIL) (-614 1432548 1432991 1433031 "LIECAT" 1433171 NIL LIECAT (NIL T) -9 NIL 1433322) (-613 1432389 1432416 1432504 "LIECAT-" 1432509 NIL LIECAT- (NIL T T) -8 NIL NIL) (-612 1425001 1431838 1432003 "LIB" 1432244 T LIB (NIL) -8 NIL NIL) (-611 1420638 1421519 1422454 "LGROBP" 1424118 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-610 1418504 1418778 1419140 "LF" 1420359 NIL LF (NIL T T) -7 NIL NIL) (-609 1417344 1418036 1418064 "LFCAT" 1418271 T LFCAT (NIL) -9 NIL 1418410) (-608 1414248 1414876 1415564 "LEXTRIPK" 1416708 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-607 1411019 1411818 1412321 "LEXP" 1413828 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-606 1410522 1410740 1410832 "LETAST" 1410947 T LETAST (NIL) -8 NIL NIL) (-605 1408920 1409233 1409634 "LEADCDET" 1410204 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-604 1408110 1408184 1408413 "LAZM3PK" 1408841 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-603 1403066 1406187 1406725 "LAUPOL" 1407622 NIL LAUPOL (NIL T T) -8 NIL NIL) (-602 1402631 1402675 1402843 "LAPLACE" 1403016 NIL LAPLACE (NIL T T) -7 NIL NIL) (-601 1400605 1401732 1401983 "LA" 1402464 NIL LA (NIL T T T) -8 NIL NIL) (-600 1399706 1400256 1400297 "LALG" 1400359 NIL LALG (NIL T) -9 NIL 1400418) (-599 1399420 1399479 1399615 "LALG-" 1399620 NIL LALG- (NIL T T) -8 NIL NIL) (-598 1398220 1398637 1398866 "KTVLOGIC" 1399211 T KTVLOGIC (NIL) -8 NIL NIL) (-597 1397124 1397311 1397610 "KOVACIC" 1398020 NIL KOVACIC (NIL T T) -7 NIL NIL) (-596 1396959 1396983 1397024 "KONVERT" 1397086 NIL KONVERT (NIL T) -9 NIL NIL) (-595 1396794 1396818 1396859 "KOERCE" 1396921 NIL KOERCE (NIL T) -9 NIL NIL) (-594 1394528 1395288 1395681 "KERNEL" 1396433 NIL KERNEL (NIL T) -8 NIL NIL) (-593 1394030 1394111 1394241 "KERNEL2" 1394442 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-592 1387881 1392569 1392623 "KDAGG" 1393000 NIL KDAGG (NIL T T) -9 NIL 1393206) (-591 1387410 1387534 1387739 "KDAGG-" 1387744 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-590 1380585 1387071 1387226 "KAFILE" 1387288 NIL KAFILE (NIL T) -8 NIL NIL) (-589 1375040 1380096 1380324 "JORDAN" 1380406 NIL JORDAN (NIL T T) -8 NIL NIL) (-588 1374446 1374689 1374810 "JOINAST" 1374939 T JOINAST (NIL) -8 NIL NIL) (-587 1374175 1374234 1374321 "JAVACODE" 1374379 T JAVACODE (NIL) -8 NIL NIL) (-586 1370474 1372380 1372434 "IXAGG" 1373363 NIL IXAGG (NIL T T) -9 NIL 1373822) (-585 1369393 1369699 1370118 "IXAGG-" 1370123 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-584 1364973 1369315 1369374 "IVECTOR" 1369379 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-583 1363739 1363976 1364242 "ITUPLE" 1364740 NIL ITUPLE (NIL T) -8 NIL NIL) (-582 1362175 1362352 1362658 "ITRIGMNP" 1363561 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-581 1360920 1361124 1361407 "ITFUN3" 1361951 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-580 1360552 1360609 1360718 "ITFUN2" 1360857 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-579 1358389 1359414 1359713 "ITAYLOR" 1360286 NIL ITAYLOR (NIL T) -8 NIL NIL) (-578 1347383 1352535 1353695 "ISUPS" 1357262 NIL ISUPS (NIL T) -8 NIL NIL) (-577 1346487 1346627 1346863 "ISUMP" 1347230 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-576 1341751 1346288 1346367 "ISTRING" 1346440 NIL ISTRING (NIL NIL) -8 NIL NIL) (-575 1341254 1341472 1341564 "ISAST" 1341679 T ISAST (NIL) -8 NIL NIL) (-574 1340464 1340545 1340761 "IRURPK" 1341168 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-573 1339400 1339601 1339841 "IRSN" 1340244 T IRSN (NIL) -7 NIL NIL) (-572 1337429 1337784 1338220 "IRRF2F" 1339038 NIL IRRF2F (NIL T) -7 NIL NIL) (-571 1337176 1337214 1337290 "IRREDFFX" 1337385 NIL IRREDFFX (NIL T) -7 NIL NIL) (-570 1335791 1336050 1336349 "IROOT" 1336909 NIL IROOT (NIL T) -7 NIL NIL) (-569 1332423 1333475 1334167 "IR" 1335131 NIL IR (NIL T) -8 NIL NIL) (-568 1330036 1330531 1331097 "IR2" 1331901 NIL IR2 (NIL T T) -7 NIL NIL) (-567 1329108 1329221 1329442 "IR2F" 1329919 NIL IR2F (NIL T T) -7 NIL NIL) (-566 1328899 1328933 1328993 "IPRNTPK" 1329068 T IPRNTPK (NIL) -7 NIL NIL) (-565 1325518 1328788 1328857 "IPF" 1328862 NIL IPF (NIL NIL) -8 NIL NIL) (-564 1323881 1325443 1325500 "IPADIC" 1325505 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-563 1323381 1323585 1323695 "IOMODE" 1323791 T IOMODE (NIL) -8 NIL NIL) (-562 1323145 1323285 1323313 "IOBCON" 1323318 T IOBCON (NIL) -9 NIL 1323339) (-561 1322642 1322700 1322890 "INVLAPLA" 1323081 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-560 1312291 1314644 1317030 "INTTR" 1320306 NIL INTTR (NIL T T) -7 NIL NIL) (-559 1308635 1309377 1310241 "INTTOOLS" 1311476 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-558 1308221 1308312 1308429 "INTSLPE" 1308538 T INTSLPE (NIL) -7 NIL NIL) (-557 1306216 1308144 1308203 "INTRVL" 1308208 NIL INTRVL (NIL T) -8 NIL NIL) (-556 1303818 1304330 1304905 "INTRF" 1305701 NIL INTRF (NIL T) -7 NIL NIL) (-555 1303229 1303326 1303468 "INTRET" 1303716 NIL INTRET (NIL T) -7 NIL NIL) (-554 1301226 1301615 1302085 "INTRAT" 1302837 NIL INTRAT (NIL T T) -7 NIL NIL) (-553 1298454 1299037 1299663 "INTPM" 1300711 NIL INTPM (NIL T T) -7 NIL NIL) (-552 1295157 1295756 1296501 "INTPAF" 1297840 NIL INTPAF (NIL T T T) -7 NIL NIL) (-551 1290336 1291298 1292349 "INTPACK" 1294126 T INTPACK (NIL) -7 NIL NIL) (-550 1287248 1290065 1290192 "INT" 1290229 T INT (NIL) -8 NIL NIL) (-549 1286500 1286652 1286860 "INTHERTR" 1287090 NIL INTHERTR (NIL T T) -7 NIL NIL) (-548 1285939 1286019 1286207 "INTHERAL" 1286414 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-547 1283785 1284228 1284685 "INTHEORY" 1285502 T INTHEORY (NIL) -7 NIL NIL) (-546 1275093 1276714 1278493 "INTG0" 1282137 NIL INTG0 (NIL T T T) -7 NIL NIL) (-545 1255666 1260456 1265266 "INTFTBL" 1270303 T INTFTBL (NIL) -8 NIL NIL) (-544 1254915 1255053 1255226 "INTFACT" 1255525 NIL INTFACT (NIL T) -7 NIL NIL) (-543 1252300 1252746 1253310 "INTEF" 1254469 NIL INTEF (NIL T T) -7 NIL NIL) (-542 1250802 1251507 1251535 "INTDOM" 1251836 T INTDOM (NIL) -9 NIL 1252043) (-541 1250171 1250345 1250587 "INTDOM-" 1250592 NIL INTDOM- (NIL T) -8 NIL NIL) (-540 1246704 1248590 1248644 "INTCAT" 1249443 NIL INTCAT (NIL T) -9 NIL 1249763) (-539 1246177 1246279 1246407 "INTBIT" 1246596 T INTBIT (NIL) -7 NIL NIL) (-538 1244848 1245002 1245316 "INTALG" 1246022 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-537 1244305 1244395 1244565 "INTAF" 1244752 NIL INTAF (NIL T T) -7 NIL NIL) (-536 1237759 1244115 1244255 "INTABL" 1244260 NIL INTABL (NIL T T T) -8 NIL NIL) (-535 1232814 1235485 1235513 "INS" 1236447 T INS (NIL) -9 NIL 1237111) (-534 1230054 1230825 1231799 "INS-" 1231872 NIL INS- (NIL T) -8 NIL NIL) (-533 1228829 1229056 1229354 "INPSIGN" 1229807 NIL INPSIGN (NIL T T) -7 NIL NIL) (-532 1227947 1228064 1228261 "INPRODPF" 1228709 NIL INPRODPF (NIL T T) -7 NIL NIL) (-531 1226841 1226958 1227195 "INPRODFF" 1227827 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-530 1225841 1225993 1226253 "INNMFACT" 1226677 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-529 1225038 1225135 1225323 "INMODGCD" 1225740 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-528 1223547 1223791 1224115 "INFSP" 1224783 NIL INFSP (NIL T T T) -7 NIL NIL) (-527 1222731 1222848 1223031 "INFPROD0" 1223427 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-526 1219613 1220796 1221311 "INFORM" 1222224 T INFORM (NIL) -8 NIL NIL) (-525 1219223 1219283 1219381 "INFORM1" 1219548 NIL INFORM1 (NIL T) -7 NIL NIL) (-524 1218746 1218835 1218949 "INFINITY" 1219129 T INFINITY (NIL) -7 NIL NIL) (-523 1217363 1217612 1217933 "INEP" 1218494 NIL INEP (NIL T T T) -7 NIL NIL) (-522 1216639 1217260 1217325 "INDE" 1217330 NIL INDE (NIL T) -8 NIL NIL) (-521 1216203 1216271 1216388 "INCRMAPS" 1216566 NIL INCRMAPS (NIL T) -7 NIL NIL) (-520 1215506 1215699 1215849 "INBFILE" 1216073 T INBFILE (NIL) -8 NIL NIL) (-519 1210817 1211742 1212686 "INBFF" 1214594 NIL INBFF (NIL T) -7 NIL NIL) (-518 1210486 1210562 1210590 "INBCON" 1210723 T INBCON (NIL) -9 NIL 1210801) (-517 1210326 1210361 1210437 "INBCON-" 1210442 NIL INBCON- (NIL T) -8 NIL NIL) (-516 1209828 1210047 1210139 "INAST" 1210254 T INAST (NIL) -8 NIL NIL) (-515 1209282 1209507 1209613 "IMPTAST" 1209742 T IMPTAST (NIL) -8 NIL NIL) (-514 1205776 1209126 1209230 "IMATRIX" 1209235 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-513 1204488 1204611 1204926 "IMATQF" 1205632 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-512 1202708 1202935 1203272 "IMATLIN" 1204244 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-511 1197334 1202632 1202690 "ILIST" 1202695 NIL ILIST (NIL T NIL) -8 NIL NIL) (-510 1195287 1197194 1197307 "IIARRAY2" 1197312 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-509 1190720 1195198 1195262 "IFF" 1195267 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-508 1190094 1190337 1190453 "IFAST" 1190624 T IFAST (NIL) -8 NIL NIL) (-507 1185137 1189386 1189574 "IFARRAY" 1189951 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-506 1184344 1185041 1185114 "IFAMON" 1185119 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-505 1183928 1183993 1184047 "IEVALAB" 1184254 NIL IEVALAB (NIL T T) -9 NIL NIL) (-504 1183603 1183671 1183831 "IEVALAB-" 1183836 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-503 1183261 1183517 1183580 "IDPO" 1183585 NIL IDPO (NIL T T) -8 NIL NIL) (-502 1182538 1183150 1183225 "IDPOAMS" 1183230 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-501 1181872 1182427 1182502 "IDPOAM" 1182507 NIL IDPOAM (NIL T T) -8 NIL NIL) (-500 1180957 1181207 1181260 "IDPC" 1181673 NIL IDPC (NIL T T) -9 NIL 1181822) (-499 1180453 1180849 1180922 "IDPAM" 1180927 NIL IDPAM (NIL T T) -8 NIL NIL) (-498 1179856 1180345 1180418 "IDPAG" 1180423 NIL IDPAG (NIL T T) -8 NIL NIL) (-497 1179586 1179771 1179821 "IDENT" 1179826 T IDENT (NIL) -8 NIL NIL) (-496 1175841 1176689 1177584 "IDECOMP" 1178743 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-495 1168714 1169764 1170811 "IDEAL" 1174877 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-494 1167878 1167990 1168189 "ICDEN" 1168598 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-493 1166977 1167358 1167505 "ICARD" 1167751 T ICARD (NIL) -8 NIL NIL) (-492 1165037 1165350 1165755 "IBPTOOLS" 1166654 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-491 1160671 1164657 1164770 "IBITS" 1164956 NIL IBITS (NIL NIL) -8 NIL NIL) (-490 1157394 1157970 1158665 "IBATOOL" 1160088 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-489 1155174 1155635 1156168 "IBACHIN" 1156929 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-488 1153051 1155020 1155123 "IARRAY2" 1155128 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-487 1149204 1152977 1153034 "IARRAY1" 1153039 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-486 1143199 1147618 1148098 "IAN" 1148744 T IAN (NIL) -8 NIL NIL) (-485 1142710 1142767 1142940 "IALGFACT" 1143136 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-484 1142238 1142351 1142379 "HYPCAT" 1142586 T HYPCAT (NIL) -9 NIL NIL) (-483 1141776 1141893 1142079 "HYPCAT-" 1142084 NIL HYPCAT- (NIL T) -8 NIL NIL) (-482 1141398 1141571 1141654 "HOSTNAME" 1141713 T HOSTNAME (NIL) -8 NIL NIL) (-481 1138077 1139408 1139449 "HOAGG" 1140430 NIL HOAGG (NIL T) -9 NIL 1141109) (-480 1136671 1137070 1137596 "HOAGG-" 1137601 NIL HOAGG- (NIL T T) -8 NIL NIL) (-479 1130559 1136112 1136278 "HEXADEC" 1136525 T HEXADEC (NIL) -8 NIL NIL) (-478 1129307 1129529 1129792 "HEUGCD" 1130336 NIL HEUGCD (NIL T) -7 NIL NIL) (-477 1128410 1129144 1129274 "HELLFDIV" 1129279 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-476 1126638 1128187 1128275 "HEAP" 1128354 NIL HEAP (NIL T) -8 NIL NIL) (-475 1125929 1126190 1126324 "HEADAST" 1126524 T HEADAST (NIL) -8 NIL NIL) (-474 1119849 1125844 1125906 "HDP" 1125911 NIL HDP (NIL NIL T) -8 NIL NIL) (-473 1113600 1119484 1119636 "HDMP" 1119750 NIL HDMP (NIL NIL T) -8 NIL NIL) (-472 1112925 1113064 1113228 "HB" 1113456 T HB (NIL) -7 NIL NIL) (-471 1106422 1112771 1112875 "HASHTBL" 1112880 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-470 1105925 1106143 1106235 "HASAST" 1106350 T HASAST (NIL) -8 NIL NIL) (-469 1103739 1105549 1105730 "HACKPI" 1105764 T HACKPI (NIL) -8 NIL NIL) (-468 1099434 1103592 1103705 "GTSET" 1103710 NIL GTSET (NIL T T T T) -8 NIL NIL) (-467 1092960 1099312 1099410 "GSTBL" 1099415 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-466 1085273 1091991 1092256 "GSERIES" 1092751 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-465 1084440 1084831 1084859 "GROUP" 1085062 T GROUP (NIL) -9 NIL 1085196) (-464 1083806 1083965 1084216 "GROUP-" 1084221 NIL GROUP- (NIL T) -8 NIL NIL) (-463 1082175 1082494 1082881 "GROEBSOL" 1083483 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-462 1081115 1081377 1081428 "GRMOD" 1081957 NIL GRMOD (NIL T T) -9 NIL 1082125) (-461 1080883 1080919 1081047 "GRMOD-" 1081052 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-460 1076208 1077237 1078237 "GRIMAGE" 1079903 T GRIMAGE (NIL) -8 NIL NIL) (-459 1074675 1074935 1075259 "GRDEF" 1075904 T GRDEF (NIL) -7 NIL NIL) (-458 1074119 1074235 1074376 "GRAY" 1074554 T GRAY (NIL) -7 NIL NIL) (-457 1073350 1073730 1073781 "GRALG" 1073934 NIL GRALG (NIL T T) -9 NIL 1074027) (-456 1073011 1073084 1073247 "GRALG-" 1073252 NIL GRALG- (NIL T T T) -8 NIL NIL) (-455 1069815 1072596 1072774 "GPOLSET" 1072918 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-454 1069169 1069226 1069484 "GOSPER" 1069752 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-453 1064928 1065607 1066133 "GMODPOL" 1068868 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-452 1063933 1064117 1064355 "GHENSEL" 1064740 NIL GHENSEL (NIL T T) -7 NIL NIL) (-451 1057984 1058827 1059854 "GENUPS" 1063017 NIL GENUPS (NIL T T) -7 NIL NIL) (-450 1057681 1057732 1057821 "GENUFACT" 1057927 NIL GENUFACT (NIL T) -7 NIL NIL) (-449 1057093 1057170 1057335 "GENPGCD" 1057599 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-448 1056567 1056602 1056815 "GENMFACT" 1057052 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-447 1055135 1055390 1055697 "GENEEZ" 1056310 NIL GENEEZ (NIL T T) -7 NIL NIL) (-446 1049048 1054746 1054908 "GDMP" 1055058 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-445 1038425 1042819 1043925 "GCNAALG" 1048031 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-444 1036887 1037715 1037743 "GCDDOM" 1037998 T GCDDOM (NIL) -9 NIL 1038155) (-443 1036357 1036484 1036699 "GCDDOM-" 1036704 NIL GCDDOM- (NIL T) -8 NIL NIL) (-442 1035029 1035214 1035518 "GB" 1036136 NIL GB (NIL T T T T) -7 NIL NIL) (-441 1023649 1025975 1028367 "GBINTERN" 1032720 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-440 1021486 1021778 1022199 "GBF" 1023324 NIL GBF (NIL T T T T) -7 NIL NIL) (-439 1020267 1020432 1020699 "GBEUCLID" 1021302 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-438 1019616 1019741 1019890 "GAUSSFAC" 1020138 T GAUSSFAC (NIL) -7 NIL NIL) (-437 1017983 1018285 1018599 "GALUTIL" 1019335 NIL GALUTIL (NIL T) -7 NIL NIL) (-436 1016291 1016565 1016889 "GALPOLYU" 1017710 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-435 1013656 1013946 1014353 "GALFACTU" 1015988 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-434 1005462 1006961 1008569 "GALFACT" 1012088 NIL GALFACT (NIL T) -7 NIL NIL) (-433 1002850 1003508 1003536 "FVFUN" 1004692 T FVFUN (NIL) -9 NIL 1005412) (-432 1002116 1002298 1002326 "FVC" 1002617 T FVC (NIL) -9 NIL 1002800) (-431 1001758 1001913 1001994 "FUNCTION" 1002068 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-430 999428 999979 1000468 "FT" 1001289 T FT (NIL) -8 NIL NIL) (-429 998246 998729 998932 "FTEM" 999245 T FTEM (NIL) -8 NIL NIL) (-428 996502 996791 997195 "FSUPFACT" 997937 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-427 994899 995188 995520 "FST" 996190 T FST (NIL) -8 NIL NIL) (-426 994070 994176 994371 "FSRED" 994781 NIL FSRED (NIL T T) -7 NIL NIL) (-425 992749 993004 993358 "FSPRMELT" 993785 