diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-06-17 06:42:50 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-17 06:42:50 +0000 |
| commit | 17259d6a532d10a2e38815f6cc394d35d7f31bd9 (patch) | |
| tree | 92276a7649ede5b5476d5383a6dec278fd9401d5 | |
| parent | 1bfecf3e58163305cb5753caab462ed57d0d67fc (diff) | |
| download | open-axiom-17259d6a532d10a2e38815f6cc394d35d7f31bd9.tar.gz | |
* algebra/catdef.spad.pamphlet (PartialDifferentialSpace): New.
(PartialDifferentialRing): Now extend PartialDifferentialSpace.
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 6 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/catdef.spad.pamphlet | 108 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2118 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 3029 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1326 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 10107 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30349 |
9 files changed, 23591 insertions, 23463 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 4074e739..713731fb 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2010-06-17 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/catdef.spad.pamphlet (PartialDifferentialSpace): New. + (PartialDifferentialRing): Now extend PartialDifferentialSpace. + 2010-06-16 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/vector.spad.pamphlet (DirectProductCategory): Extend diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index a56827df..5bbaa9dd 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -342,6 +342,7 @@ $(OUT)/DIFFDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT) $(OUT)/DIFFSPC.$(FASLEXT): $(OUT)/DIFFDOM.$(FASLEXT) $(OUT)/DIFFMOD.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT) +$(OUT)/PDSPC.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_0 = \ AHYP ATTREG CFCAT ELTAB KOERCE KONVERT \ @@ -368,7 +369,7 @@ axiom_algebra_layer_0 = \ DIOPS DIOPS- STRING STRICAT ISTRING ILIST \ LIST DIFFDOM DIFFDOM- DIFFSPC DIFFSPC- DIFFMOD \ LINEXP PATMAB REAL CHARZ LOGIC LOGIC- \ - RTVALUE SYSPTR PDDOM PDDOM- + RTVALUE SYSPTR PDDOM PDDOM- PDSPC PDSPC- axiom_algebra_layer_0_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0)) @@ -499,13 +500,14 @@ axiom_algebra_layer_4_objects = \ $(OUT)/KERNEL.$(FASLEXT): $(OUT)/KERNEL2.$(FASLEXT) $(OUT)/DVARCAT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) +$(OUT)/PDRING.$(FASLEXT): $(OUT)/PDSPC.$(FASLEXT) axiom_algebra_layer_5 = \ CHARNZ DVARCAT DVARCAT- ELEMFUN \ ELEMFUN- ESTOOLS2 FCOMP FPATMAB IDPAM IDPO \ INCRMAPS KERNEL2 MODMONOM MONADWU MONADWU- \ MRF2 NARNG NARNG- NSUP2 ODVAR OPQUERY \ - ORDMON PATMATCH PERMCAT PDRING PDRING- \ + ORDMON PATMATCH PERMCAT PDRING \ SDVAR SUP2 TRIGCAT TRIGCAT- ULS2 UP2 \ ELABEXPR KERNEL diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 3149256b..c65cf20b 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -296,6 +296,7 @@ $(OUT)/DIFFDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT) $(OUT)/DIFFSPC.$(FASLEXT): $(OUT)/DIFFDOM.$(FASLEXT) $(OUT)/DIFFMOD.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT): $(OUT)/TYPE.$(FASLEXT) +$(OUT)/PDSPC.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_0 = \ AHYP ATTREG CFCAT ELTAB KOERCE KONVERT \ @@ -322,7 +323,7 @@ axiom_algebra_layer_0 = \ DIOPS DIOPS- STRING STRICAT ISTRING ILIST \ LIST DIFFDOM DIFFDOM- DIFFSPC DIFFSPC- DIFFMOD \ LINEXP PATMAB REAL CHARZ LOGIC LOGIC- \ - RTVALUE SYSPTR PDDOM PDDOM- + RTVALUE SYSPTR PDDOM PDDOM- PDSPC PDSPC- axiom_algebra_layer_0_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_0)) @@ -478,13 +479,14 @@ axiom_algebra_layer_4_objects = \ $(OUT)/KERNEL.$(FASLEXT): $(OUT)/KERNEL2.$(FASLEXT) $(OUT)/DVARCAT.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) +$(OUT)/PDRING.$(FASLEXT): $(OUT)/PDSPC.$(FASLEXT) axiom_algebra_layer_5 = \ CHARNZ DVARCAT DVARCAT- ELEMFUN \ ELEMFUN- ESTOOLS2 FCOMP FPATMAB IDPAM IDPO \ INCRMAPS KERNEL2 MODMONOM MONADWU MONADWU- \ MRF2 NARNG NARNG- NSUP2 ODVAR OPQUERY \ - ORDMON PATMATCH PERMCAT PDRING PDRING- \ + ORDMON PATMATCH PERMCAT PDRING \ SDVAR SUP2 TRIGCAT TRIGCAT- ULS2 UP2 \ ELABEXPR KERNEL diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 735d2e43..a09a99ea 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -1430,7 +1430,7 @@ OrderedSet(): Category == SetCategory with ++ operation named \spad{differentiate} for partial differentiation with ++ respect to some domain of variables. ++ See Also: -++ DifferentialDomain +++ DifferentialDomain, PartialDifferentialSpace PartialDifferentialDomain(T: Type, S: Type): Category == Type with differentiate: (%,S) -> T ++ \spad{differentiate(x,v)} computes the partial derivative @@ -1443,6 +1443,65 @@ PartialDifferentialDomain(T: Type, S: Type): Category == Type with @ +\section{Partial Differential Space} + +<<category PDSPC PartialDifferentialSpace>>= +)abbrev category PDSPC PartialDifferentialSpace +++ Author: Gabriel Dos Reis +++ Date Created: June 16, 2010 +++ Date Last Modified: June 16, 2010 +++ Description: +++ This category captures the interface of domains stable by partial +++ differentiation with respect to variables from some domain. +++ See Also: +++ PartialDifferentialDomain +PartialDifferentialSpace(S: SetCategory): Category == + PartialDifferentialDomain(%,S) with + differentiate: (%,List S) -> % + ++ \spad{differentiate(x,[s1,...sn])} computes successive + ++ partial derivatives, i.e. + ++ \spad{differentiate(...differentiate(x, s1)..., sn)}. + differentiate: (%,S,NonNegativeInteger) -> % + ++ \spad{differentiate(x,s,n)} computes multiple partial + ++ derivatives, i.e. \spad{n}-th derivative of \spad{x} + ++ with respect to \spad{s}. + differentiate: (%,List S,List NonNegativeInteger) -> % + ++ \spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes + ++ multiple partial derivatives, i.e. + D: (%,List S) -> % + ++ \spad{D(x,[s1,...sn])} is a shorthand for + ++ \spad{differentiate(x,[s1,...sn])}. + D: (%,S,NonNegativeInteger) -> % + ++ \spad{D(x,s,n)} is a shorthand for \spad{differentiate(x,s,n)}. + D: (%,List S,List NonNegativeInteger) -> % + ++ \spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for + ++ \spad{differentiate(x,[s1,...,sn],[n1,...,nn])}. + add + differentiate(r: %,l: List S) == + for s in l repeat r := differentiate(r, s) + r + + differentiate(r: %,s: S,n: NonNegativeInteger) == + for i in 1..n repeat r := differentiate(r, s) + r + + differentiate(r: %,ls: List S,ln: List NonNegativeInteger) == + for s in ls for n in ln repeat r := differentiate(r, s, n) + r + + D(r: %,v: S) == + differentiate(r,v) + + D(r: %,lv: List S) == + differentiate(r,lv) + D(r: %,v: S,n: NonNegativeInteger) == + differentiate(r,v,n) + D(r: %,lv: List S,ln: List NonNegativeInteger) == + differentiate(r, lv, ln) + +@ + + \section{category PDRING PartialDifferentialRing} <<category PDRING PartialDifferentialRing>>= @@ -1463,49 +1522,8 @@ PartialDifferentialDomain(T: Type, S: Type): Category == Type with ++ \spad{differentiate(x+y,e) = differentiate(x,e)+differentiate(y,e)} ++ \spad{differentiate(x*y,e) = x*differentiate(y,e) + differentiate(x,e)*y} -PartialDifferentialRing(S:SetCategory): Category == Ring with - differentiate: (%, S) -> % - ++ differentiate(x,v) computes the partial derivative of x - ++ with respect to v. - differentiate: (%, List S) -> % - ++ differentiate(x,[s1,...sn]) computes successive partial derivatives, - ++ i.e. \spad{differentiate(...differentiate(x, s1)..., sn)}. - differentiate: (%, S, NonNegativeInteger) -> % - ++ differentiate(x, s, n) computes multiple partial derivatives, i.e. - ++ n-th derivative of x with respect to s. - differentiate: (%, List S, List NonNegativeInteger) -> % - ++ differentiate(x, [s1,...,sn], [n1,...,nn]) computes - ++ multiple partial derivatives, i.e. - D: (%, S) -> % - ++ D(x,v) computes the partial derivative of x - ++ with respect to v. - D: (%, List S) -> % - ++ D(x,[s1,...sn]) computes successive partial derivatives, - ++ i.e. \spad{D(...D(x, s1)..., sn)}. - D: (%, S, NonNegativeInteger) -> % - ++ D(x, s, n) computes multiple partial derivatives, i.e. - ++ n-th derivative of x with respect to s. - D: (%, List S, List NonNegativeInteger) -> % - ++ D(x, [s1,...,sn], [n1,...,nn]) computes - ++ multiple partial derivatives, i.e. - ++ \spad{D(...D(x, s1, n1)..., sn, nn)}. - add - differentiate(r:%, l:List S) == - for s in l repeat r := differentiate(r, s) - r - - differentiate(r:%, s:S, n:NonNegativeInteger) == - for i in 1..n repeat r := differentiate(r, s) - r - - differentiate(r:%, ls:List S, ln:List NonNegativeInteger) == - for s in ls for n in ln repeat r := differentiate(r, s, n) - r - - D(r:%, v:S) == differentiate(r,v) - D(r:%, lv:List S) == differentiate(r,lv) - D(r:%, v:S, n:NonNegativeInteger) == differentiate(r,v,n) - D(r:%, lv:List S, ln:List NonNegativeInteger) == differentiate(r, lv, ln) +PartialDifferentialRing(S:SetCategory): Category == + Join(Ring,PartialDifferentialSpace S) @ \section{category PFECAT PolynomialFactorizationExplicit} @@ -1966,9 +1984,11 @@ VectorSpace(S:Field): Category == Module(S) with <<category DIFRING DifferentialRing>> <<category DIFFMOD DifferentialModule>> <<category PDDOM PartialDifferentialDomain>> +<<category PDSPC PartialDifferentialSpace>> <<category PDRING PartialDifferentialRing>> <<category DIFEXT DifferentialExtension>> @ + \eject \begin{thebibliography}{99} \bibitem{1} nothing diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index cb342eef..7d7b97b7 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2266091 . 3485733144) +(2266740 . 3485743640) (-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."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4455 . T) (-4453 . T) (-4452 . T) ((-4460 "*") . T) (-4451 . T) (-4456 . T) (-4450 . T)) +((-4456 . T) (-4454 . T) (-4453 . T) ((-4461 "*") . T) (-4452 . T) (-4457 . T) (-4451 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1395) +(-32 R -1396) ((|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 -1053) (QUOTE (-574))))) +((|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (-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 -4458))) +((|HasAttribute| |#1| (QUOTE -4459))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . 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 -1395 UP UPUP -2078) +(-40 -1396 UP UPUP -1510) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4451 |has| (-417 |#2|) (-372)) (-4456 |has| (-417 |#2|) (-372)) (-4450 |has| (-417 |#2|) (-372)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2832 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2832 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2832 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2832 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) -(-41 R -1395) +((-4452 |has| (-417 |#2|) (-372)) (-4457 |has| (-417 |#2|) (-372)) (-4451 |has| (-417 |#2|) (-372)) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2833 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2833 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2833 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (-2833 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2833 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) +(-41 R -1396) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -440) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -440) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-315)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4455 |has| |#1| (-566)) (-4453 . T) (-4452 . T)) +((-4456 |has| |#1| (-566)) (-4454 . T) (-4453 . T)) ((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-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."))) -((-4458 . T) (-4459 . T)) -((-2832 (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|))))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|))))))) +((-4459 . T) (-4460 . T)) +((-2833 (-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|))))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| $ (QUOTE (-1064))) (|HasCategory| $ (LIST (QUOTE -1053) (QUOTE (-574))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| $ (QUOTE (-1065))) (|HasCategory| $ (LIST (QUOTE -1054) (QUOTE (-574))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4455 . T)) +((-4456 . 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 -1395) +(-54 |Base| R -1396) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) -(-61 -2040) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-61 -2039) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2040) +(-62 -2039) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2040) +(-63 -2039) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2040) +(-64 -2039) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2040) +(-65 -2039) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -2040) +(-66 -2039) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -2040) +(-67 -2039) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2040) +(-68 -2039) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -2040) +(-69 -2039) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -2040) +(-70 -2039) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -2040) +(-71 -2039) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -2040) +(-72 -2039) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -2040) +(-73 -2039) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -2040) +(-74 -2039) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2040) +(-77 -2039) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2040) +(-78 -2039) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2040) +(-79 -2039) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2040) +(-80 -2039) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2040) +(-81 -2039) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -2040) +(-82 -2039) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2040) +(-83 -2039) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2040) +(-84 -2039) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2040) +(-85 -2039) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2040) +(-86 -2039) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2040) +(-87 -2039) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2040) +(-88 -2039) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2040) +(-89 -2039) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-372)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4458 . T)) +((-4459 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4458 . T) ((-4460 "*") . T) (-4459 . T) (-4455 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4456 . T) (-4450 . T) (-4449 . T) (-4448 . T) (-4447 . T) (-4446 . T) (-4454 . T) (-4457 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4445 . T)) +((-4459 . T) ((-4461 "*") . T) (-4460 . T) (-4456 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4457 . T) (-4451 . T) (-4450 . T) (-4449 . T) (-4448 . T) (-4447 . T) (-4455 . T) (-4458 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4446 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4455 . T)) +((-4456 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4460 "*")))) +((|HasAttribute| |#1| (QUOTE (-4461 "*")))) (-105) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4458 . T)) +((-4459 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4459 . T)) +((-4460 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-574) (QUOTE (-922))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1037))) (|HasCategory| (-574) (QUOTE (-830))) (-2832 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1167))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1192)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (|HasCategory| (-574) (QUOTE (-146))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-574) (QUOTE (-923))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1038))) (|HasCategory| (-574) (QUOTE (-830))) (-2833 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1168))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1193)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (|HasCategory| (-574) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1115))) (|HasCategory| (-112) (LIST (QUOTE -317) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-112) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-112) (QUOTE (-1115))) (|HasCategory| (-112) (LIST (QUOTE -623) (QUOTE (-872))))) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1116))) (|HasCategory| (-112) (LIST (QUOTE -317) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-112) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-112) (QUOTE (-1116))) (|HasCategory| (-112) (LIST (QUOTE -623) (QUOTE (-872))))) (-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}"))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -1395 UP) +(-116 -1396 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 (-117 |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}."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-118 |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}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-922))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-117 |#1|) (QUOTE (-1037))) (|HasCategory| (-117 |#1|) (QUOTE (-830))) (-2832 (|HasCategory| (-117 |#1|) (QUOTE (-830))) (|HasCategory| (-117 |#1|) (QUOTE (-860)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (QUOTE (-1167))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -524) (QUOTE (-1192)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -317) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -294) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-315))) (|HasCategory| (-117 |#1|) (QUOTE (-555))) (|HasCategory| (-117 |#1|) (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-922)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-923))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-117 |#1|) (QUOTE (-1038))) (|HasCategory| (-117 |#1|) (QUOTE (-830))) (-2833 (|HasCategory| (-117 |#1|) (QUOTE (-830))) (|HasCategory| (-117 |#1|) (QUOTE (-860)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (QUOTE (-1168))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -524) (QUOTE (-1193)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -317) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -294) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-315))) (|HasCategory| (-117 |#1|) (QUOTE (-555))) (|HasCategory| (-117 |#1|) (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-923)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4459))) +((|HasAttribute| |#1| (QUOTE -4460))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -418,15 +418,15 @@ NIL NIL (-122 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"))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-128 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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1115))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130)))))) (-2832 (-12 (|HasCategory| (-130) (QUOTE (-1115))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1115)))) (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1115))) (|HasCategory| (-130) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-130) (QUOTE (-1115))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130)))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1116))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130)))))) (-2833 (-12 (|HasCategory| (-130) (QUOTE (-1116))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1116)))) (|HasCategory| (-130) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-130) (QUOTE (-1116))) (|HasCategory| (-130) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-130) (QUOTE (-1116))) (|HasCategory| (-130) (LIST (QUOTE -317) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -470,13 +470,13 @@ NIL NIL (-135) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4460 "*") . T)) +(((-4461 "*") . T)) NIL -(-136 |minix| -4105 S T$) +(-136 |minix| -4106 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -4105 R) +(-137 |minix| -4106 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -498,8 +498,8 @@ NIL NIL (-142) ((|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}."))) -((-4458 . T) (-4448 . T) (-4459 . T)) -((-2832 (-12 (|HasCategory| (-145) (QUOTE (-377))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-145) (QUOTE (-377))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) +((-4459 . T) (-4449 . T) (-4460 . T)) +((-2833 (-12 (|HasCategory| (-145) (QUOTE (-377))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-145) (QUOTE (-377))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -514,7 +514,7 @@ NIL NIL (-146) ((|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."))) -((-4455 . T)) +((-4456 . T)) NIL (-147 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}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4455 . T)) +((-4456 . T)) NIL -(-149 -1395 UP UPUP) +(-149 -1396 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 @@ -535,14 +535,14 @@ NIL (-151 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 -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasAttribute| |#1| (QUOTE -4458))) +((|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasAttribute| |#1| (QUOTE -4459))) (-152 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-153 |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."))) -((-4453 . T) (-4452 . T) (-4455 . T)) +((-4454 . T) (-4453 . T) (-4456 . T)) NIL (-154) ((|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."))) @@ -564,7 +564,7 @@ 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 -(-159 R -1395) +(-159 R -1396) ((|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 @@ -595,10 +595,10 @@ NIL (-166 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 (-922))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1218))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (QUOTE (-1037))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4454)) (|HasAttribute| |#2| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-566)))) +((|HasCategory| |#2| (QUOTE (-923))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1219))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-1038))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4455)) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-566)))) (-167 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})"))) -((-4451 -2832 (|has| |#1| (-566)) (-12 (|has| |#1| (-315)) (|has| |#1| (-922)))) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4454 |has| |#1| (-6 -4454)) (-4457 |has| |#1| (-6 -4457)) (-3535 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 -2833 (|has| |#1| (-566)) (-12 (|has| |#1| (-315)) (|has| |#1| (-923)))) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4455 |has| |#1| (-6 -4455)) (-4458 |has| |#1| (-6 -4458)) (-3536 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-168 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."))) @@ -614,8 +614,8 @@ NIL NIL (-171 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}."))) -((-4451 -2832 (|has| |#1| (-566)) (-12 (|has| |#1| (-315)) (|has| |#1| (-922)))) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4454 |has| |#1| (-6 -4454)) (-4457 |has| |#1| (-6 -4457)) (-3535 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-377)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1037)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-1218)))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| 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T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-2833 (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-358)))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| 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(QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-1076))) (-12 (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-1219)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-923))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-372)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasAttribute| |#1| (QUOTE -4455)) (|HasAttribute| |#1| (QUOTE -4458)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193))))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-358))))) (-172 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 @@ -626,7 +626,7 @@ NIL NIL (-174) ((|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."))) -(((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4460 "*") . T) (-4451 . T) (-4456 . T) (-4450 . T) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") . T) (-4452 . T) (-4457 . T) (-4451 . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-177) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -651,7 +651,7 @@ NIL (-180 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| (-965 |#2|) (LIST (QUOTE -897) (|devaluate| |#1|)))) +((|HasCategory| (-966 |#2|) (LIST (QUOTE -897) (|devaluate| |#1|)))) (-181 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 @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1395) +(-190 R -1396) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -1395 UP UPUP R) +(-217 -1396 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 -(-218 -1395 FP) +(-218 -1396 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 (-219) ((|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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-574) (QUOTE (-922))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1037))) (|HasCategory| (-574) (QUOTE (-830))) (-2832 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1167))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1192)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (|HasCategory| (-574) (QUOTE (-146))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-574) (QUOTE (-923))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1038))) (|HasCategory| (-574) (QUOTE (-830))) (-2833 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1168))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1193)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (|HasCategory| (-574) (QUOTE (-146))))) (-220) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -1395) +(-221 R -1396) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -826,19 +826,19 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-225 |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}."))) -((-4455 . T)) +((-4456 . T)) NIL -(-226 R -1395) +(-226 R -1396) ((|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 (-227) ((|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}."))) -((-3524 . T) (-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-3525 . T) (-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -846,23 +846,23 @@ NIL NIL (-229 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}"))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4460 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4461 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-230 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 (-231 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."))) -((-4459 . T)) +((-4460 . T)) NIL (-232 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 -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239)))) +((|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239)))) (-233 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}."))) -((-4455 . T)) +((-4456 . T)) NIL (-234 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -874,7 +874,7 @@ NIL NIL (-236 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL (-237 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -886,36 +886,36 @@ NIL NIL (-239) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4455 . T)) +((-4456 . T)) NIL (-240 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 -4458))) +((|HasAttribute| |#1| (QUOTE -4459))) (-241 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}."))) -((-4459 . T)) +((-4460 . T)) NIL (-242) ((|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 -(-243 S -4105 R) +(-243 S -4106 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-860))) (|HasAttribute| |#3| (QUOTE -4455)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1064))) (|HasCategory| |#3| (QUOTE (-1115)))) -(-244 -4105 R) +((|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (QUOTE (-860))) (|HasAttribute| |#3| (QUOTE -4456)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (QUOTE (-1116)))) +(-244 -4106 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4452 |has| |#2| (-1064)) (-4453 |has| |#2| (-1064)) (-4455 |has| |#2| (-6 -4455)) ((-4460 "*") |has| |#2| (-174)) (-4458 . T)) +((-4453 |has| |#2| (-1065)) (-4454 |has| |#2| (-1065)) (-4456 |has| |#2| (-6 -4456)) ((-4461 "*") |has| |#2| (-174)) (-4459 . T)) NIL -(-245 -4105 A B) +(-245 -4106 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 -(-246 -4105 R) +(-246 -4106 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."))) -((-4452 |has| |#2| (-1064)) (-4453 |has| |#2| (-1064)) (-4455 |has| |#2| (-6 -4455)) ((-4460 "*") |has| |#2| (-174)) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))))) (-2832 (-12 (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1115)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1064)))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-372))) (-2832 (|HasCategory| |#2| (QUOTE 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") 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NIL @@ -926,7 +926,7 @@ NIL NIL (-249) ((|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}."))) -((-4451 . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-250 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."))) @@ -934,16 +934,16 @@ NIL NIL (-251 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}"))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-252 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 (-253 |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"))) -(((-4460 "*") |has| |#2| (-174)) (-4451 |has| |#2| (-566)) (-4456 |has| |#2| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-922))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4461 "*") |has| |#2| (-174)) (-4452 |has| |#2| (-566)) (-4457 |has| |#2| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-923))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-146))))) (-254) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -958,23 +958,23 @@ NIL NIL (-257 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4455 -2832 (-2096 (|has| |#4| (-1064)) (|has| |#4| (-239))) (|has| |#4| (-6 -4455)) (-2096 (|has| |#4| (-1064)) (|has| |#4| (-913 (-1192))))) (-4452 |has| |#4| (-1064)) (-4453 |has| |#4| (-1064)) ((-4460 "*") |has| |#4| (-174)) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#4| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-239))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-736))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-803))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-860))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1064))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|))) 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(-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-860))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1065))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574)))))) (-2833 (-12 (|HasCategory| |#3| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-736))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-803))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-860))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -912) (QUOTE (-1193))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1065)))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-2833 (|HasCategory| |#3| (QUOTE (-1065))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1116)))) (-2833 (|HasAttribute| |#3| (QUOTE -4456)) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1065)))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -912) (QUOTE (-1193)))))) (|HasCategory| |#3| (QUOTE (-860))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) (-259 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 (-239)))) (-260 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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL (-261 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}."))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL (-262) ((|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."))) @@ -1014,8 +1014,8 @@ NIL NIL (-271 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"))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-922))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#3| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#3| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#3| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#3| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) (-272 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1060,11 +1060,11 @@ 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 -(-283 R -1395) +(-283 R -1396) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-284 R -1395) +(-284 R -1396) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1087,10 +1087,10 @@ NIL (-289 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 (-860))) (|HasCategory| |#2| (QUOTE (-1115)))) +((|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116)))) (-290 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}."))) -((-4459 . T)) +((-4460 . T)) NIL (-291 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}."))) @@ -1111,18 +1111,18 @@ NIL (-295 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 -4459))) +((|HasAttribute| |#1| (QUOTE -4460))) (-296 |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 -(-297 S R |Mod| -2432 -4297 |exactQuo|) +(-297 S R |Mod| -3607 -3404 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-298) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4451 . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-299) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1138,21 +1138,21 @@ NIL NIL (-302 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."))) -((-4455 -2832 (|has| |#1| (-1064)) (|has| |#1| (-483))) (-4452 |has| |#1| (-1064)) (-4453 |has| |#1| (-1064))) -((|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1064)))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-1064)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1064)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1064)))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1064)))) (-2832 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736)))) (|HasCategory| |#1| (QUOTE (-483))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-1115)))) (-2832 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1127)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-310))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-483)))) (-2832 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736)))) (-2832 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-1064)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-736)))) +((-4456 -2833 (|has| |#1| (-1065)) (|has| |#1| (-483))) (-4453 |has| |#1| (-1065)) (-4454 |has| |#1| (-1065))) +((|HasCategory| |#1| (QUOTE (-372))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1065)))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-1065)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1065)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1065)))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1065)))) (-2833 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736)))) (|HasCategory| |#1| (QUOTE (-483))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-1128))) (|HasCategory| |#1| (QUOTE (-1116)))) (-2833 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1128)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-310))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-483)))) (-2833 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736)))) (-2833 (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-1065)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1128))) (|HasCategory| |#1| (QUOTE (-736)))) (-303 |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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) (-304) ((|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 -(-305 -1395 S) +(-305 -1396 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 -(-306 E -1395) +(-306 E -1396) ((|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 @@ -1167,7 +1167,7 @@ NIL (-309 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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\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 -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-1064)))) +((|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-1065)))) (-310) ((|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\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 @@ -1190,7 +1190,7 @@ NIL NIL (-315) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-316 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1200,7 +1200,7 @@ 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 -(-318 -1395) +(-318 -1396) ((|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 @@ -1214,8 +1214,8 @@ NIL NIL (-321 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))}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-922))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-1037))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-830))) (-2832 (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-830))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-860)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-1167))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -524) (QUOTE (-1192)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -317) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (LIST (QUOTE -294) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1269) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-315))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-555))) (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-860))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-922))) (|HasCategory| $ (QUOTE (-146)))) (-2832 (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1269 |#1| |#2| |#3| |#4|) (QUOTE (-922))) (|HasCategory| $ (QUOTE (-146)))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-923))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-1038))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-830))) (-2833 (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-830))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-860)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-1168))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -524) (QUOTE (-1193)) (LIST (QUOTE -1270) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -317) (LIST (QUOTE -1270) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (LIST (QUOTE -294) (LIST (QUOTE -1270) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1270) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-315))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-555))) (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-860))) (-12 (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-923))) (|HasCategory| $ (QUOTE (-146)))) (-2833 (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1270 |#1| |#2| |#3| |#4|) (QUOTE (-923))) (|HasCategory| $ (QUOTE (-146)))))) (-322 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 @@ -1226,9 +1226,9 @@ NIL NIL (-324 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."))) -((-4455 -2832 (-12 (|has| |#1| (-566)) (-2832 (|has| |#1| (-1064)) (|has| |#1| (-483)))) (|has| |#1| (-1064)) (|has| |#1| (-483))) (-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) ((-4460 "*") |has| |#1| (-566)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-566)) (-4450 |has| |#1| (-566))) -((-2832 (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-1064)))) (|HasCategory| |#1| (QUOTE (-21))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1064)))) (|HasCategory| |#1| (QUOTE (-1064))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (LIST (QUOTE -649) 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(|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1238,8 +1238,8 @@ NIL NIL (-327 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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . 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(|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 @@ -1250,7 +1250,7 @@ NIL NIL (-330 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) ((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-802)))) (-331 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1266,19 +1266,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174)))) (-334 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-335 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."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) -(-336 S -1395) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +(-336 S -1396) ((|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 (-377)))) -(-337 -1395) +(-337 -1396) ((|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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-338) ((|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."))) @@ -1300,54 +1300,54 @@ 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 -(-343 S -1395 UP UPUP R) +(-343 S -1396 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 -(-344 -1395 UP UPUP R) +(-344 -1396 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 -(-345 -1395 UP UPUP R) +(-345 -1396 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-346 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|)))) (-347 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-348 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{pi(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -1053) (QUOTE (-388)))) (|HasCategory| $ (QUOTE (-1064))) (|HasCategory| $ (LIST (QUOTE -1053) (QUOTE (-574))))) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-388)))) (|HasCategory| $ (QUOTE (-1065))) (|HasCategory| $ (LIST (QUOTE -1054) (QUOTE (-574))))) (-349 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 -(-350 S -1395 UP UPUP) +(-350 S -1396 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-372)))) -(-351 -1395 UP UPUP) +(-351 -1396 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4451 |has| (-417 |#2|) (-372)) (-4456 |has| (-417 |#2|) (-372)) (-4450 |has| (-417 |#2|) (-372)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 |has| (-417 |#2|) (-372)) (-4457 |has| (-417 |#2|) (-372)) (-4451 |has| (-417 |#2|) (-372)) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-352 |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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| (-923 |#1|) (QUOTE (-146))) (|HasCategory| (-923 |#1|) (QUOTE (-377)))) (|HasCategory| (-923 |#1|) (QUOTE (-148))) (|HasCategory| (-923 |#1|) (QUOTE (-377))) (|HasCategory| (-923 |#1|) (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| (-924 |#1|) (QUOTE (-146))) (|HasCategory| (-924 |#1|) (QUOTE (-377)))) (|HasCategory| (-924 |#1|) (QUOTE (-148))) (|HasCategory| (-924 |#1|) (QUOTE (-377))) (|HasCategory| (-924 |#1|) (QUOTE (-146)))) (-353 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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) (-354 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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) (-355 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 @@ -1362,33 +1362,33 @@ NIL NIL (-358) ((|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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-359 R UP -1395) +(-359 R UP -1396) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-360 |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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| (-923 |#1|) (QUOTE (-146))) (|HasCategory| (-923 |#1|) (QUOTE (-377)))) (|HasCategory| (-923 |#1|) (QUOTE (-148))) (|HasCategory| (-923 |#1|) (QUOTE (-377))) (|HasCategory| (-923 |#1|) (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| (-924 |#1|) (QUOTE (-146))) (|HasCategory| (-924 |#1|) (QUOTE (-377)))) (|HasCategory| (-924 |#1|) (QUOTE (-148))) (|HasCategory| (-924 |#1|) (QUOTE (-377))) (|HasCategory| (-924 |#1|) (QUOTE (-146)))) (-361 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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) (-362 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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) (-363 |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}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| (-923 |#1|) (QUOTE (-146))) (|HasCategory| (-923 |#1|) (QUOTE (-377)))) (|HasCategory| (-923 |#1|) (QUOTE (-148))) (|HasCategory| (-923 |#1|) (QUOTE (-377))) (|HasCategory| (-923 |#1|) (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| (-924 |#1|) (QUOTE (-146))) (|HasCategory| (-924 |#1|) (QUOTE (-377)))) (|HasCategory| (-924 |#1|) (QUOTE (-148))) (|HasCategory| (-924 |#1|) (QUOTE (-377))) (|HasCategory| (-924 |#1|) (QUOTE (-146)))) (-364 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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) -(-365 -1395 GF) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) +(-365 -1396 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 @@ -1396,21 +1396,21 @@ 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 -(-367 -1395 FP FPP) +(-367 -1396 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-368 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}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-146)))) (-369 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 (-370 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4455 . T)) +((-4456 . T)) NIL (-371 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1418,7 +1418,7 @@ NIL NIL (-372) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-373 |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."))) @@ -1434,7 +1434,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-566)))) (-376 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4455 |has| |#1| (-566)) (-4453 . T) (-4452 . T)) +((-4456 |has| |#1| (-566)) (-4454 . T) (-4453 . T)) NIL (-377) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1446,7 +1446,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-372)))) (-379 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL (-380 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1455,14 +1455,14 @@ NIL (-381 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4459)) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115)))) +((|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116)))) (-382 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4458 . T)) +((-4459 . T)) NIL (-383 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4453 . T) (-4452 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4454 . T) (-4453 . T)) NIL (-384 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."))) @@ -1482,7 +1482,7 @@ NIL NIL (-388) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4441 . T) (-4449 . T) (-3524 . T) (-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4442 . T) (-4450 . T) (-3525 . T) (-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-389 |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}."))) @@ -1490,11 +1490,11 @@ NIL NIL (-390 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}"))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-391 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}."))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL (-392) ((|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}."))) @@ -1506,7 +1506,7 @@ NIL NIL (-394 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."))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-395 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1518,7 +1518,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-860)))) (-397) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-398) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1530,13 +1530,13 @@ NIL NIL (-400 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL (-401) ((|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 -(-402 -1395 UP UPUP R) +(-402 -1396 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 @@ -1560,11 +1560,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-408 -2040 |returnType| -1573 |symbols|) +(-408 -2039 |returnType| -1572 |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 -(-409 -1395 UP) +(-409 -1396 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1578,15 +1578,15 @@ NIL NIL (-412) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-413 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4441)) (|HasAttribute| |#1| (QUOTE -4449))) +((|HasAttribute| |#1| (QUOTE -4442)) (|HasAttribute| |#1| (QUOTE -4450))) (-414) ((|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\"."))) -((-3524 . T) (-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-3525 . T) (-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-415 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."))) @@ -1598,20 +1598,20 @@ NIL NIL (-417 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."))) -((-4445 -12 (|has| |#1| (-6 -4456)) (|has| |#1| (-462)) (|has| |#1| (-6 -4445))) (-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-922))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-1037))) (|HasCategory| |#1| (QUOTE (-830))) (-2832 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-860)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838))))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-555))) (-12 (|HasAttribute| |#1| (QUOTE -4456)) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-462)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4446 -12 (|has| |#1| (-6 -4457)) (|has| |#1| (-462)) (|has| |#1| (-6 -4446))) (-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (QUOTE (-1038))) (|HasCategory| |#1| (QUOTE (-830))) (-2833 (|HasCategory| |#1| (QUOTE (-830))) (|HasCategory| |#1| (QUOTE (-860)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-1168))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838))))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-555))) (-12 (|HasAttribute| |#1| (QUOTE -4457)) (|HasAttribute| |#1| (QUOTE -4446)) (|HasCategory| |#1| (QUOTE (-462)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) (-418 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-419 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL (-420 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 -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) +((|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-421 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 @@ -1620,14 +1620,14 @@ 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 -(-423 R -1395 UP A) +(-423 R -1396 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)}."))) -((-4455 . T)) +((-4456 . T)) NIL -(-424 R -1395 UP A |ibasis|) +(-424 R -1396 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1053) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1054) (|devaluate| |#2|)))) (-425 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1638,12 +1638,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-372)))) (-427 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4455 |has| |#1| (-566)) (-4453 . T) (-4452 . T)) +((-4456 |has| |#1| (-566)) (-4454 . T) (-4453 . T)) NIL (-428 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."