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-424 989834 990272 990771 "FSPECF" 992312 NIL FSPECF (NIL T T) -7 NIL NIL) (-423 972276 980718 980758 "FS" 984606 NIL FS (NIL T) -9 NIL 986895) (-422 960926 963916 967972 "FS-" 968269 NIL FS- (NIL T T) -8 NIL NIL) (-421 960440 960494 960671 "FSINT" 960867 NIL FSINT (NIL T T) -7 NIL NIL) (-420 958767 959433 959736 "FSERIES" 960219 NIL FSERIES (NIL T T) -8 NIL NIL) (-419 957781 957897 958128 "FSCINT" 958647 NIL FSCINT (NIL T T) -7 NIL NIL) (-418 954015 956725 956766 "FSAGG" 957136 NIL FSAGG (NIL T) -9 NIL 957395) (-417 951777 952378 953174 "FSAGG-" 953269 NIL FSAGG- (NIL T T) -8 NIL NIL) (-416 950819 950962 951189 "FSAGG2" 951630 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-415 948474 948753 949307 "FS2UPS" 950537 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-414 948056 948099 948254 "FS2" 948425 NIL FS2 (NIL T T T T) -7 NIL NIL) (-413 946913 947084 947393 "FS2EXPXP" 947881 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-412 946339 946454 946606 "FRUTIL" 946793 NIL FRUTIL (NIL T) -7 NIL NIL) (-411 937800 941838 943194 "FR" 945015 NIL FR (NIL T) -8 NIL NIL) (-410 932875 935518 935558 "FRNAALG" 936954 NIL FRNAALG (NIL T) -9 NIL 937561) (-409 928553 929624 930899 "FRNAALG-" 931649 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-408 928191 928234 928361 "FRNAAF2" 928504 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-407 926598 927045 927340 "FRMOD" 928003 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-406 924377 924981 925298 "FRIDEAL" 926389 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-405 923572 923659 923948 "FRIDEAL2" 924284 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-404 922814 923228 923269 "FRETRCT" 923274 NIL FRETRCT (NIL T) -9 NIL 923450) (-403 921926 922157 922508 "FRETRCT-" 922513 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-402 919176 920352 920411 "FRAMALG" 921293 NIL FRAMALG (NIL T T) -9 NIL 921585) (-401 917310 917765 918395 "FRAMALG-" 918618 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-400 911270 916785 917061 "FRAC" 917066 NIL FRAC (NIL T) -8 NIL NIL) (-399 910906 910963 911070 "FRAC2" 911207 NIL FRAC2 (NIL T T) -7 NIL NIL) (-398 910542 910599 910706 "FR2" 910843 NIL FR2 (NIL T T) -7 NIL NIL) (-397 905272 908120 908148 "FPS" 909267 T FPS (NIL) -9 NIL 909824) (-396 904721 904830 904994 "FPS-" 905140 NIL FPS- (NIL T) -8 NIL NIL) (-395 902227 903862 903890 "FPC" 904115 T FPC (NIL) -9 NIL 904257) (-394 902020 902060 902157 "FPC-" 902162 NIL FPC- (NIL T) -8 NIL NIL) (-393 900898 901508 901549 "FPATMAB" 901554 NIL FPATMAB (NIL T) -9 NIL 901706) (-392 898598 899074 899500 "FPARFRAC" 900535 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-391 893991 894490 895172 "FORTRAN" 898030 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-390 891707 892207 892746 "FORT" 893472 T FORT (NIL) -7 NIL NIL) (-389 889383 889945 889973 "FORTFN" 891033 T FORTFN (NIL) -9 NIL 891657) (-388 889147 889197 889225 "FORTCAT" 889284 T FORTCAT (NIL) -9 NIL 889346) (-387 887207 887690 888089 "FORMULA" 888768 T FORMULA (NIL) -8 NIL NIL) (-386 886995 887025 887094 "FORMULA1" 887171 NIL FORMULA1 (NIL T) -7 NIL NIL) (-385 886518 886570 886743 "FORDER" 886937 NIL FORDER (NIL T T T T) -7 NIL NIL) (-384 885614 885778 885971 "FOP" 886345 T FOP (NIL) -7 NIL NIL) (-383 884222 884894 885068 "FNLA" 885496 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-382 882890 883279 883307 "FNCAT" 883879 T FNCAT (NIL) -9 NIL 884172) (-381 882456 882849 882877 "FNAME" 882882 T FNAME (NIL) -8 NIL NIL) (-380 881154 882083 882111 "FMTC" 882116 T FMTC (NIL) -9 NIL 882152) (-379 877516 878677 879306 "FMONOID" 880558 NIL FMONOID (NIL T) -8 NIL NIL) (-378 876735 877258 877407 "FM" 877412 NIL FM (NIL T T) -8 NIL NIL) (-377 874159 874805 874833 "FMFUN" 875977 T FMFUN (NIL) -9 NIL 876685) (-376 873428 873609 873637 "FMC" 873927 T FMC (NIL) -9 NIL 874109) (-375 870640 871474 871528 "FMCAT" 872723 NIL FMCAT (NIL T T) -9 NIL 873218) (-374 869533 870406 870506 "FM1" 870585 NIL FM1 (NIL T T) -8 NIL NIL) (-373 867307 867723 868217 "FLOATRP" 869084 NIL FLOATRP (NIL T) -7 NIL NIL) (-372 860858 864963 865593 "FLOAT" 866697 T FLOAT (NIL) -8 NIL NIL) (-371 858296 858796 859374 "FLOATCP" 860325 NIL FLOATCP (NIL T) -7 NIL NIL) (-370 857125 857929 857970 "FLINEXP" 857975 NIL FLINEXP (NIL T) -9 NIL 858068) (-369 856279 856514 856842 "FLINEXP-" 856847 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-368 855355 855499 855723 "FLASORT" 856131 NIL FLASORT (NIL T T) -7 NIL NIL) (-367 852572 853414 853466 "FLALG" 854693 NIL FLALG (NIL T T) -9 NIL 855160) (-366 846356 850058 850099 "FLAGG" 851361 NIL FLAGG (NIL T) -9 NIL 852013) (-365 845082 845421 845911 "FLAGG-" 845916 NIL FLAGG- (NIL T T) -8 NIL NIL) (-364 844124 844267 844494 "FLAGG2" 844935 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-363 841137 842111 842170 "FINRALG" 843298 NIL FINRALG (NIL T T) -9 NIL 843806) (-362 840297 840526 840865 "FINRALG-" 840870 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-361 839703 839916 839944 "FINITE" 840140 T FINITE (NIL) -9 NIL 840247) (-360 832161 834322 834362 "FINAALG" 838029 NIL FINAALG (NIL T) -9 NIL 839482) (-359 827502 828543 829687 "FINAALG-" 831066 NIL FINAALG- (NIL T T) -8 NIL NIL) (-358 826897 827257 827360 "FILE" 827432 NIL FILE (NIL T) -8 NIL NIL) (-357 825581 825893 825947 "FILECAT" 826631 NIL FILECAT (NIL T T) -9 NIL 826847) (-356 823501 824995 825023 "FIELD" 825063 T FIELD (NIL) -9 NIL 825143) (-355 822121 822506 823017 "FIELD-" 823022 NIL FIELD- (NIL T) -8 NIL NIL) (-354 819999 820756 821103 "FGROUP" 821807 NIL FGROUP (NIL T) -8 NIL NIL) (-353 819089 819253 819473 "FGLMICPK" 819831 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-352 814956 819014 819071 "FFX" 819076 NIL FFX (NIL T NIL) -8 NIL NIL) (-351 814557 814618 814753 "FFSLPE" 814889 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-350 810550 811329 812125 "FFPOLY" 813793 NIL FFPOLY (NIL T) -7 NIL NIL) (-349 810054 810090 810299 "FFPOLY2" 810508 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-348 805940 809973 810036 "FFP" 810041 NIL FFP (NIL T NIL) -8 NIL NIL) (-347 801373 805851 805915 "FF" 805920 NIL FF (NIL NIL NIL) -8 NIL NIL) (-346 796534 800716 800906 "FFNBX" 801227 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-345 791508 795669 795927 "FFNBP" 796388 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-344 786176 790792 791003 "FFNB" 791341 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-343 785008 785206 785521 "FFINTBAS" 785973 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-342 781292 783467 783495 "FFIELDC" 784115 T FFIELDC (NIL) -9 NIL 784491) (-341 779955 780325 780822 "FFIELDC-" 780827 NIL FFIELDC- (NIL T) -8 NIL NIL) (-340 779525 779570 779694 "FFHOM" 779897 NIL FFHOM (NIL T T T) -7 NIL NIL) (-339 777223 777707 778224 "FFF" 779040 NIL FFF (NIL T) -7 NIL NIL) (-338 772876 776965 777066 "FFCGX" 777166 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-337 768543 772608 772715 "FFCGP" 772819 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-336 763761 768270 768378 "FFCG" 768479 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-335 745819 754855 754941 "FFCAT" 760106 NIL FFCAT (NIL T T T) -9 NIL 761557) (-334 741017 742064 743378 "FFCAT-" 744608 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-333 740428 740471 740706 "FFCAT2" 740968 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-332 729640 733400 734620 "FEXPR" 739280 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-331 728640 729075 729116 "FEVALAB" 729200 NIL FEVALAB (NIL T) -9 NIL 729461) (-330 727799 728009 728347 "FEVALAB-" 728352 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-329 726392 727182 727385 "FDIV" 727698 NIL FDIV (NIL T T T T) -8 NIL NIL) (-328 723458 724173 724288 "FDIVCAT" 725856 NIL FDIVCAT (NIL T T T T) -9 NIL 726293) (-327 723220 723247 723417 "FDIVCAT-" 723422 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-326 722440 722527 722804 "FDIV2" 723127 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-325 721126 721385 721674 "FCPAK1" 722171 T FCPAK1 (NIL) -7 NIL NIL) (-324 720254 720626 720767 "FCOMP" 721017 NIL FCOMP (NIL T) -8 NIL NIL) (-323 703889 707303 710864 "FC" 716713 T FC (NIL) -8 NIL NIL) (-322 696542 700523 700563 "FAXF" 702365 NIL FAXF (NIL T) -9 NIL 703057) (-321 693821 694476 695301 "FAXF-" 695766 NIL FAXF- (NIL T T) -8 NIL NIL) (-320 688921 693197 693373 "FARRAY" 693678 NIL FARRAY (NIL T) -8 NIL NIL) (-319 684328 686360 686413 "FAMR" 687436 NIL FAMR (NIL T T) -9 NIL 687896) (-318 683218 683520 683955 "FAMR-" 683960 NIL FAMR- (NIL T T T) -8 NIL NIL) (-317 682414 683140 683193 "FAMONOID" 683198 NIL FAMONOID (NIL T) -8 NIL NIL) (-316 680244 680928 680981 "FAMONC" 681922 NIL FAMONC (NIL T T) -9 NIL 682308) (-315 678936 679998 680135 "FAGROUP" 680140 NIL FAGROUP (NIL T) -8 NIL NIL) (-314 676731 677050 677453 "FACUTIL" 678617 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-313 675830 676015 676237 "FACTFUNC" 676541 NIL FACTFUNC (NIL T) -7 NIL NIL) (-312 668235 675081 675293 "EXPUPXS" 675686 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-311 665718 666258 666844 "EXPRTUBE" 667669 T EXPRTUBE (NIL) -7 NIL NIL) (-310 661912 662504 663241 "EXPRODE" 665057 NIL EXPRODE (NIL T T) -7 NIL NIL) (-309 647286 660567 660995 "EXPR" 661516 NIL EXPR (NIL T) -8 NIL NIL) (-308 641693 642280 643093 "EXPR2UPS" 646584 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-307 641329 641386 641493 "EXPR2" 641630 NIL EXPR2 (NIL T T) -7 NIL NIL) (-306 632736 640461 640758 "EXPEXPAN" 641166 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-305 632563 632693 632722 "EXIT" 632727 T EXIT (NIL) -8 NIL NIL) (-304 632070 632287 632378 "EXITAST" 632492 T EXITAST (NIL) -8 NIL NIL) (-303 631697 631759 631872 "EVALCYC" 632002 NIL EVALCYC (NIL T) -7 NIL NIL) (-302 631238 631356 631397 "EVALAB" 631567 NIL EVALAB (NIL T) -9 NIL 631671) (-301 630719 630841 631062 "EVALAB-" 631067 NIL EVALAB- (NIL T T) -8 NIL NIL) (-300 628222 629490 629518 "EUCDOM" 630073 T EUCDOM (NIL) -9 NIL 630423) (-299 626627 627069 627659 "EUCDOM-" 627664 NIL EUCDOM- (NIL T) -8 NIL NIL) (-298 614167 616925 619675 "ESTOOLS" 623897 T ESTOOLS (NIL) -7 NIL NIL) (-297 613799 613856 613965 "ESTOOLS2" 614104 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-296 613550 613592 613672 "ESTOOLS1" 613751 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-295 607475 609203 609231 "ES" 611999 T ES (NIL) -9 NIL 613408) (-294 602422 603709 605526 "ES-" 605690 NIL ES- (NIL T) -8 NIL NIL) (-293 598797 599557 600337 "ESCONT" 601662 T ESCONT (NIL) -7 NIL NIL) (-292 598542 598574 598656 "ESCONT1" 598759 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-291 598217 598267 598367 "ES2" 598486 NIL ES2 (NIL T T) -7 NIL NIL) (-290 597847 597905 598014 "ES1" 598153 NIL ES1 (NIL T T) -7 NIL NIL) (-289 597063 597192 597368 "ERROR" 597691 T ERROR (NIL) -7 NIL NIL) (-288 590566 596922 597013 "EQTBL" 597018 NIL EQTBL (NIL T T) -8 NIL NIL) (-287 583123 585880 587329 "EQ" 589150 NIL -3856 (NIL T) -8 NIL NIL) (-286 582755 582812 582921 "EQ2" 583060 NIL EQ2 (NIL T T) -7 NIL NIL) (-285 578047 579093 580186 "EP" 581694 NIL EP (NIL T) -7 NIL NIL) (-284 576629 576930 577247 "ENV" 577750 T ENV (NIL) -8 NIL NIL) (-283 575828 576348 576376 "ENTIRER" 576381 T ENTIRER (NIL) -9 NIL 576427) (-282 572330 573783 574153 "EMR" 575627 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-281 571474 571659 571713 "ELTAGG" 572093 NIL ELTAGG (NIL T T) -9 NIL 572304) (-280 571193 571255 571396 "ELTAGG-" 571401 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-279 570982 571011 571065 "ELTAB" 571149 NIL ELTAB (NIL T T) -9 NIL NIL) (-278 570108 570254 570453 "ELFUTS" 570833 NIL ELFUTS (NIL T T) -7 NIL NIL) (-277 569850 569906 569934 "ELEMFUN" 570039 T ELEMFUN (NIL) -9 NIL NIL) (-276 569720 569741 569809 "ELEMFUN-" 569814 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-275 564611 567820 567861 "ELAGG" 568801 NIL ELAGG (NIL T) -9 NIL 569264) (-274 562896 563330 563993 "ELAGG-" 563998 NIL ELAGG- (NIL T T) -8 NIL NIL) (-273 561553 561833 562128 "ELABEXPR" 562621 T ELABEXPR (NIL) -8 NIL NIL) (-272 554419 556220 557047 "EFUPXS" 560829 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-271 547869 549670 550480 "EFULS" 553695 NIL EFULS (NIL T T T) -8 NIL NIL) (-270 545291 545649 546128 "EFSTRUC" 547501 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-269 534363 535928 537488 "EF" 543806 NIL EF (NIL T T) -7 NIL NIL) (-268 533464 533848 533997 "EAB" 534234 T EAB (NIL) -8 NIL NIL) (-267 532673 533423 533451 "E04UCFA" 533456 T E04UCFA (NIL) -8 NIL NIL) (-266 531882 532632 532660 "E04NAFA" 532665 T E04NAFA (NIL) -8 NIL NIL) (-265 531091 531841 531869 "E04MBFA" 531874 T E04MBFA (NIL) -8 NIL NIL) (-264 530300 531050 531078 "E04JAFA" 531083 T E04JAFA (NIL) -8 NIL NIL) (-263 529511 530259 530287 "E04GCFA" 530292 T E04GCFA (NIL) -8 NIL NIL) (-262 528722 529470 529498 "E04FDFA" 529503 T E04FDFA (NIL) -8 NIL NIL) (-261 527931 528681 528709 "E04DGFA" 528714 T E04DGFA (NIL) -8 NIL NIL) (-260 522109 523456 524820 "E04AGNT" 526587 T E04AGNT (NIL) -7 NIL NIL) (-259 520833 521313 521353 "DVARCAT" 521828 NIL DVARCAT (NIL T) -9 NIL 522027) (-258 520037 520249 520563 "DVARCAT-" 520568 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-257 512937 519836 519965 "DSMP" 519970 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 507747 508882 509950 "DROPT" 511889 T DROPT (NIL) -8 NIL NIL) (-255 507412 507471 507569 "DROPT1" 507682 NIL DROPT1 (NIL T) -7 NIL NIL) (-254 502527 503653 504790 "DROPT0" 506295 T DROPT0 (NIL) -7 NIL NIL) (-253 500872 501197 501583 "DRAWPT" 502161 T DRAWPT (NIL) -7 NIL NIL) (-252 495459 496382 497461 "DRAW" 499846 NIL DRAW (NIL T) -7 NIL NIL) (-251 495092 495145 495263 "DRAWHACK" 495400 NIL DRAWHACK (NIL T) -7 NIL NIL) (-250 493823 494092 494383 "DRAWCX" 494821 T DRAWCX (NIL) -7 NIL NIL) (-249 493339 493407 493558 "DRAWCURV" 493749 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-248 483810 485769 487884 "DRAWCFUN" 491244 T DRAWCFUN (NIL) -7 NIL NIL) (-247 480623 482505 482546 "DQAGG" 483175 NIL DQAGG (NIL T) -9 NIL 483448) (-246 469142 475839 475922 "DPOLCAT" 477774 NIL DPOLCAT (NIL T T T T) -9 NIL 478319) (-245 463981 465327 467285 "DPOLCAT-" 467290 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 457136 463842 463940 "DPMO" 463945 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 450194 456916 457083 "DPMM" 457088 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 449614 449817 449931 "DOMAIN" 450100 T DOMAIN (NIL) -8 NIL NIL) (-241 443365 449249 449401 "DMP" 449515 NIL DMP (NIL NIL T) -8 NIL NIL) (-240 442965 443021 443165 "DLP" 443303 NIL DLP (NIL T) -7 NIL NIL) (-239 436609 442066 442293 "DLIST" 442770 NIL DLIST (NIL T) -8 NIL NIL) (-238 433455 435464 435505 "DLAGG" 436055 NIL DLAGG (NIL T) -9 NIL 436284) (-237 432305 432935 432963 "DIVRING" 433055 T DIVRING (NIL) -9 NIL 433138) (-236 431542 431732 432032 "DIVRING-" 432037 NIL DIVRING- (NIL T) -8 NIL NIL) (-235 429644 430001 430407 "DISPLAY" 431156 T DISPLAY (NIL) -7 NIL NIL) (-234 423586 429558 429621 "DIRPROD" 429626 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-233 422434 422637 422902 "DIRPROD2" 423379 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-232 411972 417924 417977 "DIRPCAT" 418387 NIL DIRPCAT (NIL NIL T) -9 NIL 419227) (-231 409298 409940 410821 "DIRPCAT-" 411158 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-230 408585 408745 408931 "DIOSP" 409132 T DIOSP (NIL) -7 NIL NIL) (-229 405287 407497 407538 "DIOPS" 407972 NIL DIOPS (NIL T) -9 NIL 408201) (-228 404836 404950 405141 "DIOPS-" 405146 NIL DIOPS- (NIL T T) -8 NIL NIL) (-227 403748 404342 404370 "DIFRING" 404557 T DIFRING (NIL) -9 NIL 404667) (-226 403394 403471 403623 "DIFRING-" 403628 NIL DIFRING- (NIL T) -8 NIL NIL) (-225 401219 402457 402498 "DIFEXT" 402861 NIL DIFEXT (NIL T) -9 NIL 403155) (-224 399504 399932 400598 "DIFEXT-" 400603 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-223 396826 399036 399077 "DIAGG" 399082 NIL DIAGG (NIL T) -9 NIL 399102) (-222 396210 396367 396619 "DIAGG-" 396624 NIL DIAGG- (NIL T T) -8 NIL NIL) (-221 391675 395169 395446 "DHMATRIX" 395979 NIL DHMATRIX (NIL T) -8 NIL NIL) (-220 387287 388196 389206 "DFSFUN" 390685 T DFSFUN (NIL) -7 NIL NIL) (-219 382255 386102 386444 "DFLOAT" 386965 T DFLOAT (NIL) -8 NIL NIL) (-218 380483 380764 381160 "DFINTTLS" 381963 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-217 377548 378504 378904 "DERHAM" 380149 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-216 375397 377323 377412 "DEQUEUE" 377492 NIL DEQUEUE (NIL T) -8 NIL NIL) (-215 374612 374745 374941 "DEGRED" 375259 NIL DEGRED (NIL T T) -7 NIL NIL) (-214 371007 371752 372605 "DEFINTRF" 373840 NIL DEFINTRF (NIL T) -7 NIL NIL) (-213 368534 369003 369602 "DEFINTEF" 370526 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-212 367911 368154 368269 "DEFAST" 368439 T DEFAST (NIL) -8 NIL NIL) (-211 361799 367352 367518 "DECIMAL" 367765 T DECIMAL (NIL) -8 NIL NIL) (-210 359311 359769 360275 "DDFACT" 361343 NIL DDFACT (NIL T T) -7 NIL NIL) (-209 358907 358950 359101 "DBLRESP" 359262 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-208 356617 356951 357320 "DBASE" 358665 NIL DBASE (NIL T) -8 NIL NIL) (-207 355886 356097 356243 "DATABUF" 356516 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-206 355019 355845 355873 "D03FAFA" 355878 T D03FAFA (NIL) -8 NIL NIL) (-205 354153 354978 355006 "D03EEFA" 355011 T D03EEFA (NIL) -8 NIL NIL) (-204 352103 352569 353058 "D03AGNT" 353684 T D03AGNT (NIL) -7 NIL NIL) (-203 351419 352062 352090 "D02EJFA" 352095 T D02EJFA (NIL) -8 NIL NIL) (-202 350735 351378 351406 "D02CJFA" 351411 T D02CJFA (NIL) -8 NIL NIL) (-201 350051 350694 350722 "D02BHFA" 350727 T D02BHFA (NIL) -8 NIL NIL) (-200 349367 350010 350038 "D02BBFA" 350043 T D02BBFA (NIL) -8 NIL NIL) (-199 342565 344153 345759 "D02AGNT" 347781 T D02AGNT (NIL) -7 NIL NIL) (-198 340334 340856 341402 "D01WGTS" 342039 T D01WGTS (NIL) -7 NIL NIL) (-197 339429 340293 340321 "D01TRNS" 340326 T D01TRNS (NIL) -8 NIL NIL) (-196 338524 339388 339416 "D01GBFA" 339421 T D01GBFA (NIL) -8 NIL NIL) (-195 337619 338483 338511 "D01FCFA" 338516 T D01FCFA (NIL) -8 NIL NIL) (-194 336714 337578 337606 "D01ASFA" 337611 T D01ASFA (NIL) -8 NIL NIL) (-193 335809 336673 336701 "D01AQFA" 336706 T D01AQFA (NIL) -8 NIL NIL) (-192 334904 335768 335796 "D01APFA" 335801 T D01APFA (NIL) -8 NIL NIL) (-191 333999 334863 334891 "D01ANFA" 334896 T D01ANFA (NIL) -8 NIL NIL) (-190 333094 333958 333986 "D01AMFA" 333991 T D01AMFA (NIL) -8 NIL NIL) (-189 332189 333053 333081 "D01ALFA" 333086 T D01ALFA (NIL) -8 NIL NIL) (-188 331284 332148 332176 "D01AKFA" 332181 T D01AKFA (NIL) -8 NIL NIL) (-187 330379 331243 331271 "D01AJFA" 331276 T D01AJFA (NIL) -8 NIL NIL) (-186 323676 325227 326788 "D01AGNT" 328838 T D01AGNT (NIL) -7 NIL NIL) (-185 323013 323141 323293 "CYCLOTOM" 323544 T CYCLOTOM (NIL) -7 NIL NIL) (-184 319748 320461 321188 "CYCLES" 322306 T CYCLES 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T) -8 NIL NIL) (-1173 2870809 2871655 2872597 "TRMANIP" 2875682 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1172 2870250 2870313 2870476 "TRIMAT" 2870741 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1171 2868046 2868283 2868647 "TRIGMNIP" 2869999 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1170 2867566 2867679 2867709 "TRIGCAT" 2867922 T TRIGCAT (NIL) -9 NIL NIL) (-1169 2867235 2867314 2867455 "TRIGCAT-" 2867460 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1168 2864134 2866095 2866375 "TREE" 2866990 NIL TREE (NIL T) -8 NIL NIL) (-1167 2863408 2863936 2863966 "TRANFUN" 2864001 T TRANFUN (NIL) -9 NIL 2864067) (-1166 2862687 2862878 2863158 "TRANFUN-" 2863163 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1165 2862491 2862523 2862584 "TOPSP" 2862648 T TOPSP (NIL) -7 NIL NIL) (-1164 2861839 2861954 2862108 "TOOLSIGN" 2862372 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1163 2860500 2861016 2861255 "TEXTFILE" 2861622 T TEXTFILE (NIL) -8 NIL NIL) (-1162 2858365 2858879 2859317 "TEX" 2860084 T TEX (NIL) -8 NIL NIL) (-1161 2858146 2858177 2858249 "TEX1" 2858328 NIL TEX1 (NIL T) -7 NIL NIL) (-1160 2857794 2857857 2857947 "TEMUTL" 2858078 T TEMUTL (NIL) -7 NIL NIL) (-1159 2855948 2856228 2856553 "TBCMPPK" 2857517 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1158 2847836 2854108 2854164 "TBAGG" 2854564 NIL TBAGG (NIL T T) -9 NIL 2854775) (-1157 2842906 2844394 2846148 "TBAGG-" 2846153 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1156 2842290 2842397 2842542 "TANEXP" 2842795 NIL TANEXP (NIL T) -7 NIL NIL) (-1155 2835791 2842147 2842240 "TABLE" 2842245 NIL TABLE (NIL T T) -8 NIL NIL) (-1154 2835203 2835302 2835440 "TABLEAU" 2835688 NIL TABLEAU (NIL T) -8 NIL NIL) (-1153 2829811 2831031 2832279 "TABLBUMP" 2833989 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1152 2829239 2829339 2829467 "SYSTEM" 2829705 T SYSTEM (NIL) -7 NIL NIL) (-1151 2825702 2826397 2827180 "SYSSOLP" 2828490 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1150 2821994 2822701 2823435 "SYNTAX" 2824990 T SYNTAX (NIL) -8 NIL NIL) (-1149 2819152 2819754 2820386 "SYMTAB" 2821384 T SYMTAB (NIL) -8 NIL NIL) (-1148 2814401 2815303 2816286 "SYMS" 2818191 T SYMS (NIL) -8 NIL NIL) (-1147 2811673 2813859 2814089 "SYMPOLY" 2814206 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1146 2811190 2811265 2811388 "SYMFUNC" 2811585 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1145 2807167 2808427 2809249 "SYMBOL" 2810390 T SYMBOL (NIL) -8 NIL NIL) (-1144 2800706 2802395 2804115 "SWITCH" 2805469 T SWITCH (NIL) -8 NIL NIL) (-1143 2793976 2799527 2799830 "SUTS" 2800461 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1142 2785945 2793091 2793373 "SUPXS" 2793752 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1141 2777474 2785563 2785689 "SUP" 2785854 NIL SUP (NIL T) -8 NIL NIL) (-1140 2776633 2776760 2776977 "SUPFRACF" 2777342 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1139 2776254 2776313 2776426 "SUP2" 2776568 NIL SUP2 (NIL T T) -7 NIL NIL) (-1138 2774667 2774941 2775304 "SUMRF" 2775953 NIL SUMRF (NIL T) -7 NIL NIL) (-1137 2773981 2774047 2774246 "SUMFS" 2774588 NIL SUMFS (NIL T T) -7 NIL NIL) (-1136 2757990 2773158 2773409 "SULS" 2773788 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1135 2757619 2757812 2757882 "SUCHTAST" 2757942 T SUCHTAST (NIL) -8 NIL NIL) (-1134 2756941 2757144 2757284 "SUCH" 2757527 NIL SUCH (NIL T T) -8 NIL NIL) (-1133 2750835 2751847 2752806 "SUBSPACE" 2756029 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1132 2750265 2750355 2750519 "SUBRESP" 2750723 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1131 2743634 2744930 2746241 "STTF" 2749001 NIL STTF (NIL T) -7 NIL NIL) (-1130 2737807 2738927 2740074 "STTFNC" 2742534 NIL STTFNC (NIL T) -7 NIL NIL) (-1129 2729122 2730989 2732783 "STTAYLOR" 2736048 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1128 2722366 2728986 2729069 "STRTBL" 2729074 NIL STRTBL (NIL T) -8 NIL NIL) (-1127 2717757 2722321 2722352 "STRING" 2722357 T STRING (NIL) -8 NIL NIL) (-1126 2712645 2717130 2717160 "STRICAT" 2717219 T STRICAT (NIL) -9 NIL 2717281) (-1125 2705358 2710168 2710788 "STREAM" 2712060 NIL STREAM (NIL T) -8 NIL NIL) (-1124 2704868 2704945 2705089 "STREAM3" 2705275 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1123 2703850 2704033 2704268 "STREAM2" 2704681 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1122 2703538 2703590 2703683 "STREAM1" 2703792 NIL STREAM1 (NIL T) -7 NIL NIL) (-1121 2702554 2702735 2702966 "STINPROD" 2703354 NIL STINPROD (NIL T) -7 NIL NIL) (-1120 2702132 2702316 2702346 "STEP" 2702426 T STEP (NIL) -9 NIL 2702504) (-1119 2695675 2702031 2702108 "STBL" 2702113 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1118 2690850 2694897 2694940 "STAGG" 2695093 NIL STAGG (NIL T) -9 NIL 2695182) (-1117 2688552 2689154 2690026 "STAGG-" 2690031 NIL STAGG- (NIL T T) -8 NIL NIL) (-1116 2686747 2688322 2688414 "STACK" 2688495 NIL STACK (NIL T) -8 NIL NIL) (-1115 2679472 2684888 2685344 "SREGSET" 2686377 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1114 2671898 2673266 2674779 "SRDCMPK" 2678078 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1113 2664865 2669338 2669368 "SRAGG" 2670671 T SRAGG (NIL) -9 NIL 2671279) (-1112 2663882 2664137 2664516 "SRAGG-" 2664521 NIL SRAGG- (NIL T) -8 NIL NIL) (-1111 2658377 2662829 2663250 "SQMATRIX" 2663508 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1110 2652129 2655097 2655823 "SPLTREE" 2657723 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1109 2648119 2648785 2649431 "SPLNODE" 2651555 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1108 2647166 2647399 2647429 "SPFCAT" 2647873 T SPFCAT (NIL) -9 NIL NIL) (-1107 2645903 2646113 2646377 "SPECOUT" 2646924 T SPECOUT (NIL) -7 NIL NIL) (-1106 2637592 2639336 2639366 "SPADXPT" 2643758 T SPADXPT (NIL) -9 NIL 2645792) (-1105 2637353 2637393 2637462 "SPADPRSR" 2637545 T SPADPRSR (NIL) -7 NIL NIL) (-1104 2635536 2637308 2637339 "SPADAST" 2637344 T SPADAST (NIL) -8 NIL NIL) (-1103 2627507 2629254 2629297 "SPACEC" 2633670 NIL SPACEC (NIL T) -9 NIL 2635486) (-1102 2625678 2627439 2627488 "SPACE3" 2627493 NIL SPACE3 (NIL T) -8 NIL NIL) (-1101 2624430 2624601 2624892 "SORTPAK" 2625483 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1100 2622480 2622783 2623202 "SOLVETRA" 2624094 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1099 2621491 2621713 2621987 "SOLVESER" 2622253 NIL SOLVESER (NIL T) -7 NIL NIL) (-1098 2616711 2617592 2618594 "SOLVERAD" 2620543 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1097 2612526 2613135 2613864 "SOLVEFOR" 2616078 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1096 2606823 2611875 2611972 "SNTSCAT" 2611977 NIL SNTSCAT (NIL T T T T) -9 NIL 2612047) (-1095 2600966 2605146 2605537 "SMTS" 2606513 NIL SMTS (NIL T T T) -8 NIL NIL) (-1094 2595416 2600854 2600931 "SMP" 2600936 NIL SMP (NIL T T) -8 NIL NIL) (-1093 2593575 2593876 2594274 "SMITH" 2595113 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1092 2586558 2590713 2590816 "SMATCAT" 2592167 NIL SMATCAT (NIL NIL T T T) -9 NIL 2592717) (-1091 2583498 2584321 2585499 "SMATCAT-" 2585504 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1090 2581211 2582734 2582777 "SKAGG" 2583038 NIL SKAGG (NIL T) -9 NIL 2583173) (-1089 2577327 2580315 2580593 "SINT" 2580955 T SINT (NIL) -8 NIL NIL) (-1088 2577099 2577137 2577203 "SIMPAN" 2577283 T SIMPAN (NIL) -7 NIL NIL) (-1087 2576406 2576634 2576774 "SIG" 2576981 T SIG (NIL) -8 NIL NIL) (-1086 2575244 2575465 2575740 "SIGNRF" 2576165 NIL SIGNRF (NIL T) -7 NIL NIL) (-1085 2574049 2574200 2574491 "SIGNEF" 2575073 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1084 2573382 2573632 2573756 "SIGAST" 2573947 T SIGAST (NIL) -8 NIL NIL) (-1083 2571072 2571526 2572032 "SHP" 2572923 NIL SHP (NIL T NIL) -7 NIL NIL) (-1082 2564978 2570973 2571049 "SHDP" 2571054 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1081 2564577 2564743 2564773 "SGROUP" 2564866 T SGROUP (NIL) -9 NIL 2564928) (-1080 2564435 2564461 2564534 "SGROUP-" 2564539 NIL SGROUP- (NIL T) -8 NIL NIL) (-1079 2561271 2561968 2562691 "SGCF" 2563734 T SGCF (NIL) -7 NIL NIL) (-1078 2555666 2560718 2560815 "SFRTCAT" 2560820 NIL SFRTCAT (NIL T T T T) -9 NIL 2560859) (-1077 2549090 2550105 2551241 "SFRGCD" 2554649 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1076 2542218 2543289 2544475 "SFQCMPK" 2548023 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1075 2541840 2541929 2542039 "SFORT" 2542159 NIL SFORT (NIL T T) -8 NIL NIL) (-1074 2540985 2541680 2541801 "SEXOF" 2541806 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1073 2540119 2540866 2540934 "SEX" 2540939 T SEX (NIL) -8 NIL NIL) (-1072 2534895 2535584 2535679 "SEXCAT" 2539450 NIL SEXCAT (NIL T T T T T) -9 NIL 2540069) (-1071 2532075 2534829 2534877 "SET" 2534882 NIL SET (NIL T) -8 NIL NIL) (-1070 2530326 2530788 2531093 "SETMN" 2531816 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1069 2529932 2530058 2530088 "SETCAT" 2530205 T SETCAT (NIL) -9 NIL 2530290) (-1068 2529712 2529764 2529863 "SETCAT-" 2529868 NIL SETCAT- (NIL T) -8 NIL NIL) (-1067 2526099 2528173 2528216 "SETAGG" 2529086 NIL SETAGG (NIL T) -9 NIL 2529426) (-1066 2525557 2525673 2525910 "SETAGG-" 2525915 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1065 2525027 2525253 2525354 "SEQAST" 2525478 T SEQAST (NIL) -8 NIL NIL) (-1064 2524231 2524524 2524585 "SEGXCAT" 2524871 NIL SEGXCAT (NIL T T) -9 NIL 2524991) (-1063 2523287 2523897 2524079 "SEG" 2524084 NIL SEG (NIL T) -8 NIL NIL) (-1062 2522194 2522407 2522450 "SEGCAT" 2523032 NIL SEGCAT (NIL T) -9 NIL 2523270) (-1061 2521243 2521573 2521773 "SEGBIND" 2522029 NIL SEGBIND (NIL T) -8 NIL NIL) (-1060 2520864 2520923 2521036 "SEGBIND2" 2521178 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1059 2520465 2520665 2520742 "SEGAST" 2520809 T SEGAST (NIL) -8 NIL NIL) (-1058 2519684 2519810 2520014 "SEG2" 2520309 NIL SEG2 (NIL T T) -7 NIL NIL) (-1057 2519121 2519619 2519666 "SDVAR" 2519671 NIL SDVAR (NIL T) -8 NIL NIL) (-1056 2511411 2518891 2519021 "SDPOL" 2519026 NIL SDPOL (NIL T) -8 NIL NIL) (-1055 2510004 2510270 2510589 "SCPKG" 2511126 NIL SCPKG (NIL T) -7 NIL NIL) (-1054 2509140 2509320 2509520 "SCOPE" 2509826 T SCOPE (NIL) -8 NIL NIL) (-1053 2508361 2508494 2508673 "SCACHE" 2508995 NIL SCACHE (NIL T) -7 NIL NIL) (-1052 2508070 2508230 2508260 "SASTCAT" 2508265 T SASTCAT (NIL) -9 NIL 2508278) (-1051 2507509 2507830 2507915 "SAOS" 2508007 T SAOS (NIL) -8 NIL NIL) (-1050 2507074 2507109 2507282 "SAERFFC" 2507468 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1049 2501048 2506971 2507051 "SAE" 2507056 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1048 2500641 2500676 2500835 "SAEFACT" 2501007 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1047 2498962 2499276 2499677 "RURPK" 2500307 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1046 2497598 2497877 2498189 "RULESET" 2498796 NIL RULESET (NIL T T T) -8 NIL NIL) (-1045 2494785 2495288 2495753 "RULE" 2497279 NIL RULE (NIL T T T) -8 NIL NIL) (-1044 2494424 2494579 2494662 "RULECOLD" 2494737 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1043 2493922 2494141 2494235 "RSTRCAST" 2494352 T RSTRCAST (NIL) -8 NIL NIL) (-1042 2488771 2489565 2490485 "RSETGCD" 2493121 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1041 2478028 2483080 2483177 "RSETCAT" 2487296 NIL RSETCAT (NIL T T T T) -9 NIL 2488393) (-1040 2475955 2476494 2477318 "RSETCAT-" 2477323 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1039 2468342 2469717 2471237 "RSDCMPK" 2474554 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1038 2466347 2466788 2466862 "RRCC" 2467948 NIL RRCC (NIL T T) -9 NIL 2468292) (-1037 2465698 2465872 2466151 "RRCC-" 2466156 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1036 2465168 2465394 2465495 "RPTAST" 2465619 T RPTAST (NIL) -8 NIL NIL) (-1035 2439396 2448981 2449048 "RPOLCAT" 2459712 NIL RPOLCAT (NIL T T T) -9 NIL 2462871) (-1034 2430896 2433234 2436356 "RPOLCAT-" 2436361 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1033 2421943 2429107 2429589 "ROUTINE" 2430436 T ROUTINE (NIL) -8 NIL NIL) (-1032 2418701 2421494 2421643 "ROMAN" 2421816 T ROMAN (NIL) -8 NIL NIL) (-1031 2416976 2417561 2417821 "ROIRC" 2418506 NIL ROIRC (NIL T T) -8 NIL NIL) (-1030 2413427 2415666 2415696 "RNS" 2416000 T RNS (NIL) -9 NIL 2416272) (-1029 2411936 2412319 2412853 "RNS-" 2412928 NIL RNS- (NIL T) -8 NIL NIL) (-1028 2411385 2411767 2411797 "RNG" 2411802 T RNG (NIL) -9 NIL 2411823) (-1027 2410777 2411139 2411182 "RMODULE" 2411244 NIL RMODULE (NIL T) -9 NIL 2411286) (-1026 2409613 2409707 2410043 "RMCAT2" 2410678 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1025 2406318 2408787 2409112 "RMATRIX" 2409347 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1024 2399260 2401494 2401609 "RMATCAT" 2404968 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2405950) (-1023 2398635 2398782 2399089 "RMATCAT-" 2399094 