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -317) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -294) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1237))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-1237)))) (|HasCategory| |#1| (QUOTE (-1037))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -294) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-462)))) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -317) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -294) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1238))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-1238)))) (|HasCategory| |#1| (QUOTE (-1038))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -294) (QUOTE $) (QUOTE $)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-462)))) (-429 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 @@ -1670,37 +1670,37 @@ NIL ((|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-377)))) (-435 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4458 . T) (-4448 . T) (-4459 . T)) +((-4459 . T) (-4449 . T) (-4460 . T)) NIL -(-436 R -1395) +(-436 R -1396) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-437 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4445 -12 (|has| |#1| (-6 -4445)) (|has| |#2| (-6 -4445))) (-4452 . T) (-4453 . T) (-4455 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#2| (QUOTE -4445)))) -(-438 R -1395) +((-4446 -12 (|has| |#1| (-6 -4446)) (|has| |#2| (-6 -4446))) (-4453 . T) (-4454 . T) (-4456 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4446)) (|HasAttribute| |#2| (QUOTE -4446)))) +(-438 R -1396) ((|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 (-439 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#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 -1053) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-1127))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) +((|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-1128))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (-440 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4455 -2832 (|has| |#1| (-1064)) (|has| |#1| (-483))) (-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) ((-4460 "*") |has| |#1| (-566)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-566)) (-4450 |has| |#1| (-566))) +((-4456 -2833 (|has| |#1| (-1065)) (|has| |#1| (-483))) (-4454 |has| |#1| (-174)) (-4453 |has| |#1| (-174)) ((-4461 "*") |has| |#1| (-566)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-566)) (-4451 |has| |#1| (-566))) NIL -(-441 R -1395) +(-441 R -1396) ((|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 -(-442 R -1395) +(-442 R -1396) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-443 R -1395) +(-443 R -1396) ((|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 @@ -1708,10 +1708,10 @@ 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 -(-445 R -1395 UP) +(-445 R -1396 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 -1053) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-48))))) (-446) ((|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 @@ -1740,7 +1740,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-453 R UP -1395) +(-453 R UP -1396) ((|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 @@ -1778,16 +1778,16 @@ NIL NIL (-462) ((|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}."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-463 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"))) -((-4455 |has| (-417 (-965 |#1|)) (-566)) (-4453 . T) (-4452 . T)) -((|HasCategory| (-417 (-965 |#1|)) (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| (-417 (-965 |#1|)) (QUOTE (-566)))) +((-4456 |has| (-417 (-966 |#1|)) (-566)) (-4454 . T) (-4453 . T)) +((|HasCategory| (-417 (-966 |#1|)) (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| (-417 (-966 |#1|)) (QUOTE (-566)))) (-464 |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"))) -(((-4460 "*") |has| |#2| (-174)) (-4451 |has| |#2| (-566)) (-4456 |has| |#2| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-922))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4461 "*") |has| |#2| (-174)) (-4452 |has| |#2| (-566)) (-4457 |has| |#2| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-923))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-146))))) (-465 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 @@ -1814,7 +1814,7 @@ NIL NIL (-471 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL (-472 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1822,8 +1822,8 @@ NIL NIL (-473 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) (-474 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 @@ -1852,7 +1852,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-481 |lv| -1395 R) +(-481 |lv| -1396 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1862,23 +1862,23 @@ NIL NIL (-483) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4455 . T)) +((-4456 . T)) NIL (-484 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -1578) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1128))) (|HasCategory| |#1| (QUOTE (-372))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2951) (LIST (|devaluate| |#1|) (QUOTE (-1193)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2833 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1219))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3342) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1193))))) (|HasSignature| |#1| (LIST (QUOTE -4350) (LIST (LIST (QUOTE -654) (QUOTE (-1193))) (|devaluate| |#1|))))))) (-485 |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."))) -((-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115)))) +((-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116)))) (-486 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)}"))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) (-487) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-488) ((|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'."))) @@ -1886,29 +1886,29 @@ NIL NIL (-489 |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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) (-490) ((|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 (-491 |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"))) -(((-4460 "*") |has| |#2| (-174)) (-4451 |has| |#2| (-566)) (-4456 |has| |#2| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . 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(-12 (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-803))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE 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(-803))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1065)))) (-12 (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193))))) (-2833 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-736)))) (-2833 (|HasCategory| |#2| (QUOTE (-1065))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-1116)))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))))) (-493) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\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| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-494 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}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) -(-495 -1395 UP UPUP R) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-495 -1396 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 @@ -1918,12 +1918,12 @@ NIL NIL (-497) ((|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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-574) (QUOTE (-922))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1037))) (|HasCategory| (-574) (QUOTE (-830))) (-2832 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1167))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1192)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (|HasCategory| (-574) (QUOTE (-146))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-574) (QUOTE (-923))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1038))) (|HasCategory| (-574) (QUOTE (-830))) (-2833 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1168))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1193)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (|HasCategory| (-574) (QUOTE (-146))))) (-498 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 -4458)) (|HasAttribute| |#1| (QUOTE -4459)) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) +((|HasAttribute| |#1| (QUOTE -4459)) (|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (-499 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1944,34 +1944,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-504 -1395 UP |AlExt| |AlPol|) +(-504 -1396 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-505) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| $ (QUOTE (-1064))) (|HasCategory| $ (LIST (QUOTE -1053) (QUOTE (-574))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| $ (QUOTE (-1065))) (|HasCategory| $ (LIST (QUOTE -1054) (QUOTE (-574))))) (-506 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-507 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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-508 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 -(-509 R UP -1395) +(-509 R UP -1396) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-510 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1115))) (|HasCategory| (-112) (LIST (QUOTE -317) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-112) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-112) (QUOTE (-1115))) (|HasCategory| (-112) (LIST (QUOTE -623) (QUOTE (-872))))) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1116))) (|HasCategory| (-112) (LIST (QUOTE -317) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-112) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-112) (QUOTE (-1116))) (|HasCategory| (-112) (LIST (QUOTE -623) (QUOTE (-872))))) (-511 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 @@ -1984,10 +1984,10 @@ 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{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-514 -1395 |Expon| |VarSet| |DPoly|) +(-514 -1396 |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 -624) (QUOTE (-1192))))) +((|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-1193))))) (-515 |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 @@ -2034,36 +2034,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-802)))) (-526 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}"))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-527) ((|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 (-528 |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}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| (-591 |#1|) (QUOTE (-146))) (|HasCategory| (-591 |#1|) (QUOTE (-377)))) (|HasCategory| (-591 |#1|) (QUOTE (-148))) (|HasCategory| (-591 |#1|) (QUOTE (-377))) (|HasCategory| (-591 |#1|) (QUOTE (-146)))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((-2833 (|HasCategory| (-591 |#1|) (QUOTE (-146))) (|HasCategory| (-591 |#1|) (QUOTE (-377)))) (|HasCategory| (-591 |#1|) (QUOTE (-148))) (|HasCategory| (-591 |#1|) (QUOTE (-377))) (|HasCategory| (-591 |#1|) (QUOTE (-146)))) (-529 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}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-530 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."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-531 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 -4459))) +((|HasAttribute| |#3| (QUOTE -4460))) (-532 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 -4459))) +((|HasAttribute| |#7| (QUOTE -4460))) (-533 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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4460 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4461 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-534) ((|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 @@ -2096,7 +2096,7 @@ 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 -(-542 K -1395 |Par|) +(-542 K -1396 |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 @@ -2120,7 +2120,7 @@ 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 -(-548 K -1395 |Par|) +(-548 K -1396 |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 @@ -2150,7 +2150,7 @@ NIL NIL (-555) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4456 . T) (-4457 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4457 . T) (-4458 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-556) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2170,13 +2170,13 @@ NIL NIL (-560 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) -(-561 R -1395) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) +(-561 R -1396) ((|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 -(-562 R0 -1395 UP UPUP R) +(-562 R0 -1396 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 @@ -2186,7 +2186,7 @@ NIL NIL (-564 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."))) -((-3524 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-3525 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-565 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."))) @@ -2194,9 +2194,9 @@ NIL NIL (-566) ((|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."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-567 R -1395) +(-567 R -1396) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2208,7 +2208,7 @@ 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 -(-570 R -1395 L) +(-570 R -1396 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -666) (|devaluate| |#2|)))) @@ -2216,31 +2216,31 @@ 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 -(-572 -1395 UP UPUP R) +(-572 -1396 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 -(-573 -1395 UP) +(-573 -1396 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 (-574) ((|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."))) -((-4440 . T) (-4446 . T) (-4450 . T) (-4445 . T) (-4456 . T) (-4457 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4441 . T) (-4447 . T) (-4451 . T) (-4446 . T) (-4457 . T) (-4458 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-575) ((|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 -(-576 R -1395 L) +(-576 R -1396 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -666) (|devaluate| |#2|)))) -(-577 R -1395) +(-577 R -1396) ((|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 -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1154)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-639))))) -(-578 -1395 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1155)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-639))))) +(-578 -1396 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2248,27 +2248,27 @@ 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 -(-580 -1395) +(-580 -1396) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-581 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."))) -((-3524 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-3525 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-582) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-583 R -1395) +(-583 R -1396) ((|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 -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-292))) (|HasCategory| |#2| (QUOTE (-639))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192))))) (-12 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-292)))) (|HasCategory| |#1| (QUOTE (-566)))) -(-584 -1395 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-292))) (|HasCategory| |#2| (QUOTE (-639))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-1193))))) (-12 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-292)))) (|HasCategory| |#1| (QUOTE (-566)))) +(-584 -1396 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-585 R -1395) +(-585 R -1396) ((|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 @@ -2290,21 +2290,21 @@ NIL NIL (-590 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-591 |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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-377)))) (-592) ((|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 -(-593 R -1395) +(-593 R -1396) ((|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 -(-594 E -1395) +(-594 E -1396) ((|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 @@ -2312,10 +2312,10 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-596 -1395) +(-596 -1396) ((|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}."))) -((-4453 . T) (-4452 . T)) -((|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-1192))))) +((-4454 . T) (-4453 . T)) +((|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-1193))))) (-597 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 @@ -2342,19 +2342,19 @@ NIL NIL (-603 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (-2832 (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1115)))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (-2833 (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1116)))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (-604 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 (-605 |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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|)))) (|HasCategory| (-574) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-574)))))) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|)))) (|HasCategory| (-574) (QUOTE (-1128))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -2951) (LIST (|devaluate| |#1|) (QUOTE (-1193)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-574)))))) (-606 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4460 "*") |has| |#1| (-566)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-566)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-566)))) (-607) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2368,7 +2368,7 @@ 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 -(-610 R -1395 FG) +(-610 R -1396 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2378,12 +2378,12 @@ NIL NIL (-612 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1064))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-1064)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1065))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1065)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-613 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 -4459)) (|HasCategory| |#2| (QUOTE (-860))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#3| (QUOTE (-1115)))) +((|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-860))) (|HasAttribute| |#1| (QUOTE -4459)) (|HasCategory| |#3| (QUOTE (-1116)))) (-614 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2398,19 +2398,19 @@ NIL NIL (-617 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4455 -2832 (-2096 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4453 . T) (-4452 . T)) -((-2832 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) +((-4456 -2833 (-2095 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4454 . T) (-4453 . T)) +((-2833 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-618 |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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| (-1174) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| (-1175) (QUOTE (-860))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) (-619 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 (-620 |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}."))) -((-4459 . T)) +((-4460 . T)) NIL (-621 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"))) @@ -2428,7 +2428,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-625 -1395 UP) +(-625 -1396 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2450,20 +2450,20 @@ NIL NIL (-630 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."))) -((-4455 . T)) +((-4456 . T)) NIL (-631 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}."))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-858)))) -(-632 R -1395) +(-632 R -1396) ((|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 (-633 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"))) -((-4453 . T) (-4452 . T) ((-4460 "*") . T) (-4451 . T) (-4455 . T)) -((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) +((-4454 . T) (-4453 . T) ((-4461 "*") . T) (-4452 . T) (-4456 . T)) +((|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239))) (-2833 (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (-634 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 @@ -2478,7 +2478,7 @@ NIL NIL (-637 |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}}."))) -((-4455 . T)) +((-4456 . T)) NIL (-638 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}}."))) @@ -2488,30 +2488,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-640 R -1395) +(-640 R -1396) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-641 |lv| -1395) +(-641 |lv| -1396) ((|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 (-642) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1917) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1174) (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 (-52))) (QUOTE (-1115)))) +((-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -1916) (QUOTE (-52))))))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-52) (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-1175) (QUOTE (-860))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 (-52))) (QUOTE (-1116)))) (-643 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-372)))) (-644 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4453 . T) (-4452 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4454 . T) (-4453 . T)) NIL (-645 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4455 -2832 (-2096 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4453 . T) (-4452 . T)) -((-2832 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) +((-4456 -2833 (-2095 (|has| |#2| (-376 |#1|)) (|has| |#1| (-566))) (-12 (|has| |#2| (-427 |#1|)) (|has| |#1| (-566)))) (-4454 . T) (-4453 . T)) +((-2833 (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -427) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -376) (|devaluate| |#1|)))) (-646 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 @@ -2523,7 +2523,7 @@ NIL (-648 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 -((-2085 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) +((-2084 (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-372)))) (-649 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{reducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL @@ -2546,8 +2546,8 @@ NIL NIL (-654 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-655 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2558,8 +2558,8 @@ NIL NIL (-657 S) ((|substitute| (($ |#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."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-658 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2571,39 +2571,39 @@ NIL (-660 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4459))) +((|HasAttribute| |#1| (QUOTE -4460))) (-661 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-662 R -1395 L) +(-662 R -1396 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 (-663 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}}"))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) (-664 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) (-665 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-372)))) (-666 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}."))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-667 -1395 UP) +(-667 -1396 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)))) -(-668 A -4129) +(-668 A -2815) ((|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}}"))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) (-669 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 @@ -2618,7 +2618,7 @@ NIL NIL (-672 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}."))