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1022 2398202 2398277 2398405 "RINTERP" 2398554 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1021 2397290 2397810 2397840 "RING" 2397952 T RING (NIL) -9 NIL 2398047) (-1020 2397082 2397126 2397223 "RING-" 2397228 NIL RING- (NIL T) -8 NIL NIL) (-1019 2395923 2396160 2396418 "RIDIST" 2396846 T RIDIST (NIL) -7 NIL NIL) (-1018 2387239 2395391 2395597 "RGCHAIN" 2395771 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1017 2384233 2384847 2385517 "RF" 2386603 NIL RF (NIL T) -7 NIL NIL) (-1016 2383879 2383942 2384045 "RFFACTOR" 2384164 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1015 2383604 2383639 2383736 "RFFACT" 2383838 NIL RFFACT (NIL T) -7 NIL NIL) (-1014 2381721 2382085 2382467 "RFDIST" 2383244 T RFDIST (NIL) -7 NIL NIL) (-1013 2381174 2381266 2381429 "RETSOL" 2381623 NIL RETSOL (NIL T T) -7 NIL NIL) (-1012 2380762 2380842 2380885 "RETRACT" 2381078 NIL RETRACT (NIL T) -9 NIL NIL) (-1011 2380611 2380636 2380723 "RETRACT-" 2380728 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1010 2380240 2380433 2380503 "RETAST" 2380563 T RETAST (NIL) -8 NIL NIL) (-1009 2373094 2379893 2380020 "RESULT" 2380135 T RESULT (NIL) -8 NIL NIL) (-1008 2371720 2372363 2372562 "RESRING" 2372997 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1007 2371356 2371405 2371503 "RESLATC" 2371657 NIL RESLATC (NIL T) -7 NIL NIL) (-1006 2371062 2371096 2371203 "REPSQ" 2371315 NIL REPSQ (NIL T) -7 NIL NIL) (-1005 2368484 2369064 2369666 "REP" 2370482 T REP (NIL) -7 NIL NIL) (-1004 2368182 2368216 2368327 "REPDB" 2368443 NIL REPDB (NIL T) -7 NIL NIL) (-1003 2362092 2363471 2364694 "REP2" 2366994 NIL REP2 (NIL T) -7 NIL NIL) (-1002 2358469 2359150 2359958 "REP1" 2361319 NIL REP1 (NIL T) -7 NIL NIL) (-1001 2351195 2356610 2357066 "REGSET" 2358099 NIL REGSET (NIL T T T T) -8 NIL NIL) (-1000 2350008 2350343 2350593 "REF" 2350980 NIL REF (NIL T) -8 NIL NIL) (-999 2349389 2349492 2349657 "REDORDER" 2349892 NIL REDORDER (NIL T T) -7 NIL NIL) (-998 2345409 2348617 2348840 "RECLOS" 2349218 NIL RECLOS (NIL T) -8 NIL NIL) (-997 2344466 2344647 2344860 "REALSOLV" 2345216 T REALSOLV (NIL) -7 NIL NIL) (-996 2344314 2344355 2344383 "REAL" 2344388 T REAL (NIL) -9 NIL 2344423) (-995 2340805 2341607 2342489 "REAL0Q" 2343479 NIL REAL0Q (NIL T) -7 NIL NIL) (-994 2336416 2337404 2338463 "REAL0" 2339786 NIL REAL0 (NIL T) -7 NIL NIL) (-993 2335918 2336137 2336229 "RDUCEAST" 2336344 T RDUCEAST (NIL) -8 NIL NIL) (-992 2335326 2335398 2335603 "RDIV" 2335840 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-991 2334399 2334573 2334784 "RDIST" 2335148 NIL RDIST (NIL T) -7 NIL NIL) (-990 2333000 2333287 2333657 "RDETRS" 2334107 NIL RDETRS (NIL T T) -7 NIL NIL) (-989 2330817 2331271 2331807 "RDETR" 2332542 NIL RDETR (NIL T T) -7 NIL NIL) (-988 2329431 2329709 2330111 "RDEEFS" 2330533 NIL RDEEFS (NIL T T) -7 NIL NIL) (-987 2327929 2328235 2328665 "RDEEF" 2329119 NIL RDEEF (NIL T T) -7 NIL NIL) (-986 2322266 2325137 2325165 "RCFIELD" 2326442 T RCFIELD (NIL) -9 NIL 2327172) (-985 2320335 2320839 2321532 "RCFIELD-" 2321605 NIL RCFIELD- (NIL T) -8 NIL NIL) (-984 2316666 2318451 2318492 "RCAGG" 2319563 NIL RCAGG (NIL T) -9 NIL 2320028) (-983 2316297 2316391 2316551 "RCAGG-" 2316556 NIL RCAGG- (NIL T T) -8 NIL NIL) (-982 2315637 2315749 2315912 "RATRET" 2316181 NIL RATRET (NIL T) -7 NIL NIL) (-981 2315194 2315261 2315380 "RATFACT" 2315565 NIL RATFACT (NIL T) -7 NIL NIL) (-980 2314509 2314629 2314779 "RANDSRC" 2315064 T RANDSRC (NIL) -7 NIL NIL) (-979 2314246 2314290 2314361 "RADUTIL" 2314458 T RADUTIL (NIL) -7 NIL NIL) (-978 2307311 2312989 2313306 "RADIX" 2313961 NIL RADIX (NIL NIL) -8 NIL NIL) (-977 2298967 2307155 2307283 "RADFF" 2307288 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-976 2298619 2298694 2298722 "RADCAT" 2298879 T RADCAT (NIL) -9 NIL NIL) (-975 2298404 2298452 2298549 "RADCAT-" 2298554 NIL RADCAT- (NIL T) -8 NIL NIL) (-974 2296555 2298179 2298268 "QUEUE" 2298348 NIL QUEUE (NIL T) -8 NIL NIL) (-973 2293131 2296492 2296537 "QUAT" 2296542 NIL QUAT (NIL T) -8 NIL NIL) (-972 2292769 2292812 2292939 "QUATCT2" 2293082 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-971 2286629 2289930 2289970 "QUATCAT" 2290750 NIL QUATCAT (NIL T) -9 NIL 2291516) (-970 2282773 2283810 2285197 "QUATCAT-" 2285291 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-969 2280293 2281857 2281898 "QUAGG" 2282273 NIL QUAGG (NIL T) -9 NIL 2282448) (-968 2279925 2280118 2280186 "QQUTAST" 2280245 T QQUTAST (NIL) -8 NIL NIL) (-967 2278850 2279323 2279495 "QFORM" 2279797 NIL QFORM (NIL NIL T) -8 NIL NIL) (-966 2270183 2275386 2275426 "QFCAT" 2276084 NIL QFCAT (NIL T) -9 NIL 2277083) (-965 2265755 2266956 2268547 "QFCAT-" 2268641 NIL QFCAT- (NIL T T) -8 NIL NIL) (-964 2265393 2265436 2265563 "QFCAT2" 2265706 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-963 2264853 2264963 2265093 "QEQUAT" 2265283 T QEQUAT (NIL) -8 NIL NIL) (-962 2258001 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1869920 1870384 1870981 "ODEPRRIC" 1872489 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-786 1867789 1868358 1868867 "ODEPROB" 1869431 T ODEPROB (NIL) -8 NIL NIL) (-785 1864311 1864794 1865441 "ODEPRIM" 1867268 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-784 1863560 1863662 1863922 "ODEPAL" 1864203 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-783 1859722 1860513 1861377 "ODEPACK" 1862716 T ODEPACK (NIL) -7 NIL NIL) (-782 1858755 1858862 1859091 "ODEINT" 1859611 NIL ODEINT (NIL T T) -7 NIL NIL) (-781 1852856 1854281 1855728 "ODEIFTBL" 1857328 T ODEIFTBL (NIL) -8 NIL NIL) (-780 1848191 1848977 1849936 "ODEEF" 1852015 NIL ODEEF (NIL T T) -7 NIL NIL) (-779 1847526 1847615 1847845 "ODECONST" 1848096 NIL ODECONST (NIL T T T) -7 NIL NIL) (-778 1845677 1846312 1846340 "ODECAT" 1846945 T ODECAT (NIL) -9 NIL 1847476) (-777 1842584 1845389 1845508 "OCT" 1845590 NIL OCT (NIL T) -8 NIL NIL) (-776 1842222 1842265 1842392 "OCTCT2" 1842535 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-775 1837083 1839483 1839523 "OC" 1840620 NIL OC (NIL T) -9 NIL 1841478) (-774 1834310 1835058 1836048 "OC-" 1836142 NIL OC- (NIL T T) -8 NIL NIL) (-773 1833688 1834130 1834158 "OCAMON" 1834163 T OCAMON (NIL) -9 NIL 1834184) (-772 1833245 1833560 1833588 "OASGP" 1833593 T OASGP (NIL) -9 NIL 1833613) (-771 1832532 1832995 1833023 "OAMONS" 1833063 T OAMONS (NIL) -9 NIL 1833106) (-770 1831972 1832379 1832407 "OAMON" 1832412 T OAMON (NIL) -9 NIL 1832432) (-769 1831276 1831768 1831796 "OAGROUP" 1831801 T OAGROUP (NIL) -9 NIL 1831821) (-768 1830966 1831016 1831104 "NUMTUBE" 1831220 NIL NUMTUBE (NIL T) -7 NIL NIL) (-767 1824539 1826057 1827593 "NUMQUAD" 1829450 T NUMQUAD (NIL) -7 NIL NIL) (-766 1820295 1821283 1822308 "NUMODE" 1823534 T NUMODE (NIL) -7 NIL NIL) (-765 1817676 1818530 1818558 "NUMINT" 1819481 T NUMINT (NIL) -9 NIL 1820245) (-764 1816624 1816821 1817039 "NUMFMT" 1817478 T NUMFMT (NIL) -7 NIL NIL) (-763 1802983 1805928 1808460 "NUMERIC" 1814131 NIL NUMERIC (NIL T) -7 NIL NIL) (-762 1797380 1802432 1802527 "NTSCAT" 1802532 NIL NTSCAT (NIL T T T T) -9 NIL 1802571) (-761 1796574 1796739 1796932 "NTPOLFN" 1797219 NIL NTPOLFN (NIL T) -7 NIL NIL) (-760 1784414 1793399 1794211 "NSUP" 1795795 NIL NSUP (NIL T) -8 NIL NIL) (-759 1784046 1784103 1784212 "NSUP2" 1784351 NIL NSUP2 (NIL T T) -7 NIL NIL) (-758 1774043 1783820 1783953 "NSMP" 1783958 NIL NSMP (NIL T T) -8 NIL NIL) (-757 1772475 1772776 1773133 "NREP" 1773731 NIL NREP (NIL T) -7 NIL NIL) (-756 1771066 1771318 1771676 "NPCOEF" 1772218 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-755 1770132 1770247 1770463 "NORMRETR" 1770947 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-754 1768173 1768463 1768872 "NORMPK" 1769840 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-753 1767858 1767886 1768010 "NORMMA" 1768139 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-752 1767685 1767815 1767844 "NONE" 1767849 T NONE (NIL) -8 NIL NIL) (-751 1767474 1767503 1767572 "NONE1" 1767649 NIL NONE1 (NIL T) -7 NIL NIL) (-750 1766957 1767019 1767205 "NODE1" 1767406 NIL NODE1 (NIL T T) -7 NIL NIL) (-749 1765297 1766120 1766375 "NNI" 1766722 T NNI (NIL) -8 NIL NIL) (-748 1763717 1764030 1764394 "NLINSOL" 1764965 NIL NLINSOL (NIL T) -7 NIL NIL) (-747 1759884 1760852 1761774 "NIPROB" 1762815 T NIPROB (NIL) -8 NIL NIL) (-746 1758641 1758875 1759177 "NFINTBAS" 1759646 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-745 1757349 1757580 1757861 "NCODIV" 1758409 NIL NCODIV (NIL T T) -7 NIL NIL) (-744 1757111 1757148 1757223 "NCNTFRAC" 1757306 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-743 1755291 1755655 1756075 "NCEP" 1756736 NIL NCEP (NIL T) -7 NIL NIL) (-742 1754202 1754941 1754969 "NASRING" 1755079 T NASRING (NIL) -9 NIL 1755153) (-741 1753997 1754041 1754135 "NASRING-" 1754140 NIL NASRING- (NIL T) -8 NIL NIL) (-740 1753150 1753649 1753677 "NARNG" 1753794 T NARNG (NIL) -9 NIL 1753885) (-739 1752842 1752909 1753043 "NARNG-" 1753048 NIL NARNG- (NIL T) -8 NIL NIL) (-738 1751721 1751928 1752163 "NAGSP" 1752627 T NAGSP (NIL) -7 NIL NIL) (-737 1742993 1744677 1746350 "NAGS" 1750068 T NAGS (NIL) -7 NIL NIL) (-736 1741541 1741849 1742180 "NAGF07" 1742682 T NAGF07 (NIL) -7 NIL NIL) (-735 1736079 1737370 1738677 "NAGF04" 1740254 T NAGF04 (NIL) -7 NIL NIL) (-734 1729047 1730661 1732294 "NAGF02" 1734466 T NAGF02 (NIL) -7 NIL NIL) (-733 1724271 1725371 1726488 "NAGF01" 1727950 T NAGF01 (NIL) -7 NIL NIL) (-732 1717899 1719465 1721050 "NAGE04" 1722706 T NAGE04 (NIL) -7 NIL NIL) (-731 1709068 1711189 1713319 "NAGE02" 1715789 T NAGE02 (NIL) -7 NIL NIL) (-730 1705021 1705968 1706932 "NAGE01" 1708124 T NAGE01 (NIL) -7 NIL NIL) (-729 1702816 1703350 1703908 "NAGD03" 1704483 T NAGD03 (NIL) -7 NIL NIL) (-728 1694566 1696494 1698448 "NAGD02" 1700882 T NAGD02 (NIL) -7 NIL NIL) (-727 1688377 1689802 1691242 "NAGD01" 1693146 T NAGD01 (NIL) -7 NIL NIL) (-726 1684586 1685408 1686245 "NAGC06" 1687560 T NAGC06 (NIL) -7 NIL NIL) (-725 1683051 1683383 1683739 "NAGC05" 1684250 T NAGC05 (NIL) -7 NIL NIL) (-724 1682427 1682546 1682690 "NAGC02" 1682927 T NAGC02 (NIL) -7 NIL NIL) (-723 1681487 1682044 1682084 "NAALG" 1682163 NIL NAALG (NIL T) -9 NIL 1682224) (-722 1681322 1681351 1681441 "NAALG-" 1681446 NIL NAALG- (NIL T T) -8 NIL NIL) (-721 1675272 1676380 1677567 "MULTSQFR" 1680218 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-720 1674591 1674666 1674850 "MULTFACT" 1675184 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-719 1667814 1671679 1671732 "MTSCAT" 1672802 NIL MTSCAT (NIL T T) -9 NIL 1673316) (-718 1667526 1667580 1667672 "MTHING" 1667754 NIL MTHING (NIL T) -7 NIL NIL) (-717 1667318 1667351 1667411 "MSYSCMD" 1667486 T MSYSCMD (NIL) -7 NIL NIL) (-716 1663430 1666073 1666393 "MSET" 1667031 NIL MSET (NIL T) -8 NIL NIL) (-715 1660525 1662991 1663032 "MSETAGG" 1663037 NIL MSETAGG (NIL T) -9 NIL 1663071) (-714 1656408 1657904 1658649 "MRING" 1659825 NIL MRING (NIL T T) -8 NIL NIL) (-713 1655974 1656041 1656172 "MRF2" 1656335 NIL MRF2 (NIL T T T) -7 NIL NIL) (-712 1655592 1655627 1655771 "MRATFAC" 1655933 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-711 1653204 1653499 1653930 "MPRFF" 1655297 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-710 1647264 1653058 1653155 "MPOLY" 1653160 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-709 1646754 1646789 1646997 "MPCPF" 1647223 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-708 1646268 1646311 1646495 "MPC3" 1646705 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-707 1645463 1645544 1645765 "MPC2" 1646183 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-706 1643764 1644101 1644491 "MONOTOOL" 1645123 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-705 1643015 1643306 1643334 "MONOID" 1643553 T MONOID (NIL) -9 NIL 1643700) (-704 1642561 1642680 1642861 "MONOID-" 1642866 NIL MONOID- (NIL T) -8 NIL NIL) (-703 1633611 1639517 1639576 "MONOGEN" 1640250 NIL MONOGEN (NIL T T) -9 NIL 1640706) (-702 1630829 1631564 1632564 "MONOGEN-" 1632683 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-701 1629688 1630108 1630136 "MONADWU" 1630528 T MONADWU (NIL) -9 NIL 1630766) (-700 1629060 1629219 1629467 "MONADWU-" 1629472 NIL MONADWU- (NIL T) -8 NIL NIL) (-699 1628445 1628663 1628691 "MONAD" 1628898 T MONAD (NIL) -9 NIL 1629010) (-698 1628130 1628208 1628340 "MONAD-" 1628345 NIL MONAD- (NIL T) -8 NIL NIL) (-697 1626446 1627043 1627322 "MOEBIUS" 1627883 NIL MOEBIUS (NIL T) -8 NIL NIL) (-696 1625838 1626216 1626256 "MODULE" 1626261 NIL MODULE (NIL T) -9 NIL 1626287) (-695 1625406 1625502 1625692 "MODULE-" 1625697 NIL MODULE- (NIL T T) -8 NIL NIL) (-694 1623121 1623770 1624097 "MODRING" 1625230 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-693 1620107 1621226 1621747 "MODOP" 1622650 NIL MODOP (NIL T T) -8 NIL NIL) (-692 1618294 1618746 1619087 "MODMONOM" 1619906 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-691 1608002 1616486 1616909 "MODMON" 1617922 NIL MODMON (NIL T T) -8 NIL NIL) (-690 1605193 1606846 1607122 "MODFIELD" 1607877 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1604197 1604474 1604664 "MMLFORM" 1605023 T MMLFORM (NIL) -8 NIL NIL) (-688 1603723 1603766 1603945 "MMAP" 1604148 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-687 1601992 1602725 1602766 "MLO" 1603189 NIL MLO (NIL T) -9 NIL 1603431) (-686 1599359 1599874 1600476 "MLIFT" 1601473 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-685 1598750 1598834 1598988 "MKUCFUNC" 1599270 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-684 1598349 1598419 1598542 "MKRECORD" 1598673 NIL MKRECORD (NIL T T) -7 NIL NIL) (-683 1597397 1597558 1597786 "MKFUNC" 1598160 NIL MKFUNC (NIL T) -7 NIL NIL) (-682 1596785 1596889 1597045 "MKFLCFN" 1597280 NIL MKFLCFN (NIL T) -7 NIL NIL) (-681 1596211 1596578 1596667 "MKCHSET" 1596729 NIL MKCHSET (NIL T) -8 NIL NIL) (-680 1595488 1595590 1595775 "MKBCFUNC" 1596104 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-679 1592230 1595042 1595178 "MINT" 1595372 T MINT (NIL) -8 NIL NIL) (-678 1591042 1591285 1591562 "MHROWRED" 1591985 NIL MHROWRED (NIL T) -7 NIL NIL) (-677 1586468 1589577 1589982 "MFLOAT" 1590657 T MFLOAT (NIL) -8 NIL NIL) (-676 1585825 1585901 1586072 "MFINFACT" 1586380 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-675 1582140 1582988 1583872 "MESH" 1584961 T MESH (NIL) -7 NIL NIL) (-674 1580530 1580842 1581195 "MDDFACT" 1581827 NIL MDDFACT (NIL T) -7 NIL NIL) (-673 1577372 1579689 1579730 "MDAGG" 1579985 NIL MDAGG (NIL T) -9 NIL 1580128) (-672 1567152 1576665 1576872 "MCMPLX" 1577185 T MCMPLX (NIL) -8 NIL NIL) (-671 1566293 1566439 1566639 "MCDEN" 1567001 NIL MCDEN (NIL T T) -7 NIL NIL) (-670 1564183 1564453 1564833 "MCALCFN" 1566023 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-669 1563094 1563267 1563508 "MAYBE" 1563981 NIL MAYBE (NIL T) -8 NIL NIL) (-668 1560706 1561229 1561791 "MATSTOR" 1562565 NIL MATSTOR (NIL T) -7 NIL NIL) (-667 1556712 1560078 1560326 "MATRIX" 1560491 NIL MATRIX (NIL T) -8 NIL NIL) (-666 1552481 1553185 1553921 "MATLIN" 1556069 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-665 1542635 1545773 1545850 "MATCAT" 1550730 NIL MATCAT (NIL T T T) -9 NIL 1552147) (-664 1538999 1540012 1541368 "MATCAT-" 1541373 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-663 1537593 1537746 1538079 "MATCAT2" 1538834 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-662 1535705 1536029 1536413 "MAPPKG3" 1537268 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-661 1534686 1534859 1535081 "MAPPKG2" 1535529 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-660 1533185 1533469 1533796 "MAPPKG1" 1534392 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-659 1532291 1532591 1532768 "MAPPAST" 1533028 T MAPPAST (NIL) -8 NIL NIL) (-658 1531902 1531960 1532083 "MAPHACK3" 1532227 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-657 1531494 1531555 1531669 "MAPHACK2" 1531834 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-656 1530932 1531035 1531177 "MAPHACK1" 1531385 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-655 1529038 1529632 1529936 "MAGMA" 1530660 NIL MAGMA (NIL T) -8 NIL NIL) (-654 1528544 1528762 1528853 "MACROAST" 1528967 T MACROAST (NIL) -8 NIL NIL) (-653 1525011 1526783 1527244 "M3D" 1528116 NIL M3D (NIL T) -8 NIL NIL) (-652 1519166 1523381 1523422 "LZSTAGG" 1524204 NIL LZSTAGG (NIL T) -9 NIL 1524499) (-651 1515139 1516297 1517754 "LZSTAGG-" 1517759 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-650 1512253 1513030 1513517 "LWORD" 1514684 NIL LWORD (NIL T) -8 NIL NIL) (-649 1511856 1512057 1512132 "LSTAST" 1512198 T LSTAST (NIL) -8 NIL NIL) (-648 1505057 1511627 1511761 "LSQM" 1511766 NIL LSQM (NIL NIL T) -8 NIL NIL) (-647 1504281 1504420 1504648 "LSPP" 1504912 NIL LSPP (NIL T T T T) -7 NIL NIL) (-646 1502093 1502394 1502850 "LSMP" 1503970 NIL LSMP (NIL T T T T) -7 NIL NIL) (-645 1498872 1499546 1500276 "LSMP1" 1501395 NIL LSMP1 (NIL T) -7 NIL NIL) (-644 1492798 1498040 1498081 "LSAGG" 1498143 NIL LSAGG (NIL T) -9 NIL 1498221) (-643 1489493 1490417 1491630 "LSAGG-" 1491635 NIL LSAGG- (NIL T T) -8 NIL NIL) (-642 1487119 1488637 1488886 "LPOLY" 1489288 NIL LPOLY (NIL T T) -8 NIL NIL) (-641 1486701 1486786 1486909 "LPEFRAC" 1487028 NIL LPEFRAC (NIL T) -7 NIL NIL) (-640 1485048 1485795 1486048 "LO" 1486533 NIL LO (NIL T T T) -8 NIL NIL) (-639 1484700 1484812 1484840 "LOGIC" 1484951 T LOGIC (NIL) -9 NIL 1485032) (-638 1484562 1484585 1484656 "LOGIC-" 1484661 NIL LOGIC- (NIL T) -8 NIL NIL) (-637 1483755 1483895 1484088 "LODOOPS" 1484418 NIL LODOOPS (NIL T T) -7 NIL NIL) (-636 1481213 1483671 1483737 "LODO" 1483742 NIL LODO (NIL T NIL) -8 NIL NIL) (-635 1479751 1479986 1480339 "LODOF" 1480960 NIL LODOF (NIL T T) -7 NIL NIL) (-634 1476194 1478591 1478632 "LODOCAT" 1479070 NIL LODOCAT (NIL T) -9 NIL 1479281) (-633 1475927 1475985 1476112 "LODOCAT-" 1476117 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-632 1473282 1475768 1475886 "LODO2" 1475891 NIL LODO2 (NIL T T) -8 NIL NIL) (-631 1470752 1473219 1473264 "LODO1" 1473269 NIL LODO1 (NIL T) -8 NIL NIL) (-630 1469612 1469777 1470089 "LODEEF" 1470575 NIL LODEEF (NIL T T T) -7 NIL NIL) (-629 1464898 1467742 1467783 "LNAGG" 1468730 NIL LNAGG (NIL T) -9 NIL 1469174) (-628 1464045 1464259 1464601 "LNAGG-" 1464606 NIL LNAGG- (NIL T T) -8 NIL NIL) (-627 1460208 1460970 1461609 "LMOPS" 1463460 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-626 1459603 1459965 1460006 "LMODULE" 1460067 NIL LMODULE (NIL T) -9 NIL 1460109) (-625 1456849 1459248 1459371 "LMDICT" 1459513 NIL LMDICT (NIL T) -8 NIL NIL) (-624 1456575 1456757 1456817 "LITERAL" 1456822 NIL LITERAL (NIL T) -8 NIL NIL) (-623 1449802 1455521 1455819 "LIST" 1456310 NIL LIST (NIL T) -8 NIL NIL) (-622 1449327 1449401 1449540 "LIST3" 1449722 NIL LIST3 (NIL T T T) -7 NIL NIL) (-621 1448334 1448512 1448740 "LIST2" 1449145 NIL LIST2 (NIL T T) -7 NIL NIL) (-620 1446468 1446780 1447179 "LIST2MAP" 1447981 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-619 1445218 1445854 1445895 "LINEXP" 1446150 NIL LINEXP (NIL T) -9 NIL 1446299) (-618 1443865 1444125 1444422 "LINDEP" 1444970 NIL LINDEP (NIL T T) -7 NIL NIL) (-617 1440632 1441351 1442128 "LIMITRF" 1443120 NIL LIMITRF (NIL T) -7 NIL NIL) (-616 1438908 1439203 1439619 "LIMITPS" 1440327 NIL LIMITPS (NIL T T) -7 NIL NIL) (-615 1433363 1438419 1438647 "LIE" 1438729 NIL LIE (NIL T T) -8 NIL NIL) (-614 1432412 1432855 1432895 "LIECAT" 1433035 NIL LIECAT (NIL T) -9 NIL 1433186) (-613 1432253 1432280 1432368 "LIECAT-" 1432373 NIL LIECAT- (NIL T T) -8 NIL NIL) (-612 1424865 1431702 1431867 "LIB" 1432108 T LIB (NIL) -8 NIL NIL) (-611 1420502 1421383 1422318 "LGROBP" 1423982 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-610 1418368 1418642 1419004 "LF" 1420223 NIL LF (NIL T T) -7 NIL NIL) (-609 1417208 1417900 1417928 "LFCAT" 1418135 T LFCAT (NIL) -9 NIL 1418274) (-608 1414112 1414740 1415428 "LEXTRIPK" 1416572 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-607 1410883 1411682 1412185 "LEXP" 1413692 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-606 1410386 1410604 1410696 "LETAST" 1410811 T LETAST (NIL) -8 NIL NIL) (-605 1408784 1409097 1409498 "LEADCDET" 1410068 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-604 1407974 1408048 1408277 "LAZM3PK" 1408705 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-603 1402930 1406051 1406589 "LAUPOL" 1407486 NIL LAUPOL (NIL T T) -8 NIL NIL) (-602 1402495 1402539 1402707 "LAPLACE" 1402880 NIL LAPLACE (NIL T T) -7 NIL NIL) (-601 1400469 1401596 1401847 "LA" 1402328 NIL LA (NIL T T T) -8 NIL NIL) (-600 1399570 1400120 1400161 "LALG" 1400223 NIL LALG (NIL T) -9 NIL 1400282) (-599 1399284 1399343 1399479 "LALG-" 1399484 NIL LALG- (NIL T T) -8 NIL NIL) (-598 1398084 1398501 1398730 "KTVLOGIC" 1399075 T KTVLOGIC (NIL) -8 NIL NIL) (-597 1396988 1397175 1397474 "KOVACIC" 1397884 NIL KOVACIC (NIL T T) -7 NIL NIL) (-596 1396823 1396847 1396888 "KONVERT" 1396950 NIL KONVERT (NIL T) -9 NIL NIL) (-595 1396658 1396682 1396723 "KOERCE" 1396785 NIL KOERCE (NIL T) -9 NIL NIL) (-594 1394392 1395152 1395545 "KERNEL" 1396297 NIL KERNEL (NIL T) -8 NIL NIL) (-593 1393894 1393975 1394105 "KERNEL2" 1394306 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-592 1387745 1392433 1392487 "KDAGG" 1392864 NIL KDAGG (NIL T T) -9 NIL 1393070) (-591 1387274 1387398 1387603 "KDAGG-" 1387608 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-590 1380449 1386935 1387090 "KAFILE" 1387152 NIL KAFILE (NIL T) -8 NIL NIL) (-589 1374904 1379960 1380188 "JORDAN" 1380270 NIL JORDAN (NIL T T) -8 NIL NIL) (-588 1374310 1374553 1374674 "JOINAST" 1374803 T JOINAST (NIL) -8 NIL NIL) (-587 1374039 1374098 1374185 "JAVACODE" 1374243 T JAVACODE (NIL) -8 NIL NIL) (-586 1370338 1372244 1372298 "IXAGG" 1373227 NIL IXAGG (NIL T T) -9 NIL 1373686) (-585 1369257 1369563 1369982 "IXAGG-" 1369987 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-584 1364837 1369179 1369238 "IVECTOR" 1369243 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-583 1363603 1363840 1364106 "ITUPLE" 1364604 NIL ITUPLE (NIL T) -8 NIL NIL) (-582 1362039 1362216 1362522 "ITRIGMNP" 1363425 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-581 1360784 1360988 1361271 "ITFUN3" 1361815 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-580 1360416 1360473 1360582 "ITFUN2" 1360721 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-579 1358253 1359278 1359577 "ITAYLOR" 1360150 NIL ITAYLOR (NIL T) -8 NIL NIL) (-578 1347235 1352390 1353553 "ISUPS" 1357123 NIL ISUPS (NIL T) -8 NIL NIL) (-577 1346339 1346479 1346715 "ISUMP" 1347082 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-576 1341603 1346140 1346219 "ISTRING" 1346292 NIL ISTRING (NIL NIL) -8 NIL NIL) (-575 1341106 1341324 1341416 "ISAST" 1341531 T ISAST (NIL) -8 NIL NIL) (-574 1340316 1340397 1340613 "IRURPK" 1341020 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-573 1339252 1339453 1339693 "IRSN" 1340096 T IRSN (NIL) -7 NIL NIL) (-572 1337281 1337636 1338072 "IRRF2F" 1338890 NIL IRRF2F (NIL T) -7 NIL NIL) (-571 1337028 1337066 1337142 "IRREDFFX" 1337237 NIL IRREDFFX (NIL T) -7 NIL NIL) (-570 1335643 1335902 1336201 "IROOT" 1336761 NIL IROOT (NIL T) -7 NIL NIL) (-569 1332275 1333327 1334019 "IR" 1334983 NIL IR (NIL T) -8 NIL NIL) (-568 1329888 1330383 1330949 "IR2" 1331753 NIL IR2 (NIL T T) -7 NIL NIL) (-567 1328960 1329073 1329294 "IR2F" 1329771 NIL IR2F (NIL T T) -7 NIL NIL) (-566 1328751 1328785 1328845 "IPRNTPK" 1328920 T IPRNTPK (NIL) -7 NIL NIL) (-565 1325370 1328640 1328709 "IPF" 1328714 NIL IPF (NIL NIL) -8 NIL NIL) (-564 1323733 1325295 1325352 "IPADIC" 1325357 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-563 1323233 1323437 1323547 "IOMODE" 1323643 T IOMODE (NIL) -8 NIL NIL) (-562 1322997 1323137 1323165 "IOBCON" 1323170 T IOBCON (NIL) -9 NIL 1323191) (-561 1322494 1322552 1322742 "INVLAPLA" 1322933 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-560 1312143 1314496 1316882 "INTTR" 1320158 NIL INTTR (NIL T T) -7 NIL NIL) (-559 1308487 1309229 1310093 "INTTOOLS" 1311328 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-558 1308073 1308164 1308281 "INTSLPE" 1308390 T INTSLPE (NIL) -7 NIL NIL) (-557 1306068 1307996 1308055 "INTRVL" 1308060 NIL INTRVL (NIL T) -8 NIL NIL) (-556 1303670 1304182 1304757 "INTRF" 1305553 NIL INTRF (NIL T) -7 NIL NIL) (-555 1303081 1303178 1303320 "INTRET" 1303568 NIL INTRET (NIL T) -7 NIL NIL) (-554 1301078 1301467 1301937 "INTRAT" 1302689 NIL INTRAT (NIL T T) -7 NIL NIL) (-553 1298306 1298889 1299515 "INTPM" 1300563 NIL INTPM (NIL T T) -7 NIL NIL) (-552 1295009 1295608 1296353 "INTPAF" 1297692 NIL INTPAF (NIL T T T) -7 NIL NIL) (-551 1290188 1291150 1292201 "INTPACK" 1293978 T INTPACK (NIL) -7 NIL NIL) (-550 1287100 1289917 1290044 "INT" 1290081 T INT (NIL) -8 NIL NIL) (-549 1286352 1286504 1286712 "INTHERTR" 1286942 NIL INTHERTR (NIL T T) -7 NIL NIL) (-548 1285791 1285871 1286059 "INTHERAL" 1286266 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-547 1283637 1284080 1284537 "INTHEORY" 1285354 T INTHEORY (NIL) -7 NIL NIL) (-546 1274945 1276566 1278345 "INTG0" 1281989 NIL INTG0 (NIL T T T) -7 NIL NIL) (-545 1255518 1260308 1265118 "INTFTBL" 1270155 T INTFTBL (NIL) -8 NIL NIL) (-544 1254767 1254905 1255078 "INTFACT" 1255377 NIL INTFACT (NIL T) -7 NIL NIL) (-543 1252152 1252598 1253162 "INTEF" 1254321 NIL INTEF (NIL T T) -7 NIL NIL) (-542 1250654 1251359 1251387 "INTDOM" 1251688 T INTDOM (NIL) -9 NIL 1251895) (-541 1250023 1250197 1250439 "INTDOM-" 1250444 NIL INTDOM- (NIL T) -8 NIL NIL) (-540 1246556 1248442 1248496 "INTCAT" 1249295 NIL INTCAT (NIL T) -9 NIL 1249615) (-539 1246029 1246131 1246259 "INTBIT" 1246448 T INTBIT (NIL) -7 NIL NIL) (-538 1244700 1244854 1245168 "INTALG" 1245874 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-537 1244157 1244247 1244417 "INTAF" 1244604 NIL INTAF (NIL T T) -7 NIL NIL) (-536 1237611 1243967 1244107 "INTABL" 1244112 NIL INTABL (NIL T T T) -8 NIL NIL) (-535 1232666 1235337 1235365 "INS" 1236299 T INS (NIL) -9 NIL 1236963) (-534 1229906 1230677 1231651 "INS-" 1231724 NIL INS- (NIL T) -8 NIL NIL) (-533 1228681 1228908 1229206 "INPSIGN" 1229659 NIL INPSIGN (NIL T T) -7 NIL NIL) (-532 1227799 1227916 1228113 "INPRODPF" 1228561 NIL INPRODPF (NIL T T) -7 NIL NIL) (-531 1226693 1226810 1227047 "INPRODFF" 1227679 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-530 1225693 1225845 1226105 "INNMFACT" 1226529 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-529 1224890 1224987 1225175 "INMODGCD" 1225592 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-528 1223399 1223643 1223967 "INFSP" 1224635 NIL INFSP (NIL T T T) -7 NIL NIL) (-527 1222583 1222700 1222883 "INFPROD0" 1223279 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-526 1219465 1220648 1221163 "INFORM" 1222076 T INFORM (NIL) -8 NIL NIL) (-525 1219075 1219135 1219233 "INFORM1" 1219400 NIL INFORM1 (NIL T) -7 NIL NIL) (-524 1218598 1218687 1218801 "INFINITY" 1218981 T INFINITY (NIL) -7 NIL NIL) (-523 1217215 1217464 1217785 "INEP" 1218346 NIL INEP (NIL T T T) -7 NIL NIL) (-522 1216491 1217112 1217177 "INDE" 1217182 NIL INDE (NIL T) -8 NIL NIL) (-521 1216055 1216123 1216240 "INCRMAPS" 1216418 NIL INCRMAPS (NIL T) -7 NIL NIL) (-520 1215358 1215551 1215701 "INBFILE" 1215925 T INBFILE (NIL) -8 NIL NIL) (-519 1210669 1211594 1212538 "INBFF" 1214446 NIL INBFF (NIL T) -7 NIL NIL) (-518 1210338 1210414 1210442 "INBCON" 1210575 T INBCON (NIL) -9 NIL 1210653) (-517 1210178 1210213 1210289 "INBCON-" 1210294 NIL INBCON- (NIL T) -8 NIL NIL) (-516 1209680 1209899 1209991 "INAST" 1210106 T INAST (NIL) -8 NIL NIL) (-515 1209134 1209359 1209465 "IMPTAST" 1209594 T IMPTAST (NIL) -8 NIL NIL) (-514 1205628 1208978 1209082 "IMATRIX" 1209087 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-513 1204340 1204463 1204778 "IMATQF" 1205484 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-512 1202560 1202787 1203124 "IMATLIN" 1204096 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-511 1197186 1202484 1202542 "ILIST" 1202547 NIL ILIST (NIL T NIL) -8 NIL NIL) (-510 1195139 1197046 1197159 "IIARRAY2" 1197164 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-509 1190572 1195050 1195114 "IFF" 1195119 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-508 1189946 1190189 1190305 "IFAST" 1190476 T IFAST (NIL) -8 NIL NIL) (-507 1184989 1189238 1189426 "IFARRAY" 1189803 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-506 1184196 1184893 1184966 "IFAMON" 1184971 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-505 1183780 1183845 1183899 "IEVALAB" 1184106 NIL IEVALAB (NIL T T) -9 NIL NIL) (-504 1183455 1183523 1183683 "IEVALAB-" 1183688 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-503 1183113 1183369 1183432 "IDPO" 1183437 NIL IDPO (NIL T T) -8 NIL NIL) (-502 1182390 1183002 1183077 "IDPOAMS" 1183082 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-501 1181724 1182279 1182354 "IDPOAM" 1182359 NIL IDPOAM (NIL T T) -8 NIL NIL) (-500 1180809 1181059 1181112 "IDPC" 1181525 NIL IDPC (NIL T T) -9 NIL 1181674) (-499 1180305 1180701 1180774 "IDPAM" 1180779 NIL IDPAM (NIL T T) -8 NIL NIL) (-498 1179708 1180197 1180270 "IDPAG" 1180275 NIL IDPAG (NIL T T) -8 NIL NIL) (-497 1179438 1179623 1179673 "IDENT" 1179678 T IDENT (NIL) -8 NIL NIL) (-496 1175693 1176541 1177436 "IDECOMP" 1178595 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-495 1168566 1169616 1170663 "IDEAL" 1174729 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-494 1167730 1167842 1168041 "ICDEN" 1168450 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-493 1166829 1167210 1167357 "ICARD" 1167603 T ICARD (NIL) -8 NIL NIL) (-492 1164889 1165202 1165607 "IBPTOOLS" 1166506 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-491 1160523 1164509 1164622 "IBITS" 1164808 NIL IBITS (NIL NIL) -8 NIL NIL) (-490 1157246 1157822 1158517 "IBATOOL" 1159940 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-489 1155026 1155487 1156020 "IBACHIN" 1156781 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-488 1152903 1154872 1154975 "IARRAY2" 1154980 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-487 1149056 1152829 1152886 "IARRAY1" 1152891 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-486 1143051 1147470 1147950 "IAN" 1148596 T IAN (NIL) -8 NIL NIL) (-485 1142562 1142619 1142792 "IALGFACT" 1142988 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-484 1142090 1142203 1142231 "HYPCAT" 1142438 T HYPCAT (NIL) -9 NIL NIL) (-483 1141628 1141745 1141931 "HYPCAT-" 1141936 NIL HYPCAT- (NIL T) -8 NIL NIL) (-482 1141250 1141423 1141506 "HOSTNAME" 1141565 T HOSTNAME (NIL) -8 NIL NIL) (-481 1137929 1139260 1139301 "HOAGG" 1140282 NIL HOAGG (NIL T) -9 NIL 1140961) (-480 1136523 1136922 1137448 "HOAGG-" 1137453 NIL HOAGG- (NIL T T) -8 NIL NIL) (-479 1130411 1135964 1136130 "HEXADEC" 1136377 T HEXADEC (NIL) -8 NIL NIL) (-478 1129159 1129381 1129644 "HEUGCD" 1130188 NIL HEUGCD (NIL T) -7 NIL NIL) (-477 1128262 1128996 1129126 "HELLFDIV" 1129131 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-476 1126490 1128039 1128127 "HEAP" 1128206 NIL HEAP (NIL T) -8 NIL NIL) (-475 1125781 1126042 1126176 "HEADAST" 1126376 T HEADAST (NIL) -8 NIL NIL) (-474 1119701 1125696 1125758 "HDP" 1125763 NIL HDP (NIL NIL T) -8 NIL NIL) (-473 1113452 1119336 1119488 "HDMP" 1119602 NIL HDMP (NIL NIL T) -8 NIL NIL) (-472 1112777 1112916 1113080 "HB" 1113308 T HB (NIL) -7 NIL NIL) (-471 1106274 1112623 1112727 "HASHTBL" 1112732 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-470 1105777 1105995 1106087 "HASAST" 1106202 T HASAST (NIL) -8 NIL NIL) (-469 1103591 1105401 1105582 "HACKPI" 1105616 T HACKPI (NIL) -8 NIL NIL) (-468 1099286 1103444 1103557 "GTSET" 1103562 NIL GTSET (NIL T T T T) -8 NIL NIL) (-467 1092812 1099164 1099262 "GSTBL" 1099267 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-466 1085125 1091843 1092108 "GSERIES" 1092603 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-465 1084292 1084683 1084711 "GROUP" 1084914 T GROUP (NIL) -9 NIL 1085048) (-464 1083658 1083817 1084068 "GROUP-" 1084073 NIL GROUP- (NIL T) -8 