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) ((|HasCategory| |#1| (QUOTE (-801)))) (-673 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2626,7 +2626,7 @@ NIL NIL (-674 |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) (-4453 . T) (-4452 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4454 . T) (-4453 . T)) ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-174)))) (-675 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}."))) @@ -2634,13 +2634,13 @@ NIL NIL (-676 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}."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-677 -1395) +(-677 -1396) ((|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 -(-678 -1395 |Row| |Col| M) +(-678 -1396 |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 @@ -2650,8 +2650,8 @@ NIL NIL (-680 |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."))) -((-4455 . T) (-4458 . T) (-4452 . T) (-4453 . T)) -((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4460 "*"))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-566))) (-2832 (|HasAttribute| |#2| (QUOTE (-4460 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4456 . T) (-4459 . T) (-4453 . T) (-4454 . T)) +((|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4461 "*"))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-566))) (-2833 (|HasAttribute| |#2| (QUOTE (-4461 "*"))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-681) ((|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 @@ -2671,7 +2671,7 @@ NIL (-685 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 -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-686) ((|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 @@ -2715,10 +2715,10 @@ NIL (-696 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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 (-4460 "*"))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-566)))) +((|HasAttribute| |#2| (QUOTE (-4461 "*"))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-566)))) (-697 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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"))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL (-698 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."))) @@ -2726,8 +2726,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566)))) (-699 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."))) -((-4458 . T) (-4459 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4460 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +((-4459 . T) (-4460 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-315))) (|HasCategory| |#1| (QUOTE (-566))) (|HasAttribute| |#1| (QUOTE (-4461 "*"))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-700 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 @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-702 S -1395 FLAF FLAS) +(-702 S -1396 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 @@ -2746,11 +2746,11 @@ NIL NIL (-704) ((|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"))) -((-4451 . T) (-4456 |has| (-709) (-372)) (-4450 |has| (-709) (-372)) (-3535 . T) (-4457 |has| (-709) (-6 -4457)) (-4454 |has| (-709) (-6 -4454)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-709) (QUOTE (-148))) (|HasCategory| (-709) (QUOTE (-146))) (|HasCategory| (-709) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-709) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-709) (QUOTE (-377))) (|HasCategory| (-709) (QUOTE (-372))) (-2832 (|HasCategory| (-709) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-709) (QUOTE (-372)))) (|HasCategory| (-709) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-709) (QUOTE (-239))) (-2832 (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-358)))) (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (LIST (QUOTE -294) (QUOTE (-709)) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -317) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -524) (QUOTE (-1192)) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-709) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-709) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-709) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (-2832 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-358)))) (|HasCategory| (-709) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-709) (QUOTE (-1037))) (|HasCategory| (-709) (QUOTE (-1218))) (-12 (|HasCategory| (-709) (QUOTE (-1017))) (|HasCategory| (-709) (QUOTE (-1218)))) (-2832 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (|HasCategory| (-709) (QUOTE (-372))) (-12 (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (QUOTE (-922))))) (-2832 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (-12 (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-922)))) (-12 (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (QUOTE (-922))))) (|HasCategory| (-709) (QUOTE (-555))) (-12 (|HasCategory| (-709) (QUOTE (-1075))) (|HasCategory| (-709) (QUOTE (-1218)))) (|HasCategory| (-709) (QUOTE (-1075))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922))) (-2832 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (|HasCategory| (-709) (QUOTE (-372)))) (-2832 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (|HasCategory| (-709) (QUOTE (-566)))) (-12 (|HasCategory| (-709) (QUOTE (-239))) (|HasCategory| (-709) (QUOTE (-372)))) (-12 (|HasCategory| (-709) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-709) (QUOTE (-372)))) (|HasCategory| (-709) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-709) (QUOTE (-566))) (|HasAttribute| (-709) (QUOTE -4457)) (|HasAttribute| (-709) (QUOTE -4454)) (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (|HasCategory| (-709) (QUOTE (-146)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-922)))) (|HasCategory| (-709) (QUOTE (-358))))) +((-4452 . T) (-4457 |has| (-709) (-372)) (-4451 |has| (-709) (-372)) (-3536 . T) (-4458 |has| (-709) (-6 -4458)) (-4455 |has| (-709) (-6 -4455)) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-709) (QUOTE (-148))) (|HasCategory| (-709) (QUOTE (-146))) (|HasCategory| (-709) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-709) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-709) (QUOTE (-377))) (|HasCategory| (-709) (QUOTE (-372))) (-2833 (|HasCategory| (-709) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-709) (QUOTE (-372)))) (|HasCategory| (-709) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-709) (QUOTE (-239))) (-2833 (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-358)))) (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (LIST (QUOTE -294) (QUOTE (-709)) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -317) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -524) (QUOTE (-1193)) (QUOTE (-709)))) (|HasCategory| (-709) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-709) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-709) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-709) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (-2833 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-358)))) (|HasCategory| (-709) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-709) (QUOTE (-1038))) (|HasCategory| (-709) (QUOTE (-1219))) (-12 (|HasCategory| (-709) (QUOTE (-1018))) (|HasCategory| (-709) (QUOTE (-1219)))) (-2833 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (|HasCategory| (-709) (QUOTE (-372))) (-12 (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (QUOTE (-923))))) (-2833 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (-12 (|HasCategory| (-709) (QUOTE (-372))) (|HasCategory| (-709) (QUOTE (-923)))) (-12 (|HasCategory| (-709) (QUOTE (-358))) (|HasCategory| (-709) (QUOTE (-923))))) (|HasCategory| (-709) (QUOTE (-555))) (-12 (|HasCategory| (-709) (QUOTE (-1076))) (|HasCategory| (-709) (QUOTE (-1219)))) (|HasCategory| (-709) (QUOTE (-1076))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923))) (-2833 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (|HasCategory| (-709) (QUOTE (-372)))) (-2833 (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (|HasCategory| (-709) (QUOTE (-566)))) (-12 (|HasCategory| (-709) (QUOTE (-239))) (|HasCategory| (-709) (QUOTE (-372)))) (-12 (|HasCategory| (-709) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-709) (QUOTE (-372)))) (|HasCategory| (-709) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-709) (QUOTE (-566))) (|HasAttribute| (-709) (QUOTE -4458)) (|HasAttribute| (-709) (QUOTE -4455)) (-12 (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (|HasCategory| (-709) (QUOTE (-146)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-709) (QUOTE (-315))) (|HasCategory| (-709) (QUOTE (-923)))) (|HasCategory| (-709) (QUOTE (-358))))) (-705 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}."))) -((-4459 . T)) +((-4460 . T)) NIL (-706 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}."))) @@ -2760,13 +2760,13 @@ 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 -(-708 OV E -1395 PG) +(-708 OV E -1396 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 (-709) ((|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}"))) -((-3524 . T) (-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-3525 . T) (-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-710 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."))) @@ -2774,7 +2774,7 @@ NIL NIL (-711) ((|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}"))) -((-4457 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4458 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-712 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"))) @@ -2792,7 +2792,7 @@ 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 -(-716 S -3583 I) +(-716 S -3584 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 @@ -2802,7 +2802,7 @@ NIL NIL (-718 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)}.}"))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL (-719 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}."))) @@ -2812,25 +2812,25 @@ 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 -(-721 R |Mod| -2432 -4297 |exactQuo|) +(-721 R |Mod| -3607 -3404 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-722 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-922))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1167))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4455 |has| |#1| (-372)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1168))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) (-723 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-724 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) (-4455 . T)) +((-4454 |has| |#1| (-174)) (-4453 |has| |#1| (-174)) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-725 R |Mod| -2432 -4297 |exactQuo|) +(-725 R |Mod| -3607 -3404 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4455 . T)) +((-4456 . T)) NIL (-726 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2838,11 +2838,11 @@ NIL NIL (-727 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL -(-728 -1395) +(-728 -1396) ((|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]]}."))) -((-4455 . T)) +((-4456 . T)) NIL (-729 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."))) @@ -2866,7 +2866,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-358))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-377)))) (-734 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."))) -((-4451 |has| |#1| (-372)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 |has| |#1| (-372)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-735 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."))) @@ -2876,7 +2876,7 @@ 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 -(-737 -1395 UP) +(-737 -1396 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 @@ -2894,8 +2894,8 @@ NIL NIL (-741 |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."))) -(((-4460 "*") |has| |#2| (-174)) (-4451 |has| |#2| (-566)) (-4456 |has| |#2| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-922))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4461 "*") |has| |#2| (-174)) (-4452 |has| |#2| (-566)) (-4457 |has| |#2| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-923))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-874 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasAttribute| |#2| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-146))))) (-742 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2910,16 +2910,16 @@ NIL NIL (-745 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) (-4455 . T)) +((-4454 |has| |#1| (-174)) (-4453 |has| |#1| (-174)) (-4456 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-860)))) (-746 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4448 . T) (-4459 . T)) +((-4449 . T) (-4460 . T)) NIL (-747 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}."))) -((-4458 . T) (-4448 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4459 . T) (-4449 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-748) ((|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 @@ -2930,7 +2930,7 @@ NIL NIL (-750 |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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4453 . T) (-4452 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL (-751 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"))) @@ -2946,7 +2946,7 @@ NIL NIL (-754 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}."))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL (-755) ((|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}."))) @@ -3028,11 +3028,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-775 -1395) +(-775 -1396) ((|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 -(-776 P -1395) +(-776 P -1396) ((|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 @@ -3040,7 +3040,7 @@ NIL NIL NIL NIL -(-778 UP -1395) +(-778 UP -1396) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3054,9 +3054,9 @@ NIL NIL (-781) ((|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."))) -(((-4460 "*") . T)) +(((-4461 "*") . T)) NIL -(-782 R -1395) +(-782 R -1396) ((|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 @@ -3076,7 +3076,7 @@ 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 -(-787 -1395 |ExtF| |SUEx| |ExtP| |n|) +(-787 -1396 |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 @@ -3090,28 +3090,28 @@ NIL NIL (-790 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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . 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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 (-792 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.")) 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-794 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.}"))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL (-795 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 (-566))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-174)))) +((-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-174)))) (-796) ((|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 @@ -3155,28 +3155,28 @@ NIL (-806 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,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-377)))) +((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-377)))) (-807 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-808 -2832 R OS S) +(-808 -2833 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-809 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (-2832 (|HasCategory| (-1014 |#1|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (|HasCategory| (-1014 |#1|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| (-1014 |#1|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1014 |#1|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (-2833 (|HasCategory| (-1015 |#1|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2833 (|HasCategory| (-1015 |#1|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| (-1015 |#1|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1015 |#1|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (-810) ((|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 -(-811 R -1395 L) +(-811 R -1396 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-812 R -1395) +(-812 R -1396) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3184,7 +3184,7 @@ 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 -(-814 R -1395) +(-814 R -1396) ((|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 @@ -3192,11 +3192,11 @@ 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 -(-816 -1395 UP UPUP R) +(-816 -1396 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 -(-817 -1395 UP L LQ) +(-817 -1396 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 @@ -3204,41 +3204,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-819 -1395 UP L LQ) +(-819 -1396 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-820 -1395 UP) +(-820 -1396 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 -(-821 -1395 L UP A LO) +(-821 -1396 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 -(-822 -1395 UP) +(-822 -1396 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-823 -1395 LO) +(-823 -1396 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 -(-824 -1395 LODO) +(-824 -1396 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-825 -4105 S |f|) +(-825 -4106 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}."))) -((-4452 |has| |#2| (-1064)) (-4453 |has| |#2| (-1064)) (-4455 |has| |#2| (-6 -4455)) ((-4460 "*") |has| |#2| (-174)) (-4458 . 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T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-828 (-1193)) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-828 (-1193)) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-828 (-1193)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-828 (-1193)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-828 (-1193)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) (-827 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4460 "*") |has| |#2| (-372)) (-4451 |has| |#2| (-372)) (-4456 |has| |#2| (-372)) (-4450 |has| |#2| (-372)) (-4455 . T) (-4453 . T) (-4452 . T)) +(((-4461 "*") |has| |#2| (-372)) (-4452 |has| |#2| (-372)) (-4457 |has| |#2| (-372)) (-4451 |has| |#2| (-372)) (-4456 . T) (-4454 . T) (-4453 . T)) ((|HasCategory| |#2| (QUOTE (-372)))) (-828 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}))."))) @@ -3250,7 +3250,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-860)))) (-830) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-831) ((|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}"))) @@ -3278,7 +3278,7 @@ NIL NIL (-837 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}."))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-239)))) (-838) ((|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."))) @@ -3290,7 +3290,7 @@ NIL NIL (-840 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4458 . T) (-4448 . T) (-4459 . T)) +((-4459 . T) (-4449 . T) (-4460 . T)) NIL (-841) ((|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."))) @@ -3302,8 +3302,8 @@ NIL NIL (-843 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."))) -((-4455 |has| |#1| (-858))) -((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-21))) (-2832 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (-2832 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-555)))) +((-4456 |has| |#1| (-858))) +((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-21))) (-2833 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (-2833 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-555)))) (-844 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3314,7 +3314,7 @@ NIL NIL (-846 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) (-4455 . T)) +((-4454 |has| |#1| (-174)) (-4453 |has| |#1| (-174)) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-847) ((|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)."))) @@ -3342,13 +3342,13 @@ NIL NIL (-853 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4455 |has| |#1| (-858))) -((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-21))) (-2832 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (-2832 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-555)))) +((-4456 |has| |#1| (-858))) +((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-21))) (-2833 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (-2833 (|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-555)))) (-854) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-855 -4105 S) +(-855 -4106 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3362,7 +3362,7 @@ NIL NIL (-858) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4455 . T)) +((-4456 . T)) NIL (-859 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3378,20 +3378,20 @@ NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174)))) (-862 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL (-863 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 (-372))) (|HasCategory| |#1| (QUOTE (-566)))) -(-864 R |sigma| -2084) +(-864 R |sigma| -2083) ((|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."))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) -(-865 |x| R |sigma| -2084) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-372)))) +(-865 |x| R |sigma| -2083) ((|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}."))) -((-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-372)))) +((-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-372)))) (-866 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 @@ -3434,7 +3434,7 @@ NIL NIL (-876 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) (-4455 . T)) +((-4454 |has| |#1| (-174)) (-4453 |has| |#1| (-174)) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) (-877 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3446,24 +3446,24 @@ NIL NIL (-879 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-880 |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)."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL (-881 |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)."