NIL NIL) (-463 1082027 1082346 1082733 "GROEBSOL" 1083335 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-462 1080967 1081229 1081280 "GRMOD" 1081809 NIL GRMOD (NIL T T) -9 NIL 1081977) (-461 1080735 1080771 1080899 "GRMOD-" 1080904 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-460 1076060 1077089 1078089 "GRIMAGE" 1079755 T GRIMAGE (NIL) -8 NIL NIL) (-459 1074527 1074787 1075111 "GRDEF" 1075756 T GRDEF (NIL) -7 NIL NIL) (-458 1073971 1074087 1074228 "GRAY" 1074406 T GRAY (NIL) -7 NIL NIL) (-457 1073202 1073582 1073633 "GRALG" 1073786 NIL GRALG (NIL T T) -9 NIL 1073879) (-456 1072863 1072936 1073099 "GRALG-" 1073104 NIL GRALG- (NIL T T T) -8 NIL NIL) (-455 1069667 1072448 1072626 "GPOLSET" 1072770 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-454 1069021 1069078 1069336 "GOSPER" 1069604 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-453 1064780 1065459 1065985 "GMODPOL" 1068720 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-452 1063785 1063969 1064207 "GHENSEL" 1064592 NIL GHENSEL (NIL T T) -7 NIL NIL) (-451 1057836 1058679 1059706 "GENUPS" 1062869 NIL GENUPS (NIL T T) -7 NIL NIL) (-450 1057533 1057584 1057673 "GENUFACT" 1057779 NIL GENUFACT (NIL T) -7 NIL NIL) (-449 1056945 1057022 1057187 "GENPGCD" 1057451 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-448 1056419 1056454 1056667 "GENMFACT" 1056904 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-447 1054987 1055242 1055549 "GENEEZ" 1056162 NIL GENEEZ (NIL T T) -7 NIL NIL) (-446 1048900 1054598 1054760 "GDMP" 1054910 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-445 1038277 1042671 1043777 "GCNAALG" 1047883 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-444 1036739 1037567 1037595 "GCDDOM" 1037850 T GCDDOM (NIL) -9 NIL 1038007) (-443 1036209 1036336 1036551 "GCDDOM-" 1036556 NIL GCDDOM- (NIL T) -8 NIL NIL) (-442 1034881 1035066 1035370 "GB" 1035988 NIL GB (NIL T T T T) -7 NIL NIL) (-441 1023501 1025827 1028219 "GBINTERN" 1032572 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-440 1021338 1021630 1022051 "GBF" 1023176 NIL GBF (NIL T T T T) -7 NIL NIL) (-439 1020119 1020284 1020551 "GBEUCLID" 1021154 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-438 1019468 1019593 1019742 "GAUSSFAC" 1019990 T GAUSSFAC (NIL) -7 NIL NIL) (-437 1017835 1018137 1018451 "GALUTIL" 1019187 NIL GALUTIL (NIL T) -7 NIL NIL) (-436 1016143 1016417 1016741 "GALPOLYU" 1017562 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-435 1013508 1013798 1014205 "GALFACTU" 1015840 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-434 1005314 1006813 1008421 "GALFACT" 1011940 NIL GALFACT (NIL T) -7 NIL NIL) (-433 1002702 1003360 1003388 "FVFUN" 1004544 T FVFUN (NIL) -9 NIL 1005264) (-432 1001968 1002150 1002178 "FVC" 1002469 T FVC (NIL) -9 NIL 1002652) (-431 1001610 1001765 1001846 "FUNCTION" 1001920 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-430 999280 999831 1000320 "FT" 1001141 T FT (NIL) -8 NIL NIL) (-429 998098 998581 998784 "FTEM" 999097 T FTEM (NIL) -8 NIL NIL) (-428 996354 996643 997047 "FSUPFACT" 997789 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-427 994751 995040 995372 "FST" 996042 T FST (NIL) -8 NIL NIL) (-426 993922 994028 994223 "FSRED" 994633 NIL FSRED (NIL T T) -7 NIL NIL) (-425 992601 992856 993210 "FSPRMELT" 993637 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-424 989686 990124 990623 "FSPECF" 992164 NIL FSPECF (NIL T T) -7 NIL NIL) (-423 972128 980570 980610 "FS" 984458 NIL FS (NIL T) -9 NIL 986747) (-422 960778 963768 967824 "FS-" 968121 NIL FS- (NIL T T) -8 NIL NIL) (-421 960292 960346 960523 "FSINT" 960719 NIL FSINT (NIL T T) -7 NIL NIL) (-420 958619 959285 959588 "FSERIES" 960071 NIL FSERIES (NIL T T) -8 NIL NIL) (-419 957633 957749 957980 "FSCINT" 958499 NIL FSCINT (NIL T T) -7 NIL NIL) (-418 953867 956577 956618 "FSAGG" 956988 NIL FSAGG (NIL T) -9 NIL 957247) (-417 951629 952230 953026 "FSAGG-" 953121 NIL FSAGG- (NIL T T) -8 NIL NIL) (-416 950671 950814 951041 "FSAGG2" 951482 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-415 948326 948605 949159 "FS2UPS" 950389 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-414 947908 947951 948106 "FS2" 948277 NIL FS2 (NIL T T T T) -7 NIL NIL) (-413 946765 946936 947245 "FS2EXPXP" 947733 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-412 946191 946306 946458 "FRUTIL" 946645 NIL FRUTIL (NIL T) -7 NIL NIL) (-411 937652 941690 943046 "FR" 944867 NIL FR (NIL T) -8 NIL NIL) (-410 932727 935370 935410 "FRNAALG" 936806 NIL FRNAALG (NIL T) -9 NIL 937413) (-409 928405 929476 930751 "FRNAALG-" 931501 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-408 928043 928086 928213 "FRNAAF2" 928356 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-407 926450 926897 927192 "FRMOD" 927855 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-406 924229 924833 925150 "FRIDEAL" 926241 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-405 923424 923511 923800 "FRIDEAL2" 924136 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-404 922666 923080 923121 "FRETRCT" 923126 NIL FRETRCT (NIL T) -9 NIL 923302) (-403 921778 922009 922360 "FRETRCT-" 922365 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-402 919028 920204 920263 "FRAMALG" 921145 NIL FRAMALG (NIL T T) -9 NIL 921437) (-401 917162 917617 918247 "FRAMALG-" 918470 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-400 911122 916637 916913 "FRAC" 916918 NIL FRAC (NIL T) -8 NIL NIL) (-399 910758 910815 910922 "FRAC2" 911059 NIL FRAC2 (NIL T T) -7 NIL NIL) (-398 910394 910451 910558 "FR2" 910695 NIL FR2 (NIL T T) -7 NIL NIL) (-397 905124 907972 908000 "FPS" 909119 T FPS (NIL) -9 NIL 909676) (-396 904573 904682 904846 "FPS-" 904992 NIL FPS- (NIL T) -8 NIL NIL) (-395 902079 903714 903742 "FPC" 903967 T FPC (NIL) -9 NIL 904109) (-394 901872 901912 902009 "FPC-" 902014 NIL FPC- (NIL T) -8 NIL NIL) (-393 900750 901360 901401 "FPATMAB" 901406 NIL FPATMAB (NIL T) -9 NIL 901558) (-392 898450 898926 899352 "FPARFRAC" 900387 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-391 893843 894342 895024 "FORTRAN" 897882 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-390 891559 892059 892598 "FORT" 893324 T FORT (NIL) -7 NIL NIL) (-389 889235 889797 889825 "FORTFN" 890885 T FORTFN (NIL) -9 NIL 891509) (-388 888999 889049 889077 "FORTCAT" 889136 T FORTCAT (NIL) -9 NIL 889198) (-387 887059 887542 887941 "FORMULA" 888620 T FORMULA (NIL) -8 NIL NIL) (-386 886847 886877 886946 "FORMULA1" 887023 NIL FORMULA1 (NIL T) -7 NIL NIL) (-385 886370 886422 886595 "FORDER" 886789 NIL FORDER (NIL T T T T) -7 NIL NIL) (-384 885466 885630 885823 "FOP" 886197 T FOP (NIL) -7 NIL NIL) (-383 884074 884746 884920 "FNLA" 885348 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-382 882742 883131 883159 "FNCAT" 883731 T FNCAT (NIL) -9 NIL 884024) (-381 882308 882701 882729 "FNAME" 882734 T FNAME (NIL) -8 NIL NIL) (-380 881006 881935 881963 "FMTC" 881968 T FMTC (NIL) -9 NIL 882004) (-379 877368 878529 879158 "FMONOID" 880410 NIL FMONOID (NIL T) -8 NIL NIL) (-378 876587 877110 877259 "FM" 877264 NIL FM (NIL T T) -8 NIL NIL) (-377 874011 874657 874685 "FMFUN" 875829 T FMFUN (NIL) -9 NIL 876537) (-376 873280 873461 873489 "FMC" 873779 T FMC (NIL) -9 NIL 873961) (-375 870492 871326 871380 "FMCAT" 872575 NIL FMCAT (NIL T T) -9 NIL 873070) (-374 869385 870258 870358 "FM1" 870437 NIL FM1 (NIL T T) -8 NIL NIL) (-373 867159 867575 868069 "FLOATRP" 868936 NIL FLOATRP (NIL T) -7 NIL NIL) (-372 860710 864815 865445 "FLOAT" 866549 T FLOAT (NIL) -8 NIL NIL) (-371 858148 858648 859226 "FLOATCP" 860177 NIL FLOATCP (NIL T) -7 NIL NIL) (-370 856977 857781 857822 "FLINEXP" 857827 NIL FLINEXP (NIL T) -9 NIL 857920) (-369 856131 856366 856694 "FLINEXP-" 856699 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-368 855207 855351 855575 "FLASORT" 855983 NIL FLASORT (NIL T T) -7 NIL NIL) (-367 852424 853266 853318 "FLALG" 854545 NIL FLALG (NIL T T) -9 NIL 855012) (-366 846208 849910 849951 "FLAGG" 851213 NIL FLAGG (NIL T) -9 NIL 851865) (-365 844934 845273 845763 "FLAGG-" 845768 NIL FLAGG- (NIL T T) -8 NIL NIL) (-364 843976 844119 844346 "FLAGG2" 844787 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-363 840989 841963 842022 "FINRALG" 843150 NIL FINRALG (NIL T T) -9 NIL 843658) (-362 840149 840378 840717 "FINRALG-" 840722 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-361 839555 839768 839796 "FINITE" 839992 T FINITE (NIL) -9 NIL 840099) (-360 832013 834174 834214 "FINAALG" 837881 NIL FINAALG (NIL T) -9 NIL 839334) (-359 827354 828395 829539 "FINAALG-" 830918 NIL FINAALG- (NIL T T) -8 NIL NIL) (-358 826749 827109 827212 "FILE" 827284 NIL FILE (NIL T) -8 NIL NIL) (-357 825433 825745 825799 "FILECAT" 826483 NIL FILECAT (NIL T T) -9 NIL 826699) (-356 823353 824847 824875 "FIELD" 824915 T FIELD (NIL) -9 NIL 824995) (-355 821973 822358 822869 "FIELD-" 822874 NIL FIELD- (NIL T) -8 NIL NIL) (-354 819851 820608 820955 "FGROUP" 821659 NIL FGROUP (NIL T) -8 NIL NIL) (-353 818941 819105 819325 "FGLMICPK" 819683 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-352 814808 818866 818923 "FFX" 818928 NIL FFX (NIL T NIL) -8 NIL NIL) (-351 814409 814470 814605 "FFSLPE" 814741 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-350 810402 811181 811977 "FFPOLY" 813645 NIL FFPOLY (NIL T) -7 NIL NIL) (-349 809906 809942 810151 "FFPOLY2" 810360 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-348 805792 809825 809888 "FFP" 809893 NIL FFP (NIL T NIL) -8 NIL NIL) (-347 801225 805703 805767 "FF" 805772 NIL FF (NIL NIL NIL) -8 NIL NIL) (-346 796386 800568 800758 "FFNBX" 801079 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-345 791360 795521 795779 "FFNBP" 796240 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-344 786028 790644 790855 "FFNB" 791193 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-343 784860 785058 785373 "FFINTBAS" 785825 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-342 781144 783319 783347 "FFIELDC" 783967 T FFIELDC (NIL) -9 NIL 784343) (-341 779807 780177 780674 "FFIELDC-" 780679 NIL FFIELDC- (NIL T) -8 NIL NIL) (-340 779377 779422 779546 "FFHOM" 779749 NIL FFHOM (NIL T T T) -7 NIL NIL) (-339 777075 777559 778076 "FFF" 778892 NIL FFF (NIL T) -7 NIL NIL) (-338 772728 776817 776918 "FFCGX" 777018 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-337 768395 772460 772567 "FFCGP" 772671 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-336 763613 768122 768230 "FFCG" 768331 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-335 745671 754707 754793 "FFCAT" 759958 NIL FFCAT (NIL T T T) -9 NIL 761409) (-334 740869 741916 743230 "FFCAT-" 744460 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-333 740280 740323 740558 "FFCAT2" 740820 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-332 729492 733252 734472 "FEXPR" 739132 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-331 728492 728927 728968 "FEVALAB" 729052 NIL FEVALAB (NIL T) -9 NIL 729313) (-330 727651 727861 728199 "FEVALAB-" 728204 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-329 726244 727034 727237 "FDIV" 727550 NIL FDIV (NIL T T T T) -8 NIL NIL) (-328 723310 724025 724140 "FDIVCAT" 725708 NIL FDIVCAT (NIL T T T T) -9 NIL 726145) (-327 723072 723099 723269 "FDIVCAT-" 723274 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-326 722292 722379 722656 "FDIV2" 722979 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-325 720978 721237 721526 "FCPAK1" 722023 T FCPAK1 (NIL) -7 NIL NIL) (-324 720106 720478 720619 "FCOMP" 720869 NIL FCOMP (NIL T) -8 NIL NIL) (-323 703741 707155 710716 "FC" 716565 T FC (NIL) -8 NIL NIL) (-322 696394 700375 700415 "FAXF" 702217 NIL FAXF (NIL T) -9 NIL 702909) (-321 693673 694328 695153 "FAXF-" 695618 NIL FAXF- (NIL T T) -8 NIL NIL) (-320 688773 693049 693225 "FARRAY" 693530 NIL FARRAY (NIL T) -8 NIL NIL) (-319 684180 686212 686265 "FAMR" 687288 NIL FAMR (NIL T T) -9 NIL 687748) (-318 683070 683372 683807 "FAMR-" 683812 NIL FAMR- (NIL T T T) -8 NIL NIL) (-317 682266 682992 683045 "FAMONOID" 683050 NIL FAMONOID (NIL T) -8 NIL NIL) (-316 680096 680780 680833 "FAMONC" 681774 NIL FAMONC (NIL T T) -9 NIL 682160) (-315 678788 679850 679987 "FAGROUP" 679992 NIL FAGROUP (NIL T) -8 NIL NIL) (-314 676583 676902 677305 "FACUTIL" 678469 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-313 675682 675867 676089 "FACTFUNC" 676393 NIL FACTFUNC (NIL T) -7 NIL NIL) (-312 668087 674933 675145 "EXPUPXS" 675538 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-311 665570 666110 666696 "EXPRTUBE" 667521 T EXPRTUBE (NIL) -7 NIL NIL) (-310 661764 662356 663093 "EXPRODE" 664909 NIL EXPRODE (NIL T T) -7 NIL NIL) (-309 647138 660419 660847 "EXPR" 661368 NIL EXPR (NIL T) -8 NIL NIL) (-308 641545 642132 642945 "EXPR2UPS" 646436 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-307 641181 641238 641345 "EXPR2" 641482 NIL EXPR2 (NIL T T) -7 NIL NIL) (-306 632588 640313 640610 "EXPEXPAN" 641018 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-305 632415 632545 632574 "EXIT" 632579 T EXIT (NIL) -8 NIL NIL) (-304 631922 632139 632230 "EXITAST" 632344 T EXITAST (NIL) -8 NIL NIL) (-303 631549 631611 631724 "EVALCYC" 631854 NIL EVALCYC (NIL T) -7 NIL NIL) (-302 631090 631208 631249 "EVALAB" 631419 NIL EVALAB (NIL T) -9 NIL 631523) (-301 630571 630693 630914 "EVALAB-" 630919 NIL EVALAB- (NIL T T) -8 NIL NIL) (-300 628074 629342 629370 "EUCDOM" 629925 T EUCDOM (NIL) -9 NIL 630275) (-299 626479 626921 627511 "EUCDOM-" 627516 NIL EUCDOM- (NIL T) -8 NIL NIL) (-298 614019 616777 619527 "ESTOOLS" 623749 T ESTOOLS (NIL) -7 NIL NIL) (-297 613651 613708 613817 "ESTOOLS2" 613956 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-296 613402 613444 613524 "ESTOOLS1" 613603 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-295 607327 609055 609083 "ES" 611851 T ES (NIL) -9 NIL 613260) (-294 602274 603561 605378 "ES-" 605542 NIL ES- (NIL T) -8 NIL NIL) (-293 598649 599409 600189 "ESCONT" 601514 T ESCONT (NIL) -7 NIL NIL) (-292 598394 598426 598508 "ESCONT1" 598611 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-291 598069 598119 598219 "ES2" 598338 NIL ES2 (NIL T T) -7 NIL NIL) (-290 597699 597757 597866 "ES1" 598005 NIL ES1 (NIL T T) -7 NIL NIL) (-289 596915 597044 597220 "ERROR" 597543 T ERROR (NIL) -7 NIL NIL) (-288 590418 596774 596865 "EQTBL" 596870 NIL EQTBL (NIL T T) -8 NIL NIL) (-287 582975 585732 587181 "EQ" 589002 NIL -3893 (NIL T) -8 NIL NIL) (-286 582607 582664 582773 "EQ2" 582912 NIL EQ2 (NIL T T) -7 NIL NIL) (-285 577899 578945 580038 "EP" 581546 NIL EP (NIL T) -7 NIL NIL) (-284 576481 576782 577099 "ENV" 577602 T ENV (NIL) -8 NIL NIL) (-283 575680 576200 576228 "ENTIRER" 576233 T ENTIRER (NIL) -9 NIL 576279) (-282 572182 573635 574005 "EMR" 575479 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-281 571326 571511 571565 "ELTAGG" 571945 NIL ELTAGG (NIL T T) -9 NIL 572156) (-280 571045 571107 571248 "ELTAGG-" 571253 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-279 570834 570863 570917 "ELTAB" 571001 NIL ELTAB (NIL T T) -9 NIL NIL) (-278 569960 570106 570305 "ELFUTS" 570685 NIL ELFUTS (NIL T T) -7 NIL NIL) (-277 569702 569758 569786 "ELEMFUN" 569891 T ELEMFUN (NIL) -9 NIL NIL) (-276 569572 569593 569661 "ELEMFUN-" 569666 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-275 564463 567672 567713 "ELAGG" 568653 NIL ELAGG (NIL T) -9 NIL 569116) (-274 562748 563182 563845 "ELAGG-" 563850 NIL ELAGG- (NIL T T) -8 NIL NIL) (-273 561405 561685 561980 "ELABEXPR" 562473 T ELABEXPR (NIL) -8 NIL NIL) (-272 554271 556072 556899 "EFUPXS" 560681 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-271 547721 549522 550332 "EFULS" 553547 NIL EFULS (NIL T T T) -8 NIL NIL) (-270 545143 545501 545980 "EFSTRUC" 547353 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-269 534215 535780 537340 "EF" 543658 NIL EF (NIL T T) -7 NIL NIL) (-268 533316 533700 533849 "EAB" 534086 T EAB (NIL) -8 NIL NIL) (-267 532525 533275 533303 "E04UCFA" 533308 T E04UCFA (NIL) -8 NIL NIL) (-266 531734 532484 532512 "E04NAFA" 532517 T E04NAFA (NIL) -8 NIL NIL) (-265 530943 531693 531721 "E04MBFA" 531726 T E04MBFA (NIL) -8 NIL NIL) (-264 530152 530902 530930 "E04JAFA" 530935 T E04JAFA (NIL) -8 NIL NIL) (-263 529363 530111 530139 "E04GCFA" 530144 T E04GCFA (NIL) -8 NIL NIL) (-262 528574 529322 529350 "E04FDFA" 529355 T E04FDFA (NIL) -8 NIL NIL) (-261 527783 528533 528561 "E04DGFA" 528566 T E04DGFA (NIL) -8 NIL NIL) (-260 521961 523308 524672 "E04AGNT" 526439 T E04AGNT (NIL) -7 NIL NIL) (-259 520685 521165 521205 "DVARCAT" 521680 NIL DVARCAT (NIL T) -9 NIL 521879) (-258 519889 520101 520415 "DVARCAT-" 520420 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-257 512789 519688 519817 "DSMP" 519822 NIL DSMP (NIL T T T) -8 NIL NIL) (-256 507599 508734 509802 "DROPT" 511741 T DROPT (NIL) -8 NIL NIL) (-255 507264 507323 507421 "DROPT1" 507534 NIL DROPT1 (NIL T) -7 NIL NIL) (-254 502379 503505 504642 "DROPT0" 506147 T DROPT0 (NIL) -7 NIL NIL) (-253 500724 501049 501435 "DRAWPT" 502013 T DRAWPT (NIL) -7 NIL NIL) (-252 495311 496234 497313 "DRAW" 499698 NIL DRAW (NIL T) -7 NIL NIL) (-251 494944 494997 495115 "DRAWHACK" 495252 NIL DRAWHACK (NIL T) -7 NIL NIL) (-250 493675 493944 494235 "DRAWCX" 494673 T DRAWCX (NIL) -7 NIL NIL) (-249 493191 493259 493410 "DRAWCURV" 493601 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-248 483662 485621 487736 "DRAWCFUN" 491096 T DRAWCFUN (NIL) -7 NIL NIL) (-247 480475 482357 482398 "DQAGG" 483027 NIL DQAGG (NIL T) -9 NIL 483300) (-246 468994 475691 475774 "DPOLCAT" 477626 NIL DPOLCAT (NIL T T T T) -9 NIL 478171) (-245 463833 465179 467137 "DPOLCAT-" 467142 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-244 456988 463694 463792 "DPMO" 463797 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-243 450046 456768 456935 "DPMM" 456940 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-242 449466 449669 449783 "DOMAIN" 449952 T DOMAIN (NIL) -8 NIL NIL) (-241 443217 449101 449253 "DMP" 449367 NIL DMP (NIL NIL T) -8 NIL NIL) (-240 442817 442873 443017 "DLP" 443155 NIL DLP (NIL T) -7 NIL NIL) (-239 436461 441918 442145 "DLIST" 442622 NIL DLIST (NIL T) -8 NIL NIL) (-238 433307 435316 435357 "DLAGG" 435907 NIL DLAGG (NIL T) -9 NIL 436136) (-237 432157 432787 432815 "DIVRING" 432907 T DIVRING (NIL) -9 NIL 432990) (-236 431394 431584 431884 "DIVRING-" 431889 NIL DIVRING- (NIL T) -8 NIL NIL) (-235 429496 429853 430259 "DISPLAY" 431008 T DISPLAY (NIL) -7 NIL NIL) (-234 423438 429410 429473 "DIRPROD" 429478 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-233 422286 422489 422754 "DIRPROD2" 423231 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-232 411824 417776 417829 "DIRPCAT" 418239 NIL DIRPCAT (NIL NIL T) -9 NIL 419079) (-231 409150 409792 410673 "DIRPCAT-" 411010 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-230 408437 408597 408783 "DIOSP" 408984 T DIOSP (NIL) -7 NIL NIL) (-229 405139 407349 407390 "DIOPS" 407824 NIL DIOPS (NIL T) -9 NIL 408053) (-228 404688 404802 404993 "DIOPS-" 404998 NIL DIOPS- (NIL T T) -8 NIL NIL) (-227 403600 404194 404222 "DIFRING" 404409 T DIFRING (NIL) -9 NIL 404519) (-226 403246 403323 403475 "DIFRING-" 403480 NIL DIFRING- (NIL T) -8 NIL NIL) (-225 401071 402309 402350 "DIFEXT" 402713 NIL DIFEXT (NIL T) -9 NIL 403007) (-224 399356 399784 400450 "DIFEXT-" 400455 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-223 396678 398888 398929 "DIAGG" 398934 NIL DIAGG (NIL T) -9 NIL 398954) (-222 396062 396219 396471 "DIAGG-" 396476 NIL DIAGG- (NIL T T) -8 NIL NIL) (-221 391527 395021 395298 "DHMATRIX" 395831 NIL DHMATRIX (NIL T) -8 NIL NIL) (-220 387139 388048 389058 "DFSFUN" 390537 T DFSFUN (NIL) -7 NIL NIL) (-219 382255 386070 386382 "DFLOAT" 386847 T DFLOAT (NIL) -8 NIL NIL) (-218 380483 380764 381160 "DFINTTLS" 381963 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-217 377548 378504 378904 "DERHAM" 380149 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-216 375397 377323 377412 "DEQUEUE" 377492 NIL DEQUEUE (NIL T) -8 NIL NIL) (-215 374612 374745 374941 "DEGRED" 375259 NIL DEGRED (NIL T T) -7 NIL NIL) (-214 371007 371752 372605 "DEFINTRF" 373840 NIL DEFINTRF (NIL T) -7 NIL NIL) (-213 368534 369003 369602 "DEFINTEF" 370526 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-212 367911 368154 368269 "DEFAST" 368439 T DEFAST (NIL) -8 NIL NIL) (-211 361799 367352 367518 "DECIMAL" 367765 T DECIMAL (NIL) -8 NIL NIL) (-210 359311 359769 360275 "DDFACT" 361343 NIL DDFACT (NIL T T) -7 NIL NIL) (-209 358907 358950 359101 "DBLRESP" 359262 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-208 356617 356951 357320 "DBASE" 358665 NIL DBASE (NIL T) -8 NIL NIL) (-207 355886 356097 356243 "DATABUF" 356516 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-206 355019 355845 355873 "D03FAFA" 355878 T D03FAFA (NIL) -8 NIL NIL) (-205 354153 354978 355006 "D03EEFA" 355011 T D03EEFA (NIL) -8 NIL NIL) (-204 352103 352569 353058 "D03AGNT" 353684 T D03AGNT (NIL) -7 NIL NIL) (-203 351419 352062 352090 "D02EJFA" 352095 T D02EJFA (NIL) -8 NIL NIL) (-202 350735 351378 351406 "D02CJFA" 351411 T D02CJFA (NIL) -8 NIL NIL) (-201 350051 350694 350722 "D02BHFA" 350727 T D02BHFA (NIL) -8 NIL NIL) (-200 349367 350010 350038 "D02BBFA" 350043 T D02BBFA (NIL) -8 NIL NIL) (-199 342565 344153 345759 "D02AGNT" 347781 T D02AGNT (NIL) -7 NIL NIL) (-198 340334 340856 341402 "D01WGTS" 342039 T D01WGTS (NIL) -7 NIL NIL) (-197 339429 340293 340321 "D01TRNS" 340326 T D01TRNS (NIL) -8 NIL NIL) (-196 338524 339388 339416 "D01GBFA" 339421 T D01GBFA (NIL) -8 NIL NIL) (-195 337619 338483 338511 "D01FCFA" 338516 T D01FCFA (NIL) -8 NIL NIL) (-194 336714 337578 337606 "D01ASFA" 337611 T D01ASFA (NIL) -8 NIL NIL) (-193 335809 336673 336701 "D01AQFA" 336706 T D01AQFA (NIL) -8 NIL NIL) (-192 334904 335768 335796 "D01APFA" 335801 T D01APFA (NIL) -8 NIL NIL) (-191 333999 334863 334891 "D01ANFA" 334896 T D01ANFA (NIL) -8 NIL NIL) (-190 333094 333958 333986 "D01AMFA" 333991 T D01AMFA (NIL) -8 NIL NIL) (-189 332189 333053 333081 "D01ALFA" 333086 T D01ALFA (NIL) -8 NIL NIL) (-188 331284 332148 332176 "D01AKFA" 332181 T D01AKFA (NIL) -8 NIL NIL) (-187 330379 331243 331271 "D01AJFA" 331276 T D01AJFA (NIL) -8 NIL NIL) (-186 323676 325227 326788 "D01AGNT" 328838 T D01AGNT (NIL) -7 NIL NIL) (-185 323013 323141 323293 "CYCLOTOM" 323544 T CYCLOTOM (NIL) -7 NIL NIL) (-184 319748 320461 321188 "CYCLES" 322306 T CYCLES (NIL) -7 NIL NIL) (-183 319060 319194 319365 "CVMP" 319609 NIL CVMP (NIL T) -7 NIL NIL) (-182 316831 317089 317465 "CTRIGMNP" 318788 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-181 316342 316531 316630 "CTORCALL" 316752 T CTORCALL (NIL) -8 NIL NIL) (-180 315716 315815 315968 "CSTTOOLS" 316239 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-179 311515 312172 312930 "CRFP" 315028 NIL CRFP (NIL T T) -7 NIL NIL) (-178 311017 311236 311328 "CRCEAST" 311443 T CRCEAST (NIL) -8 NIL NIL) (-177 310064 310249 310477 "CRAPACK" 310821 NIL CRAPACK (NIL T) -7 NIL NIL) (-176 309448 309549 309753 "CPMATCH" 309940 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-175 309173 309201 309307 "CPIMA" 309414 NIL CPIMA (NIL T T T) -7 NIL NIL) (-174 305537 306209 306927 "COORDSYS" 308508 NIL COORDSYS (NIL T) -7 NIL NIL) (-173 304921 305050 305200 "CONTOUR" 305407 T CONTOUR (NIL) -8 NIL NIL) (-172 300847 302924 303416 "CONTFRAC" 304461 NIL CONTFRAC (NIL 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NIL NIL) (-158 259948 260142 260170 "COMBOPC" 260508 T COMBOPC (NIL) -9 NIL 260683) (-157 258844 259054 259296 "COMBINAT" 259738 NIL COMBINAT (NIL T) -7 NIL NIL) (-156 255042 255615 256255 "COMBF" 258266 NIL COMBF (NIL T T) -7 NIL NIL) (-155 253828 254158 254393 "COLOR" 254827 T COLOR (NIL) -8 NIL NIL) (-154 253331 253549 253641 "COLONAST" 253756 T COLONAST (NIL) -8 NIL NIL) (-153 252971 253018 253143 "CMPLXRT" 253278 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-152 252446 252671 252770 "CLLCTAST" 252892 T CLLCTAST (NIL) -8 NIL NIL) (-151 247948 248976 250056 "CLIP" 251386 T CLIP (NIL) -7 NIL NIL) (-150 246330 247054 247293 "CLIF" 247775 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-149 242552 244476 244517 "CLAGG" 245446 NIL CLAGG (NIL T) -9 NIL 245982) (-148 240974 241431 242014 "CLAGG-" 242019 NIL CLAGG- (NIL T T) -8 NIL NIL) (-147 240518 240603 240743 "CINTSLPE" 240883 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-146 238019 238490 239038 "CHVAR" 240046 NIL CHVAR (NIL T T T) -7 NIL NIL) (-145 237282 237802 237830 "CHARZ" 237835 T CHARZ (NIL) -9 NIL 237850) (-144 237036 237076 237154 "CHARPOL" 237236 NIL CHARPOL (NIL T) -7 NIL NIL) (-143 236183 236736 236764 "CHARNZ" 236811 T CHARNZ (NIL) -9 NIL 236867) (-142 234208 234873 235208 "CHAR" 235868 T CHAR (NIL) -8 NIL NIL) (-141 233934 233995 234023 "CFCAT" 234134 T CFCAT (NIL) -9 NIL NIL) (-140 233179 233290 233472 "CDEN" 233818 NIL CDEN (NIL T T T) -7 NIL NIL) (-139 229171 232332 232612 "CCLASS" 232919 T CCLASS (NIL) -8 NIL NIL) (-138 229090 229116 229151 "CATEGORY" 229156 T -10 (NIL) -8 NIL NIL) (-137 228564 228790 228889 "CATAST" 229011 T CATAST (NIL) -8 NIL NIL) (-136 228067 228285 228377 "CASEAST" 228492 T CASEAST (NIL) -8 NIL NIL) (-135 223119 224096 224849 "CARTEN" 227370 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-134 222227 222375 222596 "CARTEN2" 222966 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-133 220569 221377 221634 "CARD" 221990 T CARD (NIL) -8 NIL NIL) (-132 220172 220373 220448 "CAPSLAST" 220514 T CAPSLAST (NIL) -8 NIL NIL) (-131 219544 219872 219900 "CACHSET" 220032 T CACHSET (NIL) -9 NIL 220109) (-130 219040 219336 219364 "CABMON" 219414 T CABMON (NIL) -9 NIL 219470) (-129 218209 218587 218730 "BYTE" 218917 T BYTE (NIL) -8 NIL NIL) (-128 214157 218156 218190 "BYTEARY" 218195 T BYTEARY (NIL) -8 NIL NIL) (-127 211714 213849 213956 "BTREE" 214083 NIL BTREE (NIL T) -8 NIL NIL) (-126 209212 211362 211484 "BTOURN" 211624 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206630 208683 208724 "BTCAT" 208792 NIL BTCAT (NIL T) -9 NIL 208869) (-124 206297 206377 206526 "BTCAT-" 206531 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 201589 205440 205468 "BTAGG" 205690 T BTAGG (NIL) -9 NIL 205851) (-122 201079 201204 201410 "BTAGG-" 201415 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 198123 200357 200572 "BSTREE" 200896 NIL BSTREE (NIL T) -8 NIL NIL) (-120 197261 197387 197571 "BRILL" 197979 NIL BRILL (NIL T) -7 NIL NIL) (-119 193962 195989 196030 "BRAGG" 196679 NIL BRAGG (NIL T) -9 NIL 196936) (-118 192491 192897 193452 "BRAGG-" 193457 NIL 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160314 160519 "BFUNCT" 160745 T BFUNCT (NIL) -8 NIL NIL) (-103 158718 158896 159184 "BEZOUT" 159852 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155235 157570 157900 "BBTREE" 158421 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154969 155022 155050 "BASTYPE" 155169 T BASTYPE (NIL) -9 NIL NIL) (-100 154821 154850 154923 "BASTYPE-" 154928 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154259 154335 154485 "BALFACT" 154732 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 153142 153674 153860 "AUTOMOR" 154104 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152868 152873 152899 "ATTREG" 152904 T ATTREG (NIL) -9 NIL NIL) (-96 151147 151565 151917 "ATTRBUT" 152534 T ATTRBUT (NIL) -8 NIL NIL) (-95 150782 150975 151041 "ATTRAST" 151099 T ATTRAST (NIL) -8 NIL NIL) (-94 150318 150431 150457 "ATRIG" 150658 T ATRIG (NIL) -9 NIL NIL) (-93 150127 150168 150255 "ATRIG-" 150260 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149749 149909 149935 "ASTCAT" 149993 T ASTCAT (NIL) -9 NIL 150056) (-91 149476 149535 149654 "ASTCAT-" 149659 NIL ASTCAT- (NIL T) 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ASP4 (NIL NIL) -8 NIL NIL) (-76 133506 134119 134229 "ASP49" 134339 NIL ASP49 (NIL NIL) -8 NIL NIL) (-75 132291 133045 133213 "ASP42" 133395 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-74 131068 131824 131994 "ASP41" 132178 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130018 130745 130863 "ASP35" 130981 NIL ASP35 (NIL NIL) -8 NIL NIL) (-72 129783 129966 130005 "ASP34" 130010 NIL ASP34 (NIL NIL) -8 NIL NIL) (-71 129520 129587 129663 "ASP33" 129738 NIL ASP33 (NIL NIL) -8 NIL NIL) (-70 128415 129155 129287 "ASP31" 129419 NIL ASP31 (NIL NIL) -8 NIL NIL) (-69 128180 128363 128402 "ASP30" 128407 NIL ASP30 (NIL NIL) -8 NIL NIL) (-68 127915 127984 128060 "ASP29" 128135 NIL ASP29 (NIL NIL) -8 NIL NIL) (-67 127680 127863 127902 "ASP28" 127907 NIL ASP28 (NIL NIL) -8 NIL NIL) (-66 127445 127628 127667 "ASP27" 127672 NIL ASP27 (NIL NIL) -8 NIL NIL) (-65 126529 127143 127254 "ASP24" 127365 NIL ASP24 (NIL NIL) -8 NIL NIL) (-64 125445 126170 126300 "ASP20" 126430 NIL ASP20 (NIL NIL) -8 NIL NIL) (-63 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ABELGRP (NIL) -9 NIL 9812) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL)) \ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 04bdef9f..33f1c1d4 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,1534 +1,1571 @@
-(737988 . 3431822562)
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+(738152 . 3431897907)
+(((*1 *1 *2)
+ (-12 (-5 *2 (-1111 *3 *4)) (-14 *3 (-895)) (-4 *4 (-356))
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(((*1 *2 *3)
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@@ -1537,67 +1574,576 @@
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((*1 *2 *2 *2)
@@ -2813,1868 +2580,1250 @@
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@@ -9550,32 +8168,32 @@
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((*1 *2 *1 *3)
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@@ -9584,1118 +8202,882 @@
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- (-12 (-5 *3 (-623 (-550))) (-5 *2 (-550)) (-5 *1 (-478 *4))
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(((*1 *2 *3)
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+ (-12 (-5 *3 (-1111 *4 *2)) (-14 *4 (-895))
+ (-4 *2 (-13 (-1021) (-10 -7 (-6 (-4346 "*")))))
+ (-5 *1 (-876 *4 *2)))))
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+ (-12 (-4 *3 (-13 (-825) (-444))) (-5 *1 (-1173 *3 *2))
+ (-4 *2 (-13 (-423 *3) (-1167))))))
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+ (-12 (-5 *2 (-309 *3)) (-4 *3 (-13 (-1021) (-825)))
+ (-5 *1 (-217 *3 *4)) (-14 *4 (-623 (-1145))))))
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+ (|partial| -12 (-5 *2 (-1243 *3 *4)) (-4 *3 (-825)) (-4 *4 (-170))
+ (-5 *1 (-642 *3 *4))))
+ ((*1 *2 *1)
+ (|partial| -12 (-5 *2 (-642 *3 *4)) (-5 *1 (-1248 *3 *4))
+ (-4 *3 (-825)) (-4 *4 (-170)))))
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(((*1 *2 *3)
- (-12
- (-5 *3
- (-623
- (-2 (|:| -2122 (-749))
- (|:| |eqns|
- (-623
- (-2 (|:| |det| *7) (|:| |rows| (-623 (-550)))
- (|:| |cols| (-623 (-550))))))
- (|:| |fgb| (-623 *7)))))
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- ((*1 *2 *3)
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- (-12 (-5 *4 (-623 (-1126))) (-5 *3 (-1126)) (-5 *2 (-305))
- (-5 *1 (-289)))))
-(((*1 *2 *1)
+ (|partial| -12 (-5 *3 (-667 (-400 (-926 (-550)))))
+ (-5 *2 (-667 (-309 (-550)))) (-5 *1 (-1005)))))
+(((*1 *1 *2)
(-12
(-5 *2
(-623
(-2
- (|:| -2763
- (-2 (|:| |var| (-1144)) (|:| |fn| (-309 (-219)))
- (|:| -3170 (-1062 (-818 (-219)))) (|:| |abserr| (-219))
+ (|:| -3549
+ (-2 (|:| |var| (-1145)) (|:| |fn| (-309 (-219)))
+ (|:| -2873 (-1063 (-818 (-219)))) (|:| |abserr| (-219))
(|:| |relerr| (-219))))
- (|:| -2119
+ (|:| -3859
(-2
(|:| |endPointContinuity|
(-3 (|:| |continuous| "Continuous at the end points")
@@ -10708,10 +9090,10 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1124 (-219)))
+ (-3 (|:| |str| (-1125 (-219)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -3170
+ (|:| -2873
(-3 (|:| |finite| "The range is finite")
(|:| |lowerInfinite|
"The bottom of range is infinite")
@@ -10719,474 +9101,1620 @@
(|:| |bothInfinite|
"Both top and bottom points are infinite")
(|:| |notEvaluated| "Range not yet evaluated"))))))))
- (-5 *1 (-545))))
- ((*1 *2 *1)
- (-12 (-4 *1 (-586 *3 *4)) (-4 *3 (-1068)) (-4 *4 (-1181))
- (-5 *2 (-623 *4)))))
+ (-5 *1 (-545)))))