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-880 |#1|) (QUOTE (-922))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-880 |#1|) (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-148))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-880 |#1|) (QUOTE (-1037))) (|HasCategory| (-880 |#1|) (QUOTE (-830))) (-2832 (|HasCategory| (-880 |#1|) (QUOTE (-830))) (|HasCategory| (-880 |#1|) (QUOTE (-860)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (QUOTE (-1167))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (QUOTE (-239))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -524) (QUOTE (-1192)) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -317) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -294) (LIST (QUOTE -880) (|devaluate| |#1|)) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (QUOTE (-315))) (|HasCategory| (-880 |#1|) (QUOTE (-555))) (|HasCategory| (-880 |#1|) (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-922)))) (|HasCategory| (-880 |#1|) (QUOTE (-146))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-880 |#1|) (QUOTE (-923))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-880 |#1|) (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-148))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-880 |#1|) (QUOTE (-1038))) (|HasCategory| (-880 |#1|) (QUOTE (-830))) (-2833 (|HasCategory| (-880 |#1|) (QUOTE (-830))) (|HasCategory| (-880 |#1|) (QUOTE (-860)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (QUOTE (-1168))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| (-880 |#1|) (QUOTE (-239))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -524) (QUOTE (-1193)) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -317) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (LIST (QUOTE -294) (LIST (QUOTE -880) (|devaluate| |#1|)) (LIST (QUOTE -880) (|devaluate| |#1|)))) (|HasCategory| (-880 |#1|) (QUOTE (-315))) (|HasCategory| (-880 |#1|) (QUOTE (-555))) (|HasCategory| (-880 |#1|) (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-880 |#1|) (QUOTE (-923)))) (|HasCategory| (-880 |#1|) (QUOTE (-146))))) (-882 |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)}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-922))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1037))) (|HasCategory| |#2| (QUOTE (-830))) (-2832 (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1167))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-146))))) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-923))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1038))) (|HasCategory| |#2| (QUOTE (-830))) (-2833 (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-860)))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1168))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-860))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-146))))) (-883 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 (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))))) (-884) ((|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 @@ -3523,7 +3523,7 @@ NIL (-898 |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 (-2085 (|HasCategory| |#2| (QUOTE (-1064)))) (-2085 (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (-12 (|HasCategory| |#2| (QUOTE (-1064))) (-2085 (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192))))) +((-12 (-2084 (|HasCategory| |#2| (QUOTE (-1065)))) (-2084 (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-1193)))))) (-12 (|HasCategory| |#2| (QUOTE (-1065))) (-2084 (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-1193)))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-1193))))) (-899 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 @@ -3532,7 +3532,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-901 R -3583) +(-901 R -3584) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3553,18 +3553,18 @@ NIL NIL NIL (-906 A T$ S) -((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) +((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL (-907 T$ S) -((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) +((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL (-908) ((|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 -(-909 UP -1395) +(-909 UP -1396) ((|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 @@ -3576,1609 +3576,1613 @@ NIL ((|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|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|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 -(-912 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}."))) +(-912 S) +((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) +((-4456 . T)) NIL +(-913 A S) +((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL -(-913 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}."))) -((-4455 . T)) NIL (-914 S) +((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|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}\\spad{-}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)}."))) +NIL +NIL +(-915 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) -(-915 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-916 |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 -(-916 S) +(-917 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4455 . T)) +((-4456 . T)) NIL -(-917 S) +(-918 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-918 S) +(-919 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4455 . T)) -((-2832 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-860)))) -(-919 R E |VarSet| S) +((-4456 . T)) +((-2833 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-860)))) +(-920 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-920 R S) +(-921 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 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 -(-921 S) +(-922 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 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 (-146)))) -(-922) +(-923) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-923 |p|) +(-924 |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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-377)))) -(-924 R0 -1395 UP UPUP R) +(-925 R0 -1396 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 -(-925 UP UPUP R) +(-926 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 -(-926 UP UPUP) +(-927 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 -(-927 R) +(-928 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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-928 R) +(-929 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 -(-929 E OV R P) +(-930 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 -(-930) +(-931) ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-931 -1395) +(-932 -1396) ((|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 -(-932 R) +(-933 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 -(-933) +(-934) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-934) +(-935) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4460 "*") . T)) +(((-4461 "*") . T)) NIL -(-935 -1395 P) +(-936 -1396 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-936 |xx| -1395) +(-937 |xx| -1396) ((|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 -(-937 R |Var| |Expon| GR) +(-938 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 -(-938 S) +(-939 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 -(-939) +(-940) ((|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 -(-940) +(-941) ((|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*\\%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 -(-941) +(-942) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-942 R -1395) +(-943 R -1396) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-943) +(-944) ((|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|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-944 S A B) +(-945 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 -(-945 S R -1395) +(-946 S R -1396) ((|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 -(-946 I) +(-947 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 -(-947 S E) +(-948 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 -(-948 S R L) +(-949 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 -(-949 S E V R P) +(-950 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 -897) (|devaluate| |#1|)))) -(-950 R -1395 -3583) +(-951 R -1396 -3584) ((|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 -(-951 -3583) +(-952 -3584) ((|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 -(-952 S R Q) +(-953 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 -(-953 S) +(-954 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 -(-954 S R P) +(-955 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 -(-955) +(-956) ((|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 -(-956 R) +(-957 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1064))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-1064)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) -(-957 |lv| R) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1065))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1065)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +(-958 |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 -(-958 |TheField| |ThePols|) +(-959 |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 (-858)))) -(-959 R S) +(-960 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 -(-960 |x| R) +(-961 |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 -(-961 S R E |VarSet|) +(-962 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 (-922))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#4| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#4| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#4| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) -(-962 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-923))) (|HasAttribute| |#2| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#4| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#4| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#4| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) +(-963 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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL -(-963 E V R P -1395) +(-964 E V R P -1396) ((|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 -(-964 E |Vars| R P S) +(-965 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 -(-965 R) +(-966 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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-922))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1192) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1192) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1192) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1192) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1192) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-966 E V R P -1395) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1193) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1193) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1193) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1193) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1193) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-967 E V R P -1396) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-462)))) -(-967) +(-968) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-968) +(-969) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-969 R L) +(-970 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-970 A B) +(-971 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-971 S) +(-972 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) -(-972) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +(-973) ((|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 -(-973 -1395) +(-974 -1396) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-974 I) +(-975 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 -(-975) +(-976) ((|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 -(-976 R E) +(-977 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}"))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4456))) -(-977 A B) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4457))) +(-978 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-860))))) +(-979) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-979 T$) +(-980 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-980 T$) +(-981 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-981 S T$) +(-982 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-982) +(-983) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-983 S) +(-984 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL -(-984 R |polR|) +(-985 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 (-462)))) -(-985) +(-986) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-986) +(-987) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\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| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-987 S |Coef| |Expon| |Var|) +(-988 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 -(-988 |Coef| |Expon| |Var|) +(-989 |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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-989) +(-990) ((|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 -(-990 S R E |VarSet| P) +(-991 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 (-566)))) -(-991 R E |VarSet| P) +(-992 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."))) -((-4458 . T)) +((-4459 . T)) NIL -(-992 R E V P) +(-993 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 (-148))) (|HasCategory| |#1| (QUOTE (-315)))) (|HasCategory| |#1| (QUOTE (-462)))) -(-993 K) +(-994 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 -(-994 |VarSet| E RC P) +(-995 |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 -(-995 R) +(-996 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-996 R1 R2) +(-997 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-997 R) +(-998 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 -(-998 K) +(-999 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 -(-999 R E OV PPR) +(-1000 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 -(-1000 K R UP -1395) +(-1001 K R UP -1396) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1001 |vl| |nv|) +(-1002 |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 -(-1002 R |Var| |Expon| |Dpoly|) +(-1003 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 (-148))) (|HasCategory| |#1| (QUOTE (-315))))) -(-1003 R E V P TS) +(-1004 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 -(-1004) +(-1005) ((|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 -(-1005 A B R S) +(-1006 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 -(-1006 A S) +(-1007 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 (-922))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1037))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1167)))) -(-1007 S) +((|HasCategory| |#2| (QUOTE (-923))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-1038))) (|HasCategory| |#2| (QUOTE (-830))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-1168)))) +(-1008 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}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1008 |n| K) +(-1009 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-1009) +(-1010) ((|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 -(-1010 S) +(-1011 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."))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL -(-1011 S R) +(-1012 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 (-555))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-298)))) -(-1012 R) +((|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1076))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-298)))) +(-1013 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}."))) -((-4451 |has| |#1| (-298)) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 |has| |#1| (-298)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1013 QR R QS S) +(-1014 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 -(-1014 R) +(-1015 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.}"))) -((-4451 |has| |#1| (-298)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-555)))) -(-1015 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}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +((-4452 |has| |#1| (-298)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-372))) (-2833 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -524) (QUOTE (-1193)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -294) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-239)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-1076))) (|HasCategory| |#1| (QUOTE (-555)))) (-1016 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}."))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1017 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1017) +(-1018) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1018 -1395 UP UPUP |radicnd| |n|) +(-1019 -1396 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4451 |has| (-417 |#2|) (-372)) (-4456 |has| (-417 |#2|) (-372)) (-4450 |has| (-417 |#2|) (-372)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2832 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2832 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2832 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2832 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) -(-1019 |bb|) +((-4452 |has| (-417 |#2|) (-372)) (-4457 |has| (-417 |#2|) (-372)) (-4451 |has| (-417 |#2|) (-372)) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-417 |#2|) (QUOTE (-146))) (|HasCategory| (-417 |#2|) (QUOTE (-148))) (|HasCategory| (-417 |#2|) (QUOTE (-358))) (-2833 (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (QUOTE (-372))) (|HasCategory| (-417 |#2|) (QUOTE (-377))) (-2833 (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (-2833 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-358))))) (-2833 (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (QUOTE (-358)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -649) (QUOTE (-574)))) (-2833 (|HasCategory| (-417 |#2|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 |#2|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-12 (|HasCategory| (-417 |#2|) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-417 |#2|) (QUOTE (-372)))) (-12 (|HasCategory| (-417 |#2|) (QUOTE (-239))) (|HasCategory| (-417 |#2|) (QUOTE (-372))))) +(-1020 |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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-574) (QUOTE (-922))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-1192)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1037))) (|HasCategory| (-574) (QUOTE (-830))) (-2832 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1167))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1192)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-922)))) (|HasCategory| (-574) (QUOTE (-146))))) -(-1020) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-574) (QUOTE (-923))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-1193)))) (|HasCategory| (-574) (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-148))) (|HasCategory| (-574) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-1038))) (|HasCategory| (-574) (QUOTE (-830))) (-2833 (|HasCategory| (-574) (QUOTE (-830))) (|HasCategory| (-574) (QUOTE (-860)))) (|HasCategory| (-574) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-1168))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| (-574) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| (-574) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| (-574) (QUOTE (-239))) (|HasCategory| (-574) (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| (-574) (LIST (QUOTE -524) (QUOTE (-1193)) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -317) (QUOTE (-574)))) (|HasCategory| (-574) (LIST (QUOTE -294) (QUOTE (-574)) (QUOTE (-574)))) (|HasCategory| (-574) (QUOTE (-315))) (|HasCategory| (-574) (QUOTE (-555))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-574) (LIST (QUOTE -649) (QUOTE (-574)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-574) (QUOTE (-923)))) (|HasCategory| (-574) (QUOTE (-146))))) +(-1021) ((|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 -(-1021) +(-1022) ((|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 -(-1022 RP) +(-1023 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 -(-1023 S) +(-1024 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 -(-1024 A S) +(-1025 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 -4459)) (|HasCategory| |#2| (QUOTE (-1115)))) -(-1025 S) +((|HasAttribute| |#1| (QUOTE -4460)) (|HasCategory| |#2| (QUOTE (-1116)))) +(-1026 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-1026 S) +(-1027 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 -(-1027) +(-1028) ((|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}}"))) -((-4451 . T) (-4456 . T) (-4450 . T) (-4453 . T) (-4452 . T) ((-4460 "*") . T) (-4455 . T)) +((-4452 . T) (-4457 . T) (-4451 . T) (-4454 . T) (-4453 . T) ((-4461 "*") . T) (-4456 . T)) NIL -(-1028 R -1395) +(-1029 R -1396) ((|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 -(-1029 R -1395) +(-1030 R -1396) ((|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 -(-1030 -1395 UP) +(-1031 -1396 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 -(-1031 -1395 UP) +(-1032 -1396 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 -(-1032 S) +(-1033 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 -(-1033 F1 UP UPUP R F2) +(-1034 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 -(-1034) +(-1035) ((|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 -(-1035 |Pol|) +(-1036 |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 -(-1036 |Pol|) +(-1037 |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 -(-1037) +(-1038) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1038) +(-1039) ((|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 -(-1039 |TheField|) +(-1040 |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"))) -((-4451 . T) (-4456 . T) (-4450 . T) (-4453 . T) (-4452 . T) ((-4460 "*") . T) (-4455 . T)) -((-2832 (|HasCategory| (-417 (-574)) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-417 (-574)) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 (-574)) (LIST (QUOTE -1053) (QUOTE (-574))))) -(-1040 -1395 L) +((-4452 . T) (-4457 . T) (-4451 . T) (-4454 . T) (-4453 . T) ((-4461 "*") . T) (-4456 . T)) +((-2833 (|HasCategory| (-417 (-574)) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-417 (-574)) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-417 (-574)) (LIST (QUOTE -1054) (QUOTE (-574))))) +(-1041 -1396 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL -(-1041 S) +(-1042 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 (-1115)))) -(-1042 R E V P) +((|HasCategory| |#1| (QUOTE (-1116)))) +(-1043 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."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1043 R) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1044 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4460 "*")))) -(-1044 R) +((|HasAttribute| |#1| (QUOTE (-4461 "*")))) +(-1045 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 (-372))) (|HasCategory| |#1| (QUOTE (-377)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-315)))) -(-1045 S) +(-1046 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 -(-1046) +(-1047) ((|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 -(-1047 S) +(-1048 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 -(-1048 S) +(-1049 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 -(-1049 -1395 |Expon| |VarSet| |FPol| |LFPol|) +(-1050 -1396 |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"))) -(((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1050) -((|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.}"))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1192))) (LIST (QUOTE |:|) (QUOTE -1917) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-1192) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) (-1051) +((|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.}"))) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (QUOTE (-1193))) (LIST (QUOTE |:|) (QUOTE -1916) (QUOTE (-52))))))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-52) (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-1193) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) +(-1052) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1052 A S) +(-1053 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}."))) NIL NIL -(-1053 S) +(-1054 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}."))) NIL NIL -(-1054 Q R) +(-1055 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 -(-1055) +(-1056) ((|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 -(-1056 UP) +(-1057 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 -(-1057 R) +(-1058 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 -(-1058 R) +(-1059 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 -(-1059 T$) +(-1060 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1060 T$) +(-1061 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1061 R |ls|) +(-1062 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}."