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+ (|partial| -12
+ (-5 *3
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+ (-3 (|:| |%expansion| (-306 *5 *3 *6 *7))
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(((*1 *2 *3 *4 *5 *5 *4 *6)
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(-5 *2
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- (-5 *1 (-546 *7 *4 *3)) (-4 *3 (-634 *4)) (-4 *3 (-1068))))
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((*1 *2 *3 *4 *5 *5 *5 *4 *6)
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(-5 *2
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(((*1 *2 *1)
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(-4 *5 (-259 *4)) (-4 *6 (-771)) (-5 *2 (-749))))
((*1 *2 *1 *3)
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(-4 *5 (-259 *3)) (-4 *6 (-771)) (-5 *2 (-749))))
((*1 *2 *1) (-12 (-4 *1 (-259 *3)) (-4 *3 (-825)) (-5 *2 (-749))))
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((*1 *2 *3)
(-12 (-5 *3 (-329 *4 *5 *6 *7)) (-4 *4 (-13 (-361) (-356)))
- (-4 *5 (-1203 *4)) (-4 *6 (-1203 (-400 *5))) (-4 *7 (-335 *4 *5 *6))
+ (-4 *5 (-1204 *4)) (-4 *6 (-1204 (-400 *5))) (-4 *7 (-335 *4 *5 *6))
(-5 *2 (-749)) (-5 *1 (-385 *4 *5 *6 *7))))
- ((*1 *2 *1) (-12 (-4 *1 (-395)) (-5 *2 (-811 (-894)))))
+ ((*1 *2 *1) (-12 (-4 *1 (-395)) (-5 *2 (-811 (-895)))))
((*1 *2 *1) (-12 (-4 *1 (-397)) (-5 *2 (-550))))
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((*1 *2 *1)
(-12 (-4 *3 (-542)) (-5 *2 (-550)) (-5 *1 (-603 *3 *4))
- (-4 *4 (-1203 *3))))
+ (-4 *4 (-1204 *3))))
((*1 *2 *1 *3 *2)
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(-4 *3 (-825))))
((*1 *2 *1 *3)
- (-12 (-4 *1 (-719 *4 *3)) (-4 *4 (-1020)) (-4 *3 (-825))
+ (-12 (-4 *1 (-719 *4 *3)) (-4 *4 (-1021)) (-4 *3 (-825))
(-5 *2 (-749))))
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((*1 *2 *3)
(|partial| -12 (-5 *3 (-329 *5 *6 *7 *8)) (-4 *5 (-423 *4))
- (-4 *6 (-1203 *5)) (-4 *7 (-1203 (-400 *6)))
+ (-4 *6 (-1204 *5)) (-4 *7 (-1204 (-400 *6)))
(-4 *8 (-335 *5 *6 *7))
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- (-5 *1 (-884 *4 *5 *6 *7 *8))))
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((*1 *2 *3)
(|partial| -12 (-5 *3 (-329 (-400 (-550)) *4 *5 *6))
- (-4 *4 (-1203 (-400 (-550)))) (-4 *5 (-1203 (-400 *4)))
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(-4 *6 (-335 (-400 (-550)) *4 *5)) (-5 *2 (-749))
- (-5 *1 (-885 *4 *5 *6))))
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((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-329 *6 *7 *4 *8)) (-5 *5 (-1 *9 *6)) (-4 *6 (-356))
- (-4 *7 (-1203 *6)) (-4 *4 (-1203 (-400 *7))) (-4 *8 (-335 *6 *7 *4))
+ (-4 *7 (-1204 *6)) (-4 *4 (-1204 (-400 *7))) (-4 *8 (-335 *6 *7 *4))
(-4 *9 (-13 (-361) (-356))) (-5 *2 (-749))
- (-5 *1 (-991 *6 *7 *4 *8 *9))))
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((*1 *2 *1 *1)
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((*1 *2 *1 *2)
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((*1 *2 *1)
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(((*1 *2 *2)
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((*1 *2 *1)
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((*1 *1 *1 *2)
(-12 (-5 *2 (-650 *3)) (-4 *3 (-825)) (-5 *1 (-642 *3 *4))
@@ -15564,193 +11609,164 @@
(-12 (-5 *2 (-650 *3)) (-4 *3 (-825)) (-5 *1 (-642 *3 *4))
(-4 *4 (-170))))
((*1 *1 *2)
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(-5 *1 (-653 *3))))
((*1 *1 *2 *3)
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(-14 *4
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((*1 *1 *2)
- (-12 (-5 *2 (-667 (-332 (-1532 'XL 'XR 'ELAM) (-1532) (-677))))
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+ (-12 (-5 *2 (-667 (-332 (-2245 'XL 'XR 'ELAM) (-2245) (-677))))
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((*1 *1 *2)
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- ((*1 *1 *2) (-12 (-5 *2 (-1149)) (-4 *1 (-92))))
- ((*1 *2 *1) (-12 (-5 *2 (-977 2)) (-5 *1 (-107))))
+ (-12 (-5 *2 (-332 (-2245 'X) (-2245 '-1932) (-677))) (-5 *1 (-88 *3))
+ (-14 *3 (-1145))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1150)) (-4 *1 (-92))))
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((*1 *2 *1) (-12 (-5 *2 (-400 (-550))) (-5 *1 (-107))))
((*1 *1 *2) (-12 (-5 *2 (-749)) (-5 *1 (-129))))
((*1 *1 *2)
@@ -15760,45 +11776,45 @@
(-12 (-5 *2 (-623 *5)) (-4 *5 (-170)) (-5 *1 (-135 *3 *4 *5))
(-14 *3 (-550)) (-14 *4 (-749))))
((*1 *1 *2)
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(-5 *1 (-135 *3 *4 *5)) (-14 *3 (-550))))
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(-12 (-5 *2 (-234 *4 *5)) (-14 *4 (-749)) (-4 *5 (-170))
(-5 *1 (-135 *3 *4 *5)) (-14 *3 (-550))))
((*1 *2 *3)
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- (-5 *2 (-1227 (-667 (-400 (-925 *4))))) (-5 *1 (-183 *4))))
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((*1 *1 *2)
(-12 (-5 *2 (-623 *3))
(-4 *3
(-13 (-825)
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- (-15 -3656 ((-1232) $)))))
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(-5 *1 (-208 *3))))
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(-4 *3 (-170)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4))
(-14 *6 (-1 (-3 *4 "failed") *4 *4))
(-14 *7 (-1 (-3 *2 "failed") *2 *2 *4))))
((*1 *1 *2)
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(-5 *1 (-306 *3 *4 *5 *6))))
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((*1 *2 *1)
(-12 (-5 *2 (-309 *5)) (-5 *1 (-332 *3 *4 *5))
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((*1 *2 *3)
(-12 (-4 *4 (-342)) (-4 *2 (-322 *4)) (-5 *1 (-340 *3 *4 *2))
(-4 *3 (-322 *4))))
@@ -15807,96 +11823,96 @@
(-4 *3 (-322 *4))))
((*1 *2 *1)
(-12 (-4 *1 (-367 *3 *4)) (-4 *3 (-825)) (-4 *4 (-170))
- (-5 *2 (-1251 *3 *4))))
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((*1 *2 *1)
(-12 (-4 *1 (-367 *3 *4)) (-4 *3 (-825)) (-4 *4 (-170))
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((*1 *1 *2) (-12 (-4 *1 (-367 *2 *3)) (-4 *2 (-825)) (-4 *3 (-170))))
((*1 *1 *2)
(-12
- (-5 *2 (-2 (|:| |localSymbols| (-1148)) (|:| -1542 (-623 (-323)))))
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(-4 *1 (-376))))
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((*1 *1 *2) (-12 (-5 *2 (-667 (-677))) (-4 *1 (-376))))
((*1 *1 *2)
(-12
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(-4 *1 (-377))))
((*1 *1 *2) (-12 (-5 *2 (-323)) (-4 *1 (-377))))
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(-4 *1 (-389))))
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(-12 (-5 *2 (-309 (-677))) (-5 *1 (-391 *3 *4 *5 *6))
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(-12 (-5 *2 (-309 (-679))) (-5 *1 (-391 *3 *4 *5 *6))
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((*1 *1 *2)
(-12 (-5 *2 (-623 (-323))) (-5 *1 (-391 *3 *4 *5 *6))
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((*1 *1 *2)
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+ (-12 (-5 *2 (-323)) (-5 *1 (-391 *3 *4 *5 *6)) (-14 *3 (-1145))
+ (-14 *4 (-3 (|:| |fst| (-427)) (|:| -2487 "void")))
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((*1 *1 *2)
(-12 (-5 *2 (-324 *4)) (-4 *4 (-13 (-825) (-21)))
(-5 *1 (-420 *3 *4)) (-4 *3 (-13 (-170) (-38 (-400 (-550)))))))
@@ -15904,86 +11920,86 @@
(-12 (-5 *1 (-420 *2 *3)) (-4 *2 (-13 (-170) (-38 (-400 (-550)))))
(-4 *3 (-13 (-825) (-21)))))
((*1 *1 *2)
- (-12 (-5 *2 (-400 (-925 (-400 *3)))) (-4 *3 (-542)) (-4 *3 (-825))
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(-4 *1 (-423 *3))))
((*1 *1 *2)
- (-12 (-5 *2 (-925 (-400 *3))) (-4 *3 (-542)) (-4 *3 (-825))
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((*1 *1 *2)
(-12 (-5 *2 (-400 *3)) (-4 *3 (-542)) (-4 *3 (-825))
(-4 *1 (-423 *3))))
((*1 *1 *2)
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(-4 *1 (-423 *3))))
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((*1 *1 *2) (-12 (-5 *2 (-427)) (-5 *1 (-430))))
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((*1 *1 *2)
(-12
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(-4 *1 (-432))))
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((*1 *1 *2)
(-12
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((*1 *1 *2)
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(-4 *4 (-771)) (-4 *5 (-825)) (-5 *1 (-495 *3 *4 *5 *6))))
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((*1 *1 *2) (-12 (-5 *2 (-129)) (-5 *1 (-587))))
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((*1 *1 *2)
(-12 (-4 *3 (-170)) (-5 *1 (-589 *3 *2)) (-4 *2 (-723 *3))))
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((*1 *2 *1)
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((*1 *1 *2)
(-12 (-4 *3 (-170)) (-5 *1 (-615 *3 *2)) (-4 *2 (-723 *3))))
((*1 *2 *1) (-12 (-5 *2 (-655 *3)) (-5 *1 (-650 *3)) (-4 *3 (-825))))
((*1 *2 *1) (-12 (-5 *2 (-797 *3)) (-5 *1 (-650 *3)) (-4 *3 (-825))))
((*1 *2 *1)
- (-12 (-5 *2 (-931 (-931 (-931 *3)))) (-5 *1 (-653 *3))
- (-4 *3 (-1068))))
+ (-12 (-5 *2 (-932 (-932 (-932 *3)))) (-5 *1 (-653 *3))
+ (-4 *3 (-1069))))
((*1 *1 *2)
- (-12 (-5 *2 (-931 (-931 (-931 *3)))) (-4 *3 (-1068))
+ (-12 (-5 *2 (-932 (-932 (-932 *3)))) (-4 *3 (-1069))
(-5 *1 (-653 *3))))
((*1 *2 *1) (-12 (-5 *2 (-797 *3)) (-5 *1 (-655 *3)) (-4 *3 (-825))))
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- ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-660 *3)) (-4 *3 (-1068))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1087)) (-5 *1 (-659))))
+ ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-660 *3)) (-4 *3 (-1069))))
((*1 *1 *2)
- (-12 (-4 *3 (-1020)) (-4 *1 (-665 *3 *4 *2)) (-4 *4 (-366 *3))
+ (-12 (-4 *3 (-1021)) (-4 *1 (-665 *3 *4 *2)) (-4 *4 (-366 *3))
(-4 *2 (-366 *3))))
- ((*1 *2 *1) (-12 (-5 *1 (-669 *2)) (-4 *2 (-595 (-836)))))
- ((*1 *1 *2) (-12 (-5 *1 (-669 *2)) (-4 *2 (-595 (-836)))))
+ ((*1 *2 *1) (-12 (-5 *1 (-669 *2)) (-4 *2 (-595 (-837)))))
+ ((*1 *1 *2) (-12 (-5 *1 (-669 *2)) (-4 *2 (-595 (-837)))))
((*1 *2 *1) (-12 (-5 *2 (-167 (-372))) (-5 *1 (-672))))
((*1 *1 *2) (-12 (-5 *2 (-167 (-679))) (-5 *1 (-672))))
((*1 *1 *2) (-12 (-5 *2 (-167 (-677))) (-5 *1 (-672))))
@@ -15993,118 +12009,118 @@
((*1 *2 *1) (-12 (-5 *2 (-372)) (-5 *1 (-677))))
((*1 *2 *3)
(-12 (-5 *3 (-309 (-550))) (-5 *2 (-309 (-679))) (-5 *1 (-679))))
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- ((*1 *2 *3) (-12 (-5 *3 (-836)) (-5 *2 (-1126)) (-5 *1 (-689))))
+ ((*1 *1 *2) (-12 (-5 *1 (-681 *2)) (-4 *2 (-1069))))
+ ((*1 *2 *3) (-12 (-5 *3 (-837)) (-5 *2 (-1127)) (-5 *1 (-689))))
((*1 *2 *1)
(-12 (-4 *2 (-170)) (-5 *1 (-690 *2 *3 *4 *5 *6)) (-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 *2)
- (-12 (-4 *3 (-1020)) (-5 *1 (-691 *3 *2)) (-4 *2 (-1203 *3))))
+ (-12 (-4 *3 (-1021)) (-5 *1 (-691 *3 *2)) (-4 *2 (-1204 *3))))
((*1 *2 *1)
- (-12 (-5 *2 (-2 (|:| -2922 *3) (|:| -3521 *4)))
- (-5 *1 (-692 *3 *4 *5)) (-4 *3 (-825)) (-4 *4 (-1068))
+ (-12 (-5 *2 (-2 (|:| -3690 *3) (|:| -3068 *4)))
+ (-5 *1 (-692 *3 *4 *5)) (-4 *3 (-825)) (-4 *4 (-1069))
(-14 *5 (-1 (-112) *2 *2))))
((*1 *1 *2)
- (-12 (-5 *2 (-2 (|:| -2922 *3) (|:| -3521 *4))) (-4 *3 (-825))
- (-4 *4 (-1068)) (-5 *1 (-692 *3 *4 *5)) (-14 *5 (-1 (-112) *2 *2))))
+ (-12 (-5 *2 (-2 (|:| -3690 *3) (|:| -3068 *4))) (-4 *3 (-825))
+ (-4 *4 (-1069)) (-5 *1 (-692 *3 *4 *5)) (-14 *5 (-1 (-112) *2 *2))))
((*1 *2 *1)
(-12 (-4 *2 (-170)) (-5 *1 (-694 *2 *3 *4 *5 *6)) (-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 *2)
- (-12 (-5 *2 (-623 (-2 (|:| -2855 *3) (|:| -1792 *4))))
- (-4 *3 (-1020)) (-4 *4 (-705)) (-5 *1 (-714 *3 *4))))
+ (-12 (-5 *2 (-623 (-2 (|:| -4304 *3) (|:| -3227 *4))))
+ (-4 *3 (-1021)) (-4 *4 (-705)) (-5 *1 (-714 *3 *4))))
((*1 *1 *2) (-12 (-5 *2 (-550)) (-4 *1 (-742))))
((*1 *1 *2)
(-12
(-5 *2
(-3
(|:| |nia|
- (-2 (|:| |var| (-1144)) (|:| |fn| (-309 (-219)))
- (|:| -3170 (-1062 (-818 (-219)))) (|:| |abserr| (-219))
+ (-2 (|:| |var| (-1145)) (|:| |fn| (-309 (-219)))
+ (|:| -2873 (-1063 (-818 (-219)))) (|:| |abserr| (-219))
(|:| |relerr| (-219))))
(|:| |mdnia|
(-2 (|:| |fn| (-309 (-219)))
- (|:| -3170 (-623 (-1062 (-818 (-219)))))
+ (|:| -2873 (-623 (-1063 (-818 (-219)))))
(|:| |abserr| (-219)) (|:| |relerr| (-219))))))
(-5 *1 (-747))))
((*1 *1 *2)
(-12
(-5 *2
(-2 (|:| |fn| (-309 (-219)))
- (|:| -3170 (-623 (-1062 (-818 (-219))))) (|:| |abserr| (-219))
+ (|:| -2873 (-623 (-1063 (-818 (-219))))) (|:| |abserr| (-219))
(|:| |relerr| (-219))))
(-5 *1 (-747))))
((*1 *1 *2)
(-12
(-5 *2
- (-2 (|:| |var| (-1144)) (|:| |fn| (-309 (-219)))
- (|:| -3170 (-1062 (-818 (-219)))) (|:| |abserr| (-219))
+ (-2 (|:| |var| (-1145)) (|:| |fn| (-309 (-219)))
+ (|:| -2873 (-1063 (-818 (-219)))) (|:| |abserr| (-219))
(|:| |relerr| (-219))))
(-5 *1 (-747))))
- ((*1 *2 *1) (-12 (-5 *2 (-836)) (-5 *1 (-747))))
- ((*1 *2 *3) (-12 (-5 *2 (-752)) (-5 *1 (-751 *3)) (-4 *3 (-1181))))
+ ((*1 *2 *1) (-12 (-5 *2 (-837)) (-5 *1 (-747))))
+ ((*1 *2 *3) (-12 (-5 *2 (-752)) (-5 *1 (-751 *3)) (-4 *3 (-1182))))
((*1 *1 *2)
(-12
(-5 *2
(-2 (|:| |xinit| (-219)) (|:| |xend| (-219))
- (|:| |fn| (-1227 (-309 (-219)))) (|:| |yinit| (-623 (-219)))
+ (|:| |fn| (-1228 (-309 (-219)))) (|:| |yinit| (-623 (-219)))
(|:| |intvals| (-623 (-219))) (|:| |g| (-309 (-219)))
(|:| |abserr| (-219)) (|:| |relerr| (-219))))
(-5 *1 (-786))))
- ((*1 *2 *1) (-12 (-5 *2 (-836)) (-5 *1 (-786))))
+ ((*1 *2 *1) (-12 (-5 *2 (-837)) (-5 *1 (-786))))
((*1 *2 *1)
- (-12 (-4 *2 (-873 *3)) (-5 *1 (-795 *3 *2 *4)) (-4 *3 (-1068))
+ (-12 (-4 *2 (-874 *3)) (-5 *1 (-795 *3 *2 *4)) (-4 *3 (-1069))
(-14 *4 *3)))
((*1 *1 *2)
- (-12 (-4 *3 (-1068)) (-14 *4 *3) (-5 *1 (-795 *3 *2 *4))
- (-4 *2 (-873 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1144)) (-5 *1 (-802))))
+ (-12 (-4 *3 (-1069)) (-14 *4 *3) (-5 *1 (-795 *3 *2 *4))
+ (-4 *2 (-874 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1145)) (-5 *1 (-802))))
((*1 *1 *2)
(-12
(-5 *2
(-3
(|:| |noa|
- (-2 (|:| |fn| (-309 (-219))) (|:| -3862 (-623 (-219)))
+ (-2 (|:| |fn| (-309 (-219))) (|:| -2463 (-623 (-219)))
(|:| |lb| (-623 (-818 (-219))))
(|:| |cf| (-623 (-309 (-219))))
(|:| |ub| (-623 (-818 (-219))))))
(|:| |lsa|
(-2 (|:| |lfn| (-623 (-309 (-219))))
- (|:| -3862 (-623 (-219)))))))
+ (|:| -2463 (-623 (-219)))))))
(-5 *1 (-816))))
((*1 *1 *2)
(-12
(-5 *2
- (-2 (|:| |lfn| (-623 (-309 (-219)))) (|:| -3862 (-623 (-219)))))
+ (-2 (|:| |lfn| (-623 (-309 (-219)))) (|:| -2463 (-623 (-219)))))
(-5 *1 (-816))))
((*1 *1 *2)
(-12
(-5 *2
- (-2 (|:| |fn| (-309 (-219))) (|:| -3862 (-623 (-219)))
+ (-2 (|:| |fn| (-309 (-219))) (|:| -2463 (-623 (-219)))
(|:| |lb| (-623 (-818 (-219)))) (|:| |cf| (-623 (-309 (-219))))
(|:| |ub| (-623 (-818 (-219))))))
(-5 *1 (-816))))
- ((*1 *2 *1) (-12 (-5 *2 (-836)) (-5 *1 (-816))))
+ ((*1 *2 *1) (-12 (-5 *2 (-837)) (-5 *1 (-816))))
((*1 *1 *2)
- (-12 (-5 *2 (-1223 *3)) (-14 *3 (-1144)) (-5 *1 (-830 *3 *4 *5 *6))
- (-4 *4 (-1020)) (-14 *5 (-98 *4)) (-14 *6 (-1 *4 *4))))
+ (-12 (-5 *2 (-1224 *3)) (-14 *3 (-1145)) (-5 *1 (-830 *3 *4 *5 *6))
+ (-4 *4 (-1021)) (-14 *5 (-98 *4)) (-14 *6 (-1 *4 *4))))
((*1 *1 *2) (-12 (-5 *2 (-550)) (-5 *1 (-833))))
((*1 *1 *2)
- (-12 (-5 *2 (-925 *3)) (-4 *3 (-1020)) (-5 *1 (-839 *3 *4 *5 *6))
- (-14 *4 (-623 (-1144))) (-14 *5 (-623 (-749))) (-14 *6 (-749))))
+ (-12 (-5 *2 (-926 *3)) (-4 *3 (-1021)) (-5 *1 (-840 *3 *4 *5 *6))
+ (-14 *4 (-623 (-1145))) (-14 *5 (-623 (-749))) (-14 *6 (-749))))
((*1 *2 *1)
- (-12 (-5 *2 (-925 *3)) (-5 *1 (-839 *3 *4 *5 *6)) (-4 *3 (-1020))
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- ((*1 *1 *2) (-12 (-5 *2 (-155)) (-5 *1 (-847))))
+ (-12 (-5 *2 (-926 *3)) (-5 *1 (-840 *3 *4 *5 *6)) (-4 *3 (-1021))
+ (-14 *4 (-623 (-1145))) (-14 *5 (-623 (-749))) (-14 *6 (-749))))
+ ((*1 *1 *2) (-12 (-5 *2 (-155)) (-5 *1 (-848))))
((*1 *2 *3)
- (-12 (-5 *3 (-925 (-48))) (-5 *2 (-309 (-550))) (-5 *1 (-848))))
+ (-12 (-5 *3 (-926 (-48))) (-5 *2 (-309 (-550))) (-5 *1 (-849))))
((*1 *2 *3)
- (-12 (-5 *3 (-400 (-925 (-48)))) (-5 *2 (-309 (-550)))
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