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| (-790 |#1| (-874 |#2|)) (QUOTE (-1115))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -790) (|devaluate| |#1|) (LIST (QUOTE -874) (|devaluate| |#2|)))))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-790 |#1| (-874 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| (-874 |#2|) (QUOTE (-377))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) -(-1062) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| (-790 |#1| (-874 |#2|)) (QUOTE (-1116))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -790) (|devaluate| |#1|) (LIST (QUOTE -874) (|devaluate| |#2|)))))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-790 |#1| (-874 |#2|)) (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| (-874 |#2|) (QUOTE (-377))) (|HasCategory| (-790 |#1| (-874 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) +(-1063) ((|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 -(-1063 S) +(-1064 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\"}.")) (|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 -(-1064) +(-1065) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4455 . T)) +((-4456 . T)) NIL -(-1065 |xx| -1395) +(-1066 |xx| -1396) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1066 S) +(-1067 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds if \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) NIL NIL -(-1067 S |m| |n| R |Row| |Col|) +(-1068 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 (-315))) (|HasCategory| |#4| (QUOTE (-372))) (|HasCategory| |#4| (QUOTE (-566))) (|HasCategory| |#4| (QUOTE (-174)))) -(-1068 |m| |n| R |Row| |Col|) +(-1069 |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"))) -((-4458 . T) (-4453 . T) (-4452 . T)) +((-4459 . T) (-4454 . T) (-4453 . T)) NIL -(-1069 |m| |n| R) +(-1070 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4458 . T) (-4453 . T) (-4452 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2832 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372)))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (QUOTE (-315))) (|HasCategory| |#3| (QUOTE (-566))) (-12 (|HasCategory| |#3| (QUOTE (-1115))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1070 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4459 . T) (-4454 . T) (-4453 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2833 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-372)))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (QUOTE (-315))) (|HasCategory| |#3| (QUOTE (-566))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1071 |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 -(-1071 R) +(-1072 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"))) NIL NIL -(-1072 S T$) +(-1073 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1115)))) -(-1073) +((|HasCategory| |#1| (QUOTE (-1116)))) +(-1074) ((|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 -(-1074 S) +(-1075 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1075) +(-1076) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1076 |TheField| |ThePolDom|) +(-1077 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1077) +(-1078) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4446 . T) (-4450 . T) (-4445 . T) (-4456 . T) (-4457 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4447 . T) (-4451 . T) (-4446 . T) (-4457 . T) (-4458 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1078) +(-1079) ((|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}"))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1192))) (LIST (QUOTE |:|) (QUOTE -1917) (QUOTE (-52))))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-52) (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1115))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (QUOTE (-1115))) (|HasCategory| (-1192) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1192)) (|:| -1917 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) -(-1079 S R E V) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (QUOTE (-1193))) (LIST (QUOTE |:|) (QUOTE -1916) (QUOTE (-52))))))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-52) (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| (-52) (QUOTE (-1116))) (|HasCategory| (-52) (LIST (QUOTE -317) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (QUOTE (-1116))) (|HasCategory| (-1193) (QUOTE (-860))) (|HasCategory| (-52) (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-52) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 (-1193)) (|:| -1916 (-52))) (LIST (QUOTE -623) (QUOTE (-872))))) +(-1080 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-1192))))) -(-1080 R E V) +((|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1008) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-1193))))) +(-1081 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL -(-1081) +(-1082) ((|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 -(-1082 S |TheField| |ThePols|) +(-1083 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 -(-1083 |TheField| |ThePols|) +(-1084 |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 -(-1084 R E V P TS) +(-1085 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 -(-1085 S R E V P) +(-1086 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,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#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 -(-1086 R E V P) +(-1087 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1087 R E V P TS) +(-1088 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 -(-1088) +(-1089) ((|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 -(-1089) +(-1090) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1090 |f|) +(-1091 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1091 |Base| R -1395) +(-1092 |Base| R -1396) ((|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 -(-1092 |Base| R -1395) +(-1093 |Base| R -1396) ((|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 -(-1093 R |ls|) +(-1094 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 -(-1094 UP SAE UPA) +(-1095 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 -(-1095 R UP M) +(-1096 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."))) -((-4451 |has| |#1| (-372)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-358)))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372))))) -(-1096 UP SAE UPA) +((-4452 |has| |#1| (-372)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-358))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-377))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-358)))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193))))) (-12 (|HasCategory| |#1| (QUOTE (-358))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193))))) (|HasCategory| |#1| (QUOTE (-358)))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-372))))) +(-1097 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 -(-1097) +(-1098) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1098) +(-1099) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1099 S) +(-1100 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 -(-1100) +(-1101) ((|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| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1101 R) +(-1102 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 -(-1102 R) +(-1103 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"))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-922))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1103 (-1192)) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1103 (-1192)) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1103 (-1192)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1103 (-1192)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1103 (-1192)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1103 S) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| (-1104 (-1193)) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1104 (-1193)) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1104 (-1193)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1104 (-1193)) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1104 (-1193)) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1104 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 -(-1104 R S) +(-1105 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 (-858)))) -(-1105) +(-1106) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1106 R S) +(-1107 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1107 S) +(-1108 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1109 |#1|) (QUOTE (-1115)))) -(-1108 S) +((|HasCategory| (-1110 |#1|) (QUOTE (-1116)))) +(-1109 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1109 S) +(-1110 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1115)))) -(-1110 S L) +((|HasCategory| |#1| (QUOTE (-858))) (|HasCategory| |#1| (QUOTE (-1116)))) +(-1111 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1111) +(-1112) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1112 A S) +(-1113 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1113 S) +(-1114 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4448 . T)) +((-4449 . T)) NIL -(-1114 S) +(-1115 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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 -(-1115) +(-1116) ((|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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 -(-1116 |m| |n|) +(-1117 |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 -(-1117 S) +(-1118 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)}}"))) -((-4458 . T) (-4448 . T) (-4459 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) -(-1118 |Str| |Sym| |Int| |Flt| |Expr|) +((-4459 . T) (-4449 . T) (-4460 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#1| (QUOTE (-377))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +(-1119 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1119) +(-1120) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1120 |Str| |Sym| |Int| |Flt| |Expr|) +(-1121 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1121 R FS) +(-1122 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 -(-1122 R E V P TS) +(-1123 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 -(-1123 R E V P TS) +(-1124 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 -(-1124 R E V P) +(-1125 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.}"))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1125) +(-1126) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1126 S) +(-1127 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1127) +(-1128) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) 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(-803))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-860))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574)))))) (|HasCategory| (-574) (QUOTE (-860))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1065)))) (-12 (|HasCategory| |#3| (QUOTE (-1065))) (|HasCategory| |#3| (LIST (QUOTE -912) (QUOTE (-1193))))) (-2833 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-736)))) (-2833 (|HasCategory| |#3| (QUOTE (-1065))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574)))))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -1054) (QUOTE (-574))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#3| (QUOTE (-1116)))) (|HasAttribute| |#3| (QUOTE -4456)) (|HasCategory| |#3| (QUOTE (-860))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#3| (QUOTE (-1116))) (|HasCategory| |#3| (LIST (QUOTE -317) (|devaluate| |#3|))))) +(-1130 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 (-462)))) -(-1130) +(-1131) ((|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 -(-1131 R -1395) +(-1132 R -1396) ((|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 -(-1132 R) +(-1133 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1133) +(-1134) ((|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 -(-1134) +(-1135) ((|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 -(-1135) +(-1136) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4446 . T) (-4450 . T) (-4445 . T) (-4456 . T) (-4457 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4447 . T) (-4451 . T) (-4446 . T) (-4457 . T) (-4458 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1136 S) +(-1137 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4458 . T) (-4459 . T)) +((-4459 . T) (-4460 . T)) NIL -(-1137 S |ndim| R |Row| |Col|) +(-1138 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-372))) (|HasAttribute| |#3| (QUOTE (-4460 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) -(-1138 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-372))) (|HasAttribute| |#3| (QUOTE (-4461 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +(-1139 |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."))) -((-4458 . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4459 . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1139 R |Row| |Col| M) +(-1140 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 -(-1140 R |VarSet|) +(-1141 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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-922))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-922)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1141 |Coef| |Var| SMP) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-923))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (|HasCategory| |#1| (QUOTE (-462))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#1| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-923)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1142 |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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372)))) -(-1142 R E V P) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372)))) +(-1143 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}"))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1143 UP -1395) +(-1144 UP -1396) ((|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 -(-1144 R) +(-1145 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 -(-1145 R) +(-1146 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 -(-1146 R) +(-1147 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 -(-1147 S A) +(-1148 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 (-860)))) -(-1148 R) +(-1149 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 -(-1149 R) +(-1150 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 -(-1150) +(-1151) ((|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 -(-1151) +(-1152) ((|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 -(-1152) +(-1153) ((|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.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst 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.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\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|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|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|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|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."))) NIL NIL -(-1153) +(-1154) ((|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 -(-1154) +(-1155) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1155 V C) +(-1156 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 -(-1156 V C) +(-1157 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-1155 |#1| |#2|) (LIST (QUOTE -317) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1155 |#1| |#2|) (QUOTE (-1115)))) (|HasCategory| (-1155 |#1| |#2|) (QUOTE (-1115))) (-2832 (|HasCategory| (-1155 |#1| |#2|) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-1155 |#1| |#2|) (LIST (QUOTE -317) (LIST (QUOTE -1155) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1155 |#1| |#2|) (QUOTE (-1115))))) (|HasCategory| (-1155 |#1| |#2|) (LIST (QUOTE -623) (QUOTE (-872))))) -(-1157 |ndim| R) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-1156 |#1| |#2|) (LIST (QUOTE -317) (LIST (QUOTE -1156) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1156 |#1| |#2|) (QUOTE (-1116)))) (|HasCategory| (-1156 |#1| |#2|) (QUOTE (-1116))) (-2833 (|HasCategory| (-1156 |#1| |#2|) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-1156 |#1| |#2|) (LIST (QUOTE -317) (LIST (QUOTE -1156) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1156 |#1| |#2|) (QUOTE (-1116))))) (|HasCategory| (-1156 |#1| |#2|) (LIST (QUOTE -623) (QUOTE (-872))))) +(-1158 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4455 . T) (-4447 |has| |#2| (-6 (-4460 "*"))) (-4458 . T) (-4452 . T) (-4453 . T)) -((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4460 "*"))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-372))) (-2832 (|HasAttribute| |#2| (QUOTE (-4460 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) -(-1158 S) +((-4456 . T) (-4448 |has| |#2| (-6 (-4461 "*"))) (-4459 . T) (-4453 . T) (-4454 . T)) +((|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4461 "*"))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (QUOTE (-315))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-372))) (-2833 (|HasAttribute| |#2| (QUOTE (-4461 "*"))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +(-1159 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1159) +(-1160) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1160 R E V P TS) +(-1161 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 -(-1161 R E V P) +(-1162 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."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1162 S) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1163 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}."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1163 A S) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1164 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 -(-1164 S) +(-1165 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 -(-1165 |Key| |Ent| |dent|) +(-1166 |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."))) -((-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115)))) -(-1166) +((-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-860))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116)))) +(-1167) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1167) +(-1168) ((|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 -(-1168 |Coef|) +(-1169 |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 -(-1169 S) +(-1170 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 -(-1170 A B) +(-1171 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 -(-1171 A B C) +(-1172 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 -(-1172 S) +(-1173 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4459 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1173) +((-4460 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1174) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1174) +(-1175) NIL -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1115))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) -(-1175 |Entry|) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| (-145) (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| (-145) (QUOTE (-1116))) (|HasCategory| (-145) (LIST (QUOTE -317) (QUOTE (-145)))))) +(-1176 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (QUOTE (-1174))) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#1|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (QUOTE (-1115))) (|HasCategory| (-1174) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 (-1174)) (|:| -1917 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) -(-1176 A) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#1|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (QUOTE (-1116))) (|HasCategory| (-1175) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 (-1175)) (|:| -1916 |#1|)) (LIST (QUOTE -623) (QUOTE (-872))))) +(-1177 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) -(-1177 |Coef|) +(-1178 |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 -(-1178 |Coef|) +(-1179 |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 -(-1179 R UP) +(-1180 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 (-315)))) -(-1180 |n| R) +(-1181 |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,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,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,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,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,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,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,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,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 -(-1181 S1 S2) +(-1182 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 -(-1182) +(-1183) ((|constructor| (NIL "This domain represents the filter iterator syntax.")) 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4460 "*") -2832 (-2096 (|has| |#1| (-372)) (|has| (-1190 |#1| |#2| |#3|) (-830))) (|has| |#1| (-174)) (-2096 (|has| |#1| (-372)) (|has| (-1190 |#1| |#2| |#3|) (-922)))) (-4451 -2832 (-2096 (|has| |#1| (-372)) (|has| (-1190 |#1| |#2| |#3|) (-830))) (|has| |#1| (-566)) (-2096 (|has| |#1| (-372)) (|has| (-1190 |#1| |#2| |#3|) (-922)))) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . 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(|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 -(-1185 R) +(-1186 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)}.") 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . 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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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1127))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -1578) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) -(-1191) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1128))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2951) (LIST (|devaluate| |#1|) (QUOTE (-1193)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2833 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1219))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3342) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1193))))) (|HasSignature| |#1| (LIST (QUOTE -4350) (LIST (LIST (QUOTE -654) (QUOTE (-1193))) (|devaluate| |#1|))))))) +(-1192) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) 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(GT (($ (|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 -(-1192) +(-1193) ((|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|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1193 R) +(-1194 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{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1194 R) +(-1195 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-6 -4456)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| (-986) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasAttribute| |#1| (QUOTE -4456))) -(-1195) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-6 -4457)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2833 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-462))) (-12 (|HasCategory| (-987) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasAttribute| |#1| (QUOTE -4457))) +(-1196) ((|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 -(-1196) +(-1197) ((|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 -(-1197) +(-1198) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. 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|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|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|) (|Identifier|) (|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| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|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.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier 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'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1198 N) +(-1199 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1199 N) +(-1200 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) NIL NIL -(-1200) +(-1201) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1201 R) +(-1202 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 -(-1202) +(-1203) ((|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} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is 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 -(-1203 S) +(-1204 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 -(-1204 S) +(-1205 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 -(-1205 |Key| |Entry|) +(-1206 |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}"))) -((-4458 . T) (-4459 . T)) -((-12 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3666) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1917) (|devaluate| |#2|)))))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-1115)))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1115))) (-2832 (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3666 |#1|) (|:| -1917 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) -(-1206 S) +((-4459 . T) (-4460 . T)) +((-12 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -317) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3667) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1916) (|devaluate| |#2|)))))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-1116)))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -624) (QUOTE (-546)))) (-12 (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#2| (QUOTE (-1116))) (-2833 (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#2| (LIST (QUOTE -623) (QUOTE (-872)))) (|HasCategory| (-2 (|:| -3667 |#1|) (|:| -1916 |#2|)) (LIST (QUOTE -623) (QUOTE (-872))))) +(-1207 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1207 R) +(-1208 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{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1208 S |Key| |Entry|) +(-1209 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 -(-1209 |Key| |Entry|) +(-1210 |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})}."))) -((-4459 . T)) +((-4460 . T)) NIL -(-1210 |Key| |Entry|) +(-1211 |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 -(-1211) +(-1212) ((|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 -(-1212 S) +(-1213 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 -(-1213) +(-1214) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1214) +(-1215) ((|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 -(-1215 R) +(-1216 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 -(-1216) +(-1217) ((|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 -(-1217 S) +(-1218 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1218) +(-1219) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1219 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}."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1115))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (-1220 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1116))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1221 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1221) +(-1222) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1222 R -1395) +(-1223 R -1396) ((|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 -(-1223 R |Row| |Col| M) +(-1224 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 -(-1224 R -1395) +(-1225 R -1396) ((|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 -624) (LIST (QUOTE -903) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -897) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -897) (|devaluate| |#1|))))) -(-1225 S R E V P) +(-1226 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 (-377)))) -(-1226 R E V P) +(-1227 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1227 |Coef|) +(-1228 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372)))) -(-1228 |Curve|) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-372)))) +(-1229 |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 -(-1229) +(-1230) ((|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 -(-1230 S) +(-1231 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1231 -1395) +((|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1232 -1396) ((|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 -(-1232) +(-1233) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1233) +(-1234) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1234 S) +(-1235 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 < 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 < 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 (-860)))) -(-1235) +(-1236) ((|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 -(-1236 S) +(-1237 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 -(-1237) +(-1238) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1238) +(-1239) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1239) +(-1240) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1240) +(-1241) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1241) +(-1242) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1242 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1243 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1243 |Coef|) +(-1244 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1244 S |Coef| UTS) +(-1245 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-372)))) -(-1245 |Coef| UTS) +(-1246 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1246 |Coef| UTS) +(-1247 |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)}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) -((-2832 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -294) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -524) (QUOTE (-1192)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-830)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-860)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-922)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-1037)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-1167)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -317) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-1192)))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-146))))) (-2832 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-148))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-574)) (|devaluate| |#1|))))) (|HasCategory| (-574) (QUOTE 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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 -(-1249 R S) +(-1250 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) 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NIL NIL -(-1252 R Q UP) +(-1253 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 -(-1253 R UP) +(-1254 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 -(-1254 R UP) +(-1255 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1255 R U) +(-1256 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 -(-1256 |x| R) +(-1257 |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}"))) -(((-4460 "*") |has| |#2| (-174)) (-4451 |has| |#2| (-566)) (-4454 |has| |#2| (-372)) (-4456 |has| |#2| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-922))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1097) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (QUOTE (-574)))) (-2832 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (-2832 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-1167))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (-2832 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-922)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-1257 R PR S PS) +(((-4461 "*") |has| |#2| (-174)) (-4452 |has| |#2| (-566)) (-4455 |has| |#2| (-372)) (-4457 |has| |#2| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-923))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-566)))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -897) (QUOTE (-388)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-388))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -897) (QUOTE (-574)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-574))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-388)))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -624) (LIST (QUOTE -903) (QUOTE (-574)))))) (-12 (|HasCategory| (-1098) (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-546))))) (|HasCategory| |#2| (LIST (QUOTE -649) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (QUOTE (-574)))) (-2833 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| |#2| (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (-2833 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-1168))) (|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE -4457)) (|HasCategory| |#2| (QUOTE (-462))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (-2833 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-923)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-1258 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 -(-1258 S R) +(-1259 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 -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1167)))) -(-1259 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-462))) (|HasCategory| |#2| (QUOTE (-566))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1168)))) +(-1260 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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4454 |has| |#1| (-372)) (-4456 |has| |#1| (-6 -4456)) (-4453 . T) (-4452 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4455 |has| |#1| (-372)) (-4457 |has| |#1| (-6 -4457)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL -(-1260 S |Coef| |Expon|) +(-1261 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1127))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2950) (LIST (|devaluate| |#2|) (QUOTE (-1192)))))) -(-1261 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1128))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2951) (LIST (|devaluate| |#2|) (QUOTE (-1193)))))) +(-1262 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1262 RC P) +(-1263 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1263 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1264 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1264 |Coef|) +(-1265 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1265 S |Coef| ULS) +(-1266 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1266 |Coef| ULS) +(-1267 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1267 |Coef| ULS) +(-1268 |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)}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -1578) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) -(-1268 |Coef| |var| |cen|) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1128))) (|HasCategory| |#1| (QUOTE (-372))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2951) (LIST (|devaluate| |#1|) (QUOTE (-1193)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2833 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1219))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3342) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1193))))) (|HasSignature| |#1| (LIST (QUOTE -4350) (LIST (LIST (QUOTE -654) (QUOTE (-1193))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) +(-1269 |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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4456 |has| |#1| (-372)) (-4450 |has| |#1| (-372)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1127))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2832 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -1578) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) -(-1269 R FE |var| |cen|) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4457 |has| |#1| (-372)) (-4451 |has| |#1| (-372)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#1| (QUOTE (-174))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574))) (|devaluate| |#1|)))) (|HasCategory| (-417 (-574)) (QUOTE (-1128))) (|HasCategory| |#1| (QUOTE (-372))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-2833 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-566)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasSignature| |#1| (LIST (QUOTE -2951) (LIST (|devaluate| |#1|) (QUOTE (-1193)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -417) (QUOTE (-574)))))) (-2833 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1219))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3342) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1193))))) (|HasSignature| |#1| (LIST (QUOTE -4350) (LIST (LIST (QUOTE -654) (QUOTE (-1193))) (|devaluate| |#1|))))))) +(-1270 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))}."))) -(((-4460 "*") |has| (-1268 |#2| |#3| |#4|) (-174)) (-4451 |has| (-1268 |#2| |#3| |#4|) (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| (-1268 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-174))) (-2832 (|HasCategory| (-1268 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (LIST (QUOTE -1053) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1268 |#2| |#3| |#4|) (LIST (QUOTE -1053) (QUOTE (-574)))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-372))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-462))) (|HasCategory| (-1268 |#2| |#3| |#4|) (QUOTE (-566)))) -(-1270 A S) +(((-4461 "*") |has| (-1269 |#2| |#3| |#4|) (-174)) (-4452 |has| (-1269 |#2| |#3| |#4|) (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| (-1269 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-174))) (-2833 (|HasCategory| (-1269 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574)))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (LIST (QUOTE -1054) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| (-1269 |#2| |#3| |#4|) (LIST (QUOTE -1054) (QUOTE (-574)))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-372))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-462))) (|HasCategory| (-1269 |#2| |#3| |#4|) (QUOTE (-566)))) +(-1271 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4459))) -(-1271 S) +((|HasAttribute| |#1| (QUOTE -4460))) +(-1272 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1272 |Coef1| |Coef2| UTS1 UTS2) +(-1273 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1273 S |Coef|) +(-1274 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-1218))) (|HasSignature| |#2| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1578) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1192))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) -(-1274 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-1219))) (|HasSignature| |#2| (LIST (QUOTE -4350) (LIST (LIST (QUOTE -654) (QUOTE (-1193))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3342) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1193))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#2| (QUOTE (-372)))) +(-1275 |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."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1275 |Coef| |var| |cen|) +(-1276 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|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}."))) -(((-4460 "*") |has| |#1| (-174)) (-4451 |has| |#1| (-566)) (-4452 . T) (-4453 . T) (-4455 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2832 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1192)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1127))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2950) (LIST (|devaluate| |#1|) (QUOTE (-1192)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2832 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-1218))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -1578) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1192))))) (|HasSignature| |#1| (LIST (QUOTE -4349) (LIST (LIST (QUOTE -654) (QUOTE (-1192))) (|devaluate| |#1|))))))) -(-1276 |Coef| UTS) +(((-4461 "*") |has| |#1| (-174)) (-4452 |has| |#1| (-566)) (-4453 . T) (-4454 . T) (-4456 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasCategory| |#1| (QUOTE (-566))) (-2833 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -912) (QUOTE (-1193)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-781)) (|devaluate| |#1|)))) (|HasCategory| (-781) (QUOTE (-1128))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasSignature| |#1| (LIST (QUOTE -2951) (LIST (|devaluate| |#1|) (QUOTE (-1193)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-781))))) (|HasCategory| |#1| (QUOTE (-372))) (-2833 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-574)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1219))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasSignature| |#1| (LIST (QUOTE -3342) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1193))))) (|HasSignature| |#1| (LIST (QUOTE -4350) (LIST (LIST (QUOTE -654) (QUOTE (-1193))) (|devaluate| |#1|))))))) +(-1277 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1277 -1395 UP L UTS) +(-1278 -1396 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 (-566)))) -(-1278) +(-1279) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1279 |sym|) +(-1280 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1280 S R) +(-1281 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#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 -((|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1281 R) +((|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-736))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1282 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4459 . T) (-4458 . T)) +((-4460 . T) (-4459 . T)) NIL -(-1282 A B) +(-1283 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1283 R) +(-1284 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4459 . T) (-4458 . T)) -((-2832 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2832 (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2832 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1064))) (-12 (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (QUOTE (-1064)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) -(-1284) +((-4460 . T) (-4459 . T)) +((-2833 (-12 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) (-2833 (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-546)))) (-2833 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| (-574) (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-736))) (|HasCategory| |#1| (QUOTE (-1065))) (-12 (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-1065)))) (|HasCategory| |#1| (LIST (QUOTE -623) (QUOTE (-872)))) (-12 (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (LIST (QUOTE -317) (|devaluate| |#1|))))) +(-1285) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1285) +(-1286) ((|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 -(-1286) +(-1287) ((|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 -(-1287) +(-1288) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(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 -(-1288) +(-1289) ((|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.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1289 A S) +(-1290 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1290 S) +(-1291 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}."))) -((-4453 . T) (-4452 . T)) +((-4454 . T) (-4453 . T)) NIL -(-1291 R) +(-1292 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 -(-1292 K R UP -1395) +(-1293 K R UP -1396) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1293) +(-1294) ((|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 -(-1294) +(-1295) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1295 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1296 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)"))) -((-4453 |has| |#1| (-174)) (-4452 |has| |#1| (-174)) (-4455 . T)) +((-4454 |has| |#1| (-174)) (-4453 |has| |#1| (-174)) (-4456 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372)))) -(-1296 R E V P) +(-1297 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}}."))) -((-4459 . T) (-4458 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) -(-1297 R) +((-4460 . T) (-4459 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#4| (LIST (QUOTE -317) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -624) (QUOTE (-546)))) (|HasCategory| |#4| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-566))) (|HasCategory| |#3| (QUOTE (-377))) (|HasCategory| |#4| (LIST (QUOTE -623) (QUOTE (-872))))) +(-1298 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})"))) -((-4452 . T) (-4453 . T) (-4455 . T)) +((-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1298 |vl| R) +(-1299 |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."))) -((-4455 . T) (-4451 |has| |#2| (-6 -4451)) (-4453 . T) (-4452 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4451))) -(-1299 R |VarSet| XPOLY) +((-4456 . T) (-4452 |has| |#2| (-6 -4452)) (-4454 . T) (-4453 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4452))) +(-1300 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 -(-1300 |vl| R) +(-1301 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4451 |has| |#2| (-6 -4451)) (-4453 . T) (-4452 . T) (-4455 . T)) +((-4452 |has| |#2| (-6 -4452)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL -(-1301 S -1395) +(-1302 S -1396) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-377))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1302 -1395) +(-1303 -1396) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4450 . T) (-4456 . T) (-4451 . T) ((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +((-4451 . T) (-4457 . T) (-4452 . T) ((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL -(-1303 |VarSet| R) +(-1304 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4451 |has| |#2| (-6 -4451)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -727) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasAttribute| |#2| (QUOTE -4451))) -(-1304 |vl| R) +((-4452 |has| |#2| (-6 -4452)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -727) (LIST (QUOTE -417) (QUOTE (-574))))) (|HasAttribute| |#2| (QUOTE -4452))) +(-1305 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4451 |has| |#2| (-6 -4451)) (-4453 . T) (-4452 . T) (-4455 . T)) +((-4452 |has| |#2| (-6 -4452)) (-4454 . T) (-4453 . T) (-4456 . T)) NIL -(-1305 R) +(-1306 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4451 |has| |#1| (-6 -4451)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4451))) -(-1306 R E) +((-4452 |has| |#1| (-6 -4452)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4452))) +(-1307 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4455 . T) (-4456 |has| |#1| (-6 -4456)) (-4451 |has| |#1| (-6 -4451)) (-4453 . T) (-4452 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4455)) (|HasAttribute| |#1| (QUOTE -4456)) (|HasAttribute| |#1| (QUOTE -4451))) -(-1307 |VarSet| R) +((-4456 . T) (-4457 |has| |#1| (-6 -4457)) (-4452 |has| |#1| (-6 -4452)) (-4454 . T) (-4453 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-372))) (|HasAttribute| |#1| (QUOTE -4456)) (|HasAttribute| |#1| (QUOTE -4457)) (|HasAttribute| |#1| (QUOTE -4452))) +(-1308 |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."))) -((-4451 |has| |#2| (-6 -4451)) (-4453 . T) (-4452 . T) (-4455 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4451))) -(-1308) +((-4452 |has| |#2| (-6 -4452)) (-4454 . T) (-4453 . T) (-4456 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4452))) +(-1309) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1309 A) +(-1310 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 -(-1310 R |ls| |ls2|) +(-1311 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 -(-1311 R) +(-1312 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 -(-1312 |p|) +(-1313 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4460 "*") . T) (-4452 . T) (-4453 . T) (-4455 . T)) +(((-4461 "*") . T) (-4453 . T) (-4454 . T) (-4456 . T)) NIL NIL NIL @@ -5196,4 +5200,4 @@ NIL NIL NIL NIL -((-3 NIL 2266071 2266076 2266081 2266086) (-2 NIL 2266051 2266056 2266061 2266066) (-1 NIL 2266031 2266036 2266041 2266046) (0 NIL 2266011 2266016 2266021 2266026) (-1312 "ZMOD.spad" 2265820 2265833 2265949 2266006) (-1311 "ZLINDEP.spad" 2264886 2264897 2265810 2265815) (-1310 "ZDSOLVE.spad" 2254831 2254853 2264876 2264881) (-1309 "YSTREAM.spad" 2254326 2254337 2254821 2254826) (-1308 "YDIAGRAM.spad" 2253960 2253969 2254316 2254321) (-1307 "XRPOLY.spad" 2253180 2253200 2253816 2253885) (-1306 "XPR.spad" 2250975 2250988 2252898 2252997) (-1305 "XPOLY.spad" 2250530 2250541 2250831 2250900) (-1304 "XPOLYC.spad" 2249849 2249865 2250456 2250525) (-1303 "XPBWPOLY.spad" 2248286 2248306 2249629 2249698) (-1302 "XF.spad" 2246749 2246764 2248188 2248281) (-1301 "XF.spad" 2245192 2245209 2246633 2246638) (-1300 "XFALG.spad" 2242240 2242256 2245118 2245187) (-1299 "XEXPPKG.spad" 2241491 2241517 2242230 2242235) (-1298 "XDPOLY.spad" 2241105 2241121 2241347 2241416) (-1297 "XALG.spad" 2240765 2240776 2241061 2241100) (-1296 "WUTSET.spad" 2236604 2236621 2240411 2240438) (-1295 "WP.spad" 2235803 2235847 2236462 2236529) (-1294 "WHILEAST.spad" 2235601 2235610 2235793 2235798) (-1293 "WHEREAST.spad" 2235272 2235281 2235591 2235596) (-1292 "WFFINTBS.spad" 2232935 2232957 2235262 2235267) (-1291 "WEIER.spad" 2231157 2231168 2232925 2232930) (-1290 "VSPACE.spad" 2230830 2230841 2231125 2231152) (-1289 "VSPACE.spad" 2230523 2230536 2230820 2230825) (-1288 "VOID.spad" 2230200 2230209 2230513 2230518) (-1287 "VIEW.spad" 2227880 2227889 2230190 2230195) (-1286 "VIEWDEF.spad" 2223081 2223090 2227870 2227875) (-1285 "VIEW3D.spad" 2207042 2207051 2223071 2223076) (-1284 "VIEW2D.spad" 2194933 2194942 2207032 2207037) (-1283 "VECTOR.spad" 2193607 2193618 2193858 2193885) (-1282 "VECTOR2.spad" 2192246 2192259 2193597 2193602) (-1281 "VECTCAT.spad" 2190150 2190161 2192214 2192241) (-1280 "VECTCAT.spad" 2187861 2187874 2189927 2189932) (-1279 "VARIABLE.spad" 2187641 2187656 2187851 2187856) (-1278 "UTYPE.spad" 2187285 2187294 2187631 2187636) (-1277 "UTSODETL.spad" 2186580 2186604 2187241 2187246) (-1276 "UTSODE.spad" 2184796 2184816 2186570 2186575) (-1275 "UTS.spad" 2179600 2179628 2183263 2183360) (-1274 "UTSCAT.spad" 2177079 2177095 2179498 2179595) (-1273 "UTSCAT.spad" 2174202 2174220 2176623 2176628) (-1272 "UTS2.spad" 2173797 2173832 2174192 2174197) (-1271 "URAGG.spad" 2168470 2168481 2173787 2173792) (-1270 "URAGG.spad" 2163107 2163120 2168426 2168431) (-1269 "UPXSSING.spad" 2160752 2160778 2162188 2162321) (-1268 "UPXS.spad" 2157906 2157934 2158884 2159033) (-1267 "UPXSCONS.spad" 2155665 2155685 2156038 2156187) (-1266 "UPXSCCA.spad" 2154236 2154256 2155511 2155660) (-1265 "UPXSCCA.spad" 2152949 2152971 2154226 2154231) (-1264 "UPXSCAT.spad" 2151538 2151554 2152795 2152944) (-1263 "UPXS2.spad" 2151081 2151134 2151528 2151533) (-1262 "UPSQFREE.spad" 2149495 2149509 2151071 2151076) (-1261 "UPSCAT.spad" 2147282 2147306 2149393 2149490) (-1260 "UPSCAT.spad" 2144775 2144801 2146888 2146893) (-1259 "UPOLYC.spad" 2139815 2139826 2144617 2144770) (-1258 "UPOLYC.spad" 2134747 2134760 2139551 2139556) (-1257 "UPOLYC2.spad" 2134218 2134237 2134737 2134742) (-1256 "UP.spad" 2131417 2131432 2131804 2131957) (-1255 "UPMP.spad" 2130317 2130330 2131407 2131412) (-1254 "UPDIVP.spad" 2129882 2129896 2130307 2130312) (-1253 "UPDECOMP.spad" 2128127 2128141 2129872 2129877) (-1252 "UPCDEN.spad" 2127336 2127352 2128117 2128122) (-1251 "UP2.spad" 2126700 2126721 2127326 2127331) (-1250 "UNISEG.spad" 2126053 2126064 2126619 2126624) (-1249 "UNISEG2.spad" 2125550 2125563 2126009 2126014) (-1248 "UNIFACT.spad" 2124653 2124665 2125540 2125545) (-1247 "ULS.spad" 2115211 2115239 2116298 2116727) (-1246 "ULSCONS.spad" 2107607 2107627 2107977 2108126) (-1245 "ULSCCAT.spad" 2105344 2105364 2107453 2107602) (-1244 "ULSCCAT.spad" 2103189 2103211 2105300 2105305) (-1243 "ULSCAT.spad" 2101421 2101437 2103035 2103184) (-1242 "ULS2.spad" 2100935 2100988 2101411 2101416) (-1241 "UINT8.spad" 2100812 2100821 2100925 2100930) (-1240 "UINT64.spad" 2100688 2100697 2100802 2100807) (-1239 "UINT32.spad" 2100564 2100573 2100678 2100683) (-1238 "UINT16.spad" 2100440 2100449 2100554 2100559) (-1237 "UFD.spad" 2099505 2099514 2100366 2100435) (-1236 "UFD.spad" 2098632 2098643 2099495 2099500) (-1235 "UDVO.spad" 2097513 2097522 2098622 2098627) (-1234 "UDPO.spad" 2095006 2095017 2097469 2097474) (-1233 "TYPE.spad" 2094938 2094947 2094996 2095001) (-1232 "TYPEAST.spad" 2094857 2094866 2094928 2094933) (-1231 "TWOFACT.spad" 2093509 2093524 2094847 2094852) (-1230 "TUPLE.spad" 2092995 2093006 2093408 2093413) (-1229 "TUBETOOL.spad" 2089862 2089871 2092985 2092990) (-1228 "TUBE.spad" 2088509 2088526 2089852 2089857) (-1227 "TS.spad" 2087108 2087124 2088074 2088171) (-1226 "TSETCAT.spad" 2074235 2074252 2087076 2087103) (-1225 "TSETCAT.spad" 2061348 2061367 2074191 2074196) (-1224 "TRMANIP.spad" 2055714 2055731 2061054 2061059) (-1223 "TRIMAT.spad" 2054677 2054702 2055704 2055709) (-1222 "TRIGMNIP.spad" 2053204 2053221 2054667 2054672) (-1221 "TRIGCAT.spad" 2052716 2052725 2053194 2053199) (-1220 "TRIGCAT.spad" 2052226 2052237 2052706 2052711) (-1219 "TREE.spad" 2050801 2050812 2051833 2051860) (-1218 "TRANFUN.spad" 2050640 2050649 2050791 2050796) (-1217 "TRANFUN.spad" 2050477 2050488 2050630 2050635) (-1216 "TOPSP.spad" 2050151 2050160 2050467 2050472) (-1215 "TOOLSIGN.spad" 2049814 2049825 2050141 2050146) (-1214 "TEXTFILE.spad" 2048375 2048384 2049804 2049809) (-1213 "TEX.spad" 2045521 2045530 2048365 2048370) (-1212 "TEX1.spad" 2045077 2045088 2045511 2045516) (-1211 "TEMUTL.spad" 2044632 2044641 2045067 2045072) (-1210 "TBCMPPK.spad" 2042725 2042748 2044622 2044627) (-1209 "TBAGG.spad" 2041775 2041798 2042705 2042720) (-1208 "TBAGG.spad" 2040833 2040858 2041765 2041770) (-1207 "TANEXP.spad" 2040241 2040252 2040823 2040828) (-1206 "TALGOP.spad" 2039965 2039976 2040231 2040236) (-1205 "TABLE.spad" 2038376 2038399 2038646 2038673) (-1204 "TABLEAU.spad" 2037857 2037868 2038366 2038371) (-1203 "TABLBUMP.spad" 2034660 2034671 2037847 2037852) (-1202 "SYSTEM.spad" 2033888 2033897 2034650 2034655) (-1201 "SYSSOLP.spad" 2031371 2031382 2033878 2033883) (-1200 "SYSPTR.spad" 2031270 2031279 2031361 2031366) (-1199 "SYSNNI.spad" 2030452 2030463 2031260 2031265) (-1198 "SYSINT.spad" 2029856 2029867 2030442 2030447) (-1197 "SYNTAX.spad" 2026062 2026071 2029846 2029851) (-1196 "SYMTAB.spad" 2024130 2024139 2026052 2026057) (-1195 "SYMS.spad" 2020153 2020162 2024120 2024125) (-1194 "SYMPOLY.spad" 2019160 2019171 2019242 2019369) (-1193 "SYMFUNC.spad" 2018661 2018672 2019150 2019155) (-1192 "SYMBOL.spad" 2016164 2016173 2018651 2018656) (-1191 "SWITCH.spad" 2012935 2012944 2016154 2016159) (-1190 "SUTS.spad" 2009840 2009868 2011402 2011499) (-1189 "SUPXS.spad" 2006981 2007009 2007972 2008121) (-1188 "SUP.spad" 2003794 2003805 2004567 2004720) (-1187 "SUPFRACF.spad" 2002899 2002917 2003784 2003789) (-1186 "SUP2.spad" 2002291 2002304 2002889 2002894) (-1185 "SUMRF.spad" 2001265 2001276 2002281 2002286) (-1184 "SUMFS.spad" 2000902 2000919 2001255 2001260) (-1183 "SULS.spad" 1991447 1991475 1992547 1992976) (-1182 "SUCHTAST.spad" 1991216 1991225 1991437 1991442) (-1181 "SUCH.spad" 1990898 1990913 1991206 1991211) (-1180 "SUBSPACE.spad" 1983013 1983028 1990888 1990893) (-1179 "SUBRESP.spad" 1982183 1982197 1982969 1982974) (-1178 "STTF.spad" 1978282 1978298 1982173 1982178) (-1177 "STTFNC.spad" 1974750 1974766 1978272 1978277) (-1176 "STTAYLOR.spad" 1967385 1967396 1974631 1974636) (-1175 "STRTBL.spad" 1965890 1965907 1966039 1966066) (-1174 "STRING.spad" 1965299 1965308 1965313 1965340) (-1173 "STRICAT.spad" 1965087 1965096 1965267 1965294) (-1172 "STREAM.spad" 1962005 1962016 1964612 1964627) (-1171 "STREAM3.spad" 1961578 1961593 1961995 1962000) (-1170 "STREAM2.spad" 1960706 1960719 1961568 1961573) (-1169 "STREAM1.spad" 1960412 1960423 1960696 1960701) (-1168 "STINPROD.spad" 1959348 1959364 1960402 1960407) (-1167 "STEP.spad" 1958549 1958558 1959338 1959343) (-1166 "STEPAST.spad" 1957783 1957792 1958539 1958544) (-1165 "STBL.spad" 1956309 1956337 1956476 1956491) (-1164 "STAGG.spad" 1955384 1955395 1956299 1956304) (-1163 "STAGG.spad" 1954457 1954470 1955374 1955379) (-1162 "STACK.spad" 1953814 1953825 1954064 1954091) (-1161 "SREGSET.spad" 1951518 1951535 1953460 1953487) (-1160 "SRDCMPK.spad" 1950079 1950099 1951508 1951513) (-1159 "SRAGG.spad" 1945222 1945231 1950047 1950074) (-1158 "SRAGG.spad" 1940385 1940396 1945212 1945217) (-1157 "SQMATRIX.spad" 1938057 1938075 1938973 1939060) (-1156 "SPLTREE.spad" 1932609 1932622 1937493 1937520) (-1155 "SPLNODE.spad" 1929197 1929210 1932599 1932604) (-1154 "SPFCAT.spad" 1928006 1928015 1929187 1929192) (-1153 "SPECOUT.spad" 1926558 1926567 1927996 1928001) (-1152 "SPADXPT.spad" 1918153 1918162 1926548 1926553) (-1151 "spad-parser.spad" 1917618 1917627 1918143 1918148) (-1150 "SPADAST.spad" 1917319 1917328 1917608 1917613) (-1149 "SPACEC.spad" 1901518 1901529 1917309 1917314) (-1148 "SPACE3.spad" 1901294 1901305 1901508 1901513) (-1147 "SORTPAK.spad" 1900843 1900856 1901250 1901255) (-1146 "SOLVETRA.spad" 1898606 1898617 1900833 1900838) (-1145 "SOLVESER.spad" 1897134 1897145 1898596 1898601) (-1144 "SOLVERAD.spad" 1893160 1893171 1897124 1897129) (-1143 "SOLVEFOR.spad" 1891622 1891640 1893150 1893155) (-1142 "SNTSCAT.spad" 1891222 1891239 1891590 1891617) (-1141 "SMTS.spad" 1889494 1889520 1890787 1890884) (-1140 "SMP.spad" 1886969 1886989 1887359 1887486) (-1139 "SMITH.spad" 1885814 1885839 1886959 1886964) (-1138 "SMATCAT.spad" 1883924 1883954 1885758 1885809) (-1137 "SMATCAT.spad" 1881966 1881998 1883802 1883807) (-1136 "SKAGG.spad" 1880929 1880940 1881934 1881961) (-1135 "SINT.spad" 1879869 1879878 1880795 1880924) (-1134 "SIMPAN.spad" 1879597 1879606 1879859 1879864) (-1133 "SIG.spad" 1878927 1878936 1879587 1879592) (-1132 "SIGNRF.spad" 1878045 1878056 1878917 1878922) (-1131 "SIGNEF.spad" 1877324 1877341 1878035 1878040) (-1130 "SIGAST.spad" 1876709 1876718 1877314 1877319) (-1129 "SHP.spad" 1874637 1874652 1876665 1876670) (-1128 "SHDP.spad" 1864583 1864610 1865092 1865223) (-1127 "SGROUP.spad" 1864191 1864200 1864573 1864578) (-1126 "SGROUP.spad" 1863797 1863808 1864181 1864186) (-1125 "SGCF.spad" 1856936 1856945 1863787 1863792) (-1124 "SFRTCAT.spad" 1855866 1855883 1856904 1856931) (-1123 "SFRGCD.spad" 1854929 1854949 1855856 1855861) (-1122 "SFQCMPK.spad" 1849566 1849586 1854919 1854924) (-1121 "SFORT.spad" 1849005 1849019 1849556 1849561) (-1120 "SEXOF.spad" 1848848 1848888 1848995 1849000) (-1119 "SEX.spad" 1848740 1848749 1848838 1848843) (-1118 "SEXCAT.spad" 1846521 1846561 1848730 1848735) (-1117 "SET.spad" 1844845 1844856 1845942 1845981) (-1116 "SETMN.spad" 1843295 1843312 1844835 1844840) (-1115 "SETCAT.spad" 1842617 1842626 1843285 1843290) (-1114 "SETCAT.spad" 1841937 1841948 1842607 1842612) (-1113 "SETAGG.spad" 1838486 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(-964 "POLYLIFT.spad" 1559349 1559372 1560074 1560079) (-963 "POLYCATQ.spad" 1557467 1557489 1559339 1559344) (-962 "POLYCAT.spad" 1550937 1550958 1557335 1557462) (-961 "POLYCAT.spad" 1543745 1543768 1550145 1550150) (-960 "POLY2UP.spad" 1543197 1543211 1543735 1543740) (-959 "POLY2.spad" 1542794 1542806 1543187 1543192) (-958 "POLUTIL.spad" 1541735 1541764 1542750 1542755) (-957 "POLTOPOL.spad" 1540483 1540498 1541725 1541730) (-956 "POINT.spad" 1539321 1539331 1539408 1539435) (-955 "PNTHEORY.spad" 1536023 1536031 1539311 1539316) (-954 "PMTOOLS.spad" 1534798 1534812 1536013 1536018) (-953 "PMSYM.spad" 1534347 1534357 1534788 1534793) (-952 "PMQFCAT.spad" 1533938 1533952 1534337 1534342) (-951 "PMPRED.spad" 1533417 1533431 1533928 1533933) (-950 "PMPREDFS.spad" 1532871 1532893 1533407 1533412) (-949 "PMPLCAT.spad" 1531951 1531969 1532803 1532808) (-948 "PMLSAGG.spad" 1531536 1531550 1531941 1531946) (-947 "PMKERNEL.spad" 1531115 1531127 1531526 1531531) (-946 "PMINS.spad" 1530695 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1404820) (-870 "OUTBCON.spad" 1403249 1403257 1404233 1404238) (-869 "OUTBCON.spad" 1402253 1402263 1403239 1403244) (-868 "OSI.spad" 1401728 1401736 1402243 1402248) (-867 "OSGROUP.spad" 1401646 1401654 1401718 1401723) (-866 "ORTHPOL.spad" 1400131 1400141 1401563 1401568) (-865 "OREUP.spad" 1399584 1399612 1399811 1399850) (-864 "ORESUP.spad" 1398885 1398909 1399264 1399303) (-863 "OREPCTO.spad" 1396742 1396754 1398805 1398810) (-862 "OREPCAT.spad" 1390889 1390899 1396698 1396737) (-861 "OREPCAT.spad" 1384926 1384938 1390737 1390742) (-860 "ORDSET.spad" 1384098 1384106 1384916 1384921) (-859 "ORDSET.spad" 1383268 1383278 1384088 1384093) (-858 "ORDRING.spad" 1382658 1382666 1383248 1383263) (-857 "ORDRING.spad" 1382056 1382066 1382648 1382653) (-856 "ORDMON.spad" 1381911 1381919 1382046 1382051) (-855 "ORDFUNS.spad" 1381043 1381059 1381901 1381906) (-854 "ORDFIN.spad" 1380863 1380871 1381033 1381038) (-853 "ORDCOMP.spad" 1379328 1379338 1380410 1380439) (-852 "ORDCOMP2.spad" 1378621 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(-757 "NAGC06.spad" 1154516 1154524 1158631 1158636) (-756 "NAGC05.spad" 1153017 1153025 1154506 1154511) (-755 "NAGC02.spad" 1152284 1152292 1153007 1153012) (-754 "NAALG.spad" 1151825 1151835 1152252 1152279) (-753 "NAALG.spad" 1151386 1151398 1151815 1151820) (-752 "MULTSQFR.spad" 1148344 1148361 1151376 1151381) (-751 "MULTFACT.spad" 1147727 1147744 1148334 1148339) (-750 "MTSCAT.spad" 1145821 1145842 1147625 1147722) (-749 "MTHING.spad" 1145480 1145490 1145811 1145816) (-748 "MSYSCMD.spad" 1144914 1144922 1145470 1145475) (-747 "MSET.spad" 1142872 1142882 1144620 1144659) (-746 "MSETAGG.spad" 1142717 1142727 1142840 1142867) (-745 "MRING.spad" 1139694 1139706 1142425 1142492) (-744 "MRF2.spad" 1139264 1139278 1139684 1139689) (-743 "MRATFAC.spad" 1138810 1138827 1139254 1139259) (-742 "MPRFF.spad" 1136850 1136869 1138800 1138805) (-741 "MPOLY.spad" 1134321 1134336 1134680 1134807) (-740 "MPCPF.spad" 1133585 1133604 1134311 1134316) (-739 "MPC3.spad" 1133402 1133442 1133575 1133580) (-738 "MPC2.spad" 1133048 1133081 1133392 1133397) (-737 "MONOTOOL.spad" 1131399 1131416 1133038 1133043) (-736 "MONOID.spad" 1130718 1130726 1131389 1131394) (-735 "MONOID.spad" 1130035 1130045 1130708 1130713) (-734 "MONOGEN.spad" 1128783 1128796 1129895 1130030) (-733 "MONOGEN.spad" 1127553 1127568 1128667 1128672) (-732 "MONADWU.spad" 1125583 1125591 1127543 1127548) (-731 "MONADWU.spad" 1123611 1123621 1125573 1125578) (-730 "MONAD.spad" 1122771 1122779 1123601 1123606) (-729 "MONAD.spad" 1121929 1121939 1122761 1122766) (-728 "MOEBIUS.spad" 1120665 1120679 1121909 1121924) (-727 "MODULE.spad" 1120535 1120545 1120633 1120660) (-726 "MODULE.spad" 1120425 1120437 1120525 1120530) (-725 "MODRING.spad" 1119760 1119799 1120405 1120420) (-724 "MODOP.spad" 1118425 1118437 1119582 1119649) (-723 "MODMONOM.spad" 1118156 1118174 1118415 1118420) (-722 "MODMON.spad" 1114951 1114967 1115670 1115823) (-721 "MODFIELD.spad" 1114313 1114352 1114853 1114946) (-720 "MMLFORM.spad" 1113173 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(-682 "LWORD.spad" 1047633 1047650 1050918 1050923) (-681 "LSTAST.spad" 1047417 1047425 1047623 1047628) (-680 "LSQM.spad" 1045703 1045717 1046097 1046148) (-679 "LSPP.spad" 1045238 1045255 1045693 1045698) (-678 "LSMP.spad" 1044088 1044116 1045228 1045233) (-677 "LSMP1.spad" 1041906 1041920 1044078 1044083) (-676 "LSAGG.spad" 1041575 1041585 1041874 1041901) (-675 "LSAGG.spad" 1041264 1041276 1041565 1041570) (-674 "LPOLY.spad" 1040218 1040237 1041120 1041189) (-673 "LPEFRAC.spad" 1039489 1039499 1040208 1040213) (-672 "LO.spad" 1038890 1038904 1039423 1039450) (-671 "LOGIC.spad" 1038492 1038500 1038880 1038885) (-670 "LOGIC.spad" 1038092 1038102 1038482 1038487) (-669 "LODOOPS.spad" 1037022 1037034 1038082 1038087) (-668 "LODO.spad" 1036406 1036422 1036702 1036741) (-667 "LODOF.spad" 1035452 1035469 1036363 1036368) (-666 "LODOCAT.spad" 1034118 1034128 1035408 1035447) (-665 "LODOCAT.spad" 1032782 1032794 1034074 1034079) (-664 "LODO2.spad" 1032055 1032067 1032462 1032501) (-663 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(-644 "LIECAT.spad" 1002502 1002512 1002952 1003021) (-643 "LIECAT.spad" 1002006 1002018 1002458 1002463) (-642 "LIB.spad" 1000219 1000227 1000665 1000680) (-641 "LGROBP.spad" 997572 997591 1000209 1000214) (-640 "LF.spad" 996527 996543 997562 997567) (-639 "LFCAT.spad" 995586 995594 996517 996522) (-638 "LEXTRIPK.spad" 991089 991104 995576 995581) (-637 "LEXP.spad" 989092 989119 991069 991084) (-636 "LETAST.spad" 988791 988799 989082 989087) (-635 "LEADCDET.spad" 987189 987206 988781 988786) (-634 "LAZM3PK.spad" 985893 985915 987179 987184) (-633 "LAUPOL.spad" 984586 984599 985486 985555) (-632 "LAPLACE.spad" 984169 984185 984576 984581) (-631 "LA.spad" 983609 983623 984091 984130) (-630 "LALG.spad" 983385 983395 983589 983604) (-629 "LALG.spad" 983169 983181 983375 983380) (-628 "KVTFROM.spad" 982904 982914 983159 983164) (-627 "KTVLOGIC.spad" 982416 982424 982894 982899) (-626 "KRCFROM.spad" 982154 982164 982406 982411) (-625 "KOVACIC.spad" 980877 980894 982144 982149) (-624 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196014 200156 200249) (-175 "CONDUIT.spad" 195762 195770 195994 195999) (-174 "COMRING.spad" 195436 195444 195700 195757) (-173 "COMPPROP.spad" 194954 194962 195426 195431) (-172 "COMPLPAT.spad" 194721 194736 194944 194949) (-171 "COMPLEX.spad" 188858 188868 189102 189363) (-170 "COMPLEX2.spad" 188573 188585 188848 188853) (-169 "COMPILER.spad" 188122 188130 188563 188568) (-168 "COMPFACT.spad" 187724 187738 188112 188117) (-167 "COMPCAT.spad" 185796 185806 187458 187719) (-166 "COMPCAT.spad" 183596 183608 185260 185265) (-165 "COMMUPC.spad" 183344 183362 183586 183591) (-164 "COMMONOP.spad" 182877 182885 183334 183339) (-163 "COMM.spad" 182688 182696 182867 182872) (-162 "COMMAAST.spad" 182451 182459 182678 182683) (-161 "COMBOPC.spad" 181366 181374 182441 182446) (-160 "COMBINAT.spad" 180133 180143 181356 181361) (-159 "COMBF.spad" 177515 177531 180123 180128) (-158 "COLOR.spad" 176352 176360 177505 177510) (-157 "COLONAST.spad" 176018 176026 176342 176347) (-156 "CMPLXRT.spad" 175729 175746 176008 176013) (-155 "CLLCTAST.spad" 175391 175399 175719 175724) (-154 "CLIP.spad" 171499 171507 175381 175386) (-153 "CLIF.spad" 170154 170170 171455 171494) (-152 "CLAGG.spad" 166659 166669 170144 170149) (-151 "CLAGG.spad" 163035 163047 166522 166527) (-150 "CINTSLPE.spad" 162366 162379 163025 163030) (-149 "CHVAR.spad" 160504 160526 162356 162361) (-148 "CHARZ.spad" 160419 160427 160484 160499) (-147 "CHARPOL.spad" 159929 159939 160409 160414) (-146 "CHARNZ.spad" 159682 159690 159909 159924) (-145 "CHAR.spad" 157556 157564 159672 159677) (-144 "CFCAT.spad" 156884 156892 157546 157551) (-143 "CDEN.spad" 156080 156094 156874 156879) (-142 "CCLASS.spad" 154229 154237 155491 155530) (-141 "CATEGORY.spad" 153271 153279 154219 154224) (-140 "CATCTOR.spad" 153162 153170 153261 153266) (-139 "CATAST.spad" 152780 152788 153152 153157) (-138 "CASEAST.spad" 152494 152502 152770 152775) (-137 "CARTEN.spad" 147861 147885 152484 152489) (-136 "CARTEN2.spad" 147251 147278 147851 147856) (-135 "CARD.spad" 144546 144554 147225 147246) (-134 "CAPSLAST.spad" 144320 144328 144536 144541) (-133 "CACHSET.spad" 143944 143952 144310 144315) (-132 "CABMON.spad" 143499 143507 143934 143939) (-131 "BYTEORD.spad" 143174 143182 143489 143494) (-130 "BYTE.spad" 142601 142609 143164 143169) (-129 "BYTEBUF.spad" 140460 140468 141770 141797) (-128 "BTREE.spad" 139533 139543 140067 140094) (-127 "BTOURN.spad" 138538 138548 139140 139167) (-126 "BTCAT.spad" 137930 137940 138506 138533) (-125 "BTCAT.spad" 137342 137354 137920 137925) (-124 "BTAGG.spad" 136808 136816 137310 137337) (-123 "BTAGG.spad" 136294 136304 136798 136803) (-122 "BSTREE.spad" 135035 135045 135901 135928) (-121 "BRILL.spad" 133232 133243 135025 135030) (-120 "BRAGG.spad" 132172 132182 133222 133227) (-119 "BRAGG.spad" 131076 131088 132128 132133) (-118 "BPADICRT.spad" 129057 129069 129312 129405) (-117 "BPADIC.spad" 128721 128733 128983 129052) (-116 "BOUNDZRO.spad" 128377 128394 128711 128716) (-115 "BOP.spad" 123559 123567 128367 128372) (-114 "BOP1.spad" 121025 121035 123549 123554) (-113 "BOOLE.spad" 120675 120683 121015 121020) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2266720 2266725 2266730 2266735) (-2 NIL 2266700 2266705 2266710 2266715) (-1 NIL 2266680 2266685 2266690 2266695) (0 NIL 2266660 2266665 2266670 2266675) (-1313 "ZMOD.spad" 2266469 2266482 2266598 2266655) (-1312 "ZLINDEP.spad" 2265535 2265546 2266459 2266464) (-1311 "ZDSOLVE.spad" 2255480 2255502 2265525 2265530) (-1310 "YSTREAM.spad" 2254975 2254986 2255470 2255475) (-1309 "YDIAGRAM.spad" 2254609 2254618 2254965 2254970) (-1308 "XRPOLY.spad" 2253829 2253849 2254465 2254534) (-1307 "XPR.spad" 2251624 2251637 2253547 2253646) (-1306 "XPOLY.spad" 2251179 2251190 2251480 2251549) (-1305 "XPOLYC.spad" 2250498 2250514 2251105 2251174) (-1304 "XPBWPOLY.spad" 2248935 2248955 2250278 2250347) (-1303 "XF.spad" 2247398 2247413 2248837 2248930) (-1302 "XF.spad" 2245841 2245858 2247282 2247287) (-1301 "XFALG.spad" 2242889 2242905 2245767 2245836) (-1300 "XEXPPKG.spad" 2242140 2242166 2242879 2242884) (-1299 "XDPOLY.spad" 2241754 2241770 2241996 2242065) (-1298 "XALG.spad" 2241414 2241425 2241710 2241749) (-1297 "WUTSET.spad" 2237253 2237270 2241060 2241087) (-1296 "WP.spad" 2236452 2236496 2237111 2237178) (-1295 "WHILEAST.spad" 2236250 2236259 2236442 2236447) (-1294 "WHEREAST.spad" 2235921 2235930 2236240 2236245) (-1293 "WFFINTBS.spad" 2233584 2233606 2235911 2235916) (-1292 "WEIER.spad" 2231806 2231817 2233574 2233579) (-1291 "VSPACE.spad" 2231479 2231490 2231774 2231801) (-1290 "VSPACE.spad" 2231172 2231185 2231469 2231474) (-1289 "VOID.spad" 2230849 2230858 2231162 2231167) (-1288 "VIEW.spad" 2228529 2228538 2230839 2230844) (-1287 "VIEWDEF.spad" 2223730 2223739 2228519 2228524) (-1286 "VIEW3D.spad" 2207691 2207700 2223720 2223725) (-1285 "VIEW2D.spad" 2195582 2195591 2207681 2207686) (-1284 "VECTOR.spad" 2194256 2194267 2194507 2194534) (-1283 "VECTOR2.spad" 2192895 2192908 2194246 2194251) (-1282 "VECTCAT.spad" 2190799 2190810 2192863 2192890) (-1281 "VECTCAT.spad" 2188510 2188523 2190576 2190581) (-1280 "VARIABLE.spad" 2188290 2188305 2188500 2188505) (-1279 "UTYPE.spad" 2187934 2187943 2188280 2188285) (-1278 "UTSODETL.spad" 2187229 2187253 2187890 2187895) (-1277 "UTSODE.spad" 2185445 2185465 2187219 2187224) (-1276 "UTS.spad" 2180249 2180277 2183912 2184009) (-1275 "UTSCAT.spad" 2177728 2177744 2180147 2180244) (-1274 "UTSCAT.spad" 2174851 2174869 2177272 2177277) (-1273 "UTS2.spad" 2174446 2174481 2174841 2174846) (-1272 "URAGG.spad" 2169119 2169130 2174436 2174441) (-1271 "URAGG.spad" 2163756 2163769 2169075 2169080) (-1270 "UPXSSING.spad" 2161401 2161427 2162837 2162970) (-1269 "UPXS.spad" 2158555 2158583 2159533 2159682) (-1268 "UPXSCONS.spad" 2156314 2156334 2156687 2156836) (-1267 "UPXSCCA.spad" 2154885 2154905 2156160 2156309) (-1266 "UPXSCCA.spad" 2153598 2153620 2154875 2154880) (-1265 "UPXSCAT.spad" 2152187 2152203 2153444 2153593) (-1264 "UPXS2.spad" 2151730 2151783 2152177 2152182) (-1263 "UPSQFREE.spad" 2150144 2150158 2151720 2151725) (-1262 "UPSCAT.spad" 2147931 2147955 2150042 2150139) (-1261 "UPSCAT.spad" 2145424 2145450 2147537 2147542) (-1260 "UPOLYC.spad" 2140464 2140475 2145266 2145419) (-1259 "UPOLYC.spad" 2135396 2135409 2140200 2140205) (-1258 "UPOLYC2.spad" 2134867 2134886 2135386 2135391) (-1257 "UP.spad" 2132066 2132081 2132453 2132606) (-1256 "UPMP.spad" 2130966 2130979 2132056 2132061) (-1255 "UPDIVP.spad" 2130531 2130545 2130956 2130961) (-1254 "UPDECOMP.spad" 2128776 2128790 2130521 2130526) (-1253 "UPCDEN.spad" 2127985 2128001 2128766 2128771) (-1252 "UP2.spad" 2127349 2127370 2127975 2127980) (-1251 "UNISEG.spad" 2126702 2126713 2127268 2127273) (-1250 "UNISEG2.spad" 2126199 2126212 2126658 2126663) (-1249 "UNIFACT.spad" 2125302 2125314 2126189 2126194) (-1248 "ULS.spad" 2115860 2115888 2116947 2117376) (-1247 "ULSCONS.spad" 2108256 2108276 2108626 2108775) (-1246 "ULSCCAT.spad" 2105993 2106013 2108102 2108251) (-1245 "ULSCCAT.spad" 2103838 2103860 2105949 2105954) (-1244 "ULSCAT.spad" 2102070 2102086 2103684 2103833) (-1243 "ULS2.spad" 2101584 2101637 2102060 2102065) (-1242 "UINT8.spad" 2101461 2101470 2101574 2101579) (-1241 "UINT64.spad" 2101337 2101346 2101451 2101456) (-1240 "UINT32.spad" 2101213 2101222 2101327 2101332) (-1239 "UINT16.spad" 2101089 2101098 2101203 2101208) (-1238 "UFD.spad" 2100154 2100163 2101015 2101084) (-1237 "UFD.spad" 2099281 2099292 2100144 2100149) (-1236 "UDVO.spad" 2098162 2098171 2099271 2099276) (-1235 "UDPO.spad" 2095655 2095666 2098118 2098123) (-1234 "TYPE.spad" 2095587 2095596 2095645 2095650) (-1233 "TYPEAST.spad" 2095506 2095515 2095577 2095582) (-1232 "TWOFACT.spad" 2094158 2094173 2095496 2095501) (-1231 "TUPLE.spad" 2093644 2093655 2094057 2094062) (-1230 "TUBETOOL.spad" 2090511 2090520 2093634 2093639) (-1229 "TUBE.spad" 2089158 2089175 2090501 2090506) (-1228 "TS.spad" 2087757 2087773 2088723 2088820) (-1227 "TSETCAT.spad" 2074884 2074901 2087725 2087752) (-1226 "TSETCAT.spad" 2061997 2062016 2074840 2074845) (-1225 "TRMANIP.spad" 2056363 2056380 2061703 2061708) (-1224 "TRIMAT.spad" 2055326 2055351 2056353 2056358) (-1223 "TRIGMNIP.spad" 2053853 2053870 2055316 2055321) (-1222 "TRIGCAT.spad" 2053365 2053374 2053843 2053848) (-1221 "TRIGCAT.spad" 2052875 2052886 2053355 2053360) (-1220 "TREE.spad" 2051450 2051461 2052482 2052509) (-1219 "TRANFUN.spad" 2051289 2051298 2051440 2051445) (-1218 "TRANFUN.spad" 2051126 2051137 2051279 2051284) (-1217 "TOPSP.spad" 2050800 2050809 2051116 2051121) (-1216 "TOOLSIGN.spad" 2050463 2050474 2050790 2050795) (-1215 "TEXTFILE.spad" 2049024 2049033 2050453 2050458) (-1214 "TEX.spad" 2046170 2046179 2049014 2049019) (-1213 "TEX1.spad" 2045726 2045737 2046160 2046165) (-1212 "TEMUTL.spad" 2045281 2045290 2045716 2045721) (-1211 "TBCMPPK.spad" 2043374 2043397 2045271 2045276) (-1210 "TBAGG.spad" 2042424 2042447 2043354 2043369) (-1209 "TBAGG.spad" 2041482 2041507 2042414 2042419) (-1208 "TANEXP.spad" 2040890 2040901 2041472 2041477) (-1207 "TALGOP.spad" 2040614 2040625 2040880 2040885) (-1206 "TABLE.spad" 2039025 2039048 2039295 2039322) (-1205 "TABLEAU.spad" 2038506 2038517 2039015 2039020) (-1204 "TABLBUMP.spad" 2035309 2035320 2038496 2038501) (-1203 "SYSTEM.spad" 2034537 2034546 2035299 2035304) (-1202 "SYSSOLP.spad" 2032020 2032031 2034527 2034532) (-1201 "SYSPTR.spad" 2031919 2031928 2032010 2032015) (-1200 "SYSNNI.spad" 2031101 2031112 2031909 2031914) (-1199 "SYSINT.spad" 2030505 2030516 2031091 2031096) (-1198 "SYNTAX.spad" 2026711 2026720 2030495 2030500) (-1197 "SYMTAB.spad" 2024779 2024788 2026701 2026706) (-1196 "SYMS.spad" 2020802 2020811 2024769 2024774) (-1195 "SYMPOLY.spad" 2019809 2019820 2019891 2020018) (-1194 "SYMFUNC.spad" 2019310 2019321 2019799 2019804) (-1193 "SYMBOL.spad" 2016813 2016822 2019300 2019305) (-1192 "SWITCH.spad" 2013584 2013593 2016803 2016808) (-1191 "SUTS.spad" 2010489 2010517 2012051 2012148) (-1190 "SUPXS.spad" 2007630 2007658 2008621 2008770) (-1189 "SUP.spad" 2004443 2004454 2005216 2005369) (-1188 "SUPFRACF.spad" 2003548 2003566 2004433 2004438) (-1187 "SUP2.spad" 2002940 2002953 2003538 2003543) (-1186 "SUMRF.spad" 2001914 2001925 2002930 2002935) (-1185 "SUMFS.spad" 2001551 2001568 2001904 2001909) (-1184 "SULS.spad" 1992096 1992124 1993196 1993625) (-1183 "SUCHTAST.spad" 1991865 1991874 1992086 1992091) (-1182 "SUCH.spad" 1991547 1991562 1991855 1991860) (-1181 "SUBSPACE.spad" 1983662 1983677 1991537 1991542) (-1180 "SUBRESP.spad" 1982832 1982846 1983618 1983623) (-1179 "STTF.spad" 1978931 1978947 1982822 1982827) (-1178 "STTFNC.spad" 1975399 1975415 1978921 1978926) (-1177 "STTAYLOR.spad" 1968034 1968045 1975280 1975285) (-1176 "STRTBL.spad" 1966539 1966556 1966688 1966715) (-1175 "STRING.spad" 1965948 1965957 1965962 1965989) (-1174 "STRICAT.spad" 1965736 1965745 1965916 1965943) (-1173 "STREAM.spad" 1962654 1962665 1965261 1965276) (-1172 "STREAM3.spad" 1962227 1962242 1962644 1962649) (-1171 "STREAM2.spad" 1961355 1961368 1962217 1962222) (-1170 "STREAM1.spad" 1961061 1961072 1961345 1961350) (-1169 "STINPROD.spad" 1959997 1960013 1961051 1961056) (-1168 "STEP.spad" 1959198 1959207 1959987 1959992) (-1167 "STEPAST.spad" 1958432 1958441 1959188 1959193) (-1166 "STBL.spad" 1956958 1956986 1957125 1957140) (-1165 "STAGG.spad" 1956033 1956044 1956948 1956953) (-1164 "STAGG.spad" 1955106 1955119 1956023 1956028) (-1163 "STACK.spad" 1954463 1954474 1954713 1954740) (-1162 "SREGSET.spad" 1952167 1952184 1954109 1954136) (-1161 "SRDCMPK.spad" 1950728 1950748 1952157 1952162) (-1160 "SRAGG.spad" 1945871 1945880 1950696 1950723) (-1159 "SRAGG.spad" 1941034 1941045 1945861 1945866) (-1158 "SQMATRIX.spad" 1938706 1938724 1939622 1939709) (-1157 "SPLTREE.spad" 1933258 1933271 1938142 1938169) (-1156 "SPLNODE.spad" 1929846 1929859 1933248 1933253) (-1155 "SPFCAT.spad" 1928655 1928664 1929836 1929841) (-1154 "SPECOUT.spad" 1927207 1927216 1928645 1928650) (-1153 "SPADXPT.spad" 1918802 1918811 1927197 1927202) (-1152 "spad-parser.spad" 1918267 1918276 1918792 1918797) (-1151 "SPADAST.spad" 1917968 1917977 1918257 1918262) (-1150 "SPACEC.spad" 1902167 1902178 1917958 1917963) (-1149 "SPACE3.spad" 1901943 1901954 1902157 1902162) (-1148 "SORTPAK.spad" 1901492 1901505 1901899 1901904) (-1147 "SOLVETRA.spad" 1899255 1899266 1901482 1901487) (-1146 "SOLVESER.spad" 1897783 1897794 1899245 1899250) (-1145 "SOLVERAD.spad" 1893809 1893820 1897773 1897778) (-1144 "SOLVEFOR.spad" 1892271 1892289 1893799 1893804) (-1143 "SNTSCAT.spad" 1891871 1891888 1892239 1892266) (-1142 "SMTS.spad" 1890143 1890169 1891436 1891533) (-1141 "SMP.spad" 1887618 1887638 1888008 1888135) (-1140 "SMITH.spad" 1886463 1886488 1887608 1887613) (-1139 "SMATCAT.spad" 1884573 1884603 1886407 1886458) (-1138 "SMATCAT.spad" 1882615 1882647 1884451 1884456) (-1137 "SKAGG.spad" 1881578 1881589 1882583 1882610) (-1136 "SINT.spad" 1880518 1880527 1881444 1881573) (-1135 "SIMPAN.spad" 1880246 1880255 1880508 1880513) (-1134 "SIG.spad" 1879576 1879585 1880236 1880241) (-1133 "SIGNRF.spad" 1878694 1878705 1879566 1879571) (-1132 "SIGNEF.spad" 1877973 1877990 1878684 1878689) (-1131 "SIGAST.spad" 1877358 1877367 1877963 1877968) (-1130 "SHP.spad" 1875286 1875301 1877314 1877319) (-1129 "SHDP.spad" 1865232 1865259 1865741 1865872) (-1128 "SGROUP.spad" 1864840 1864849 1865222 1865227) (-1127 "SGROUP.spad" 1864446 1864457 1864830 1864835) (-1126 "SGCF.spad" 1857585 1857594 1864436 1864441) (-1125 "SFRTCAT.spad" 1856515 1856532 1857553 1857580) (-1124 "SFRGCD.spad" 1855578 1855598 1856505 1856510) (-1123 "SFQCMPK.spad" 1850215 1850235 1855568 1855573) (-1122 "SFORT.spad" 1849654 1849668 1850205 1850210) (-1121 "SEXOF.spad" 1849497 1849537 1849644 1849649) (-1120 "SEX.spad" 1849389 1849398 1849487 1849492) (-1119 "SEXCAT.spad" 1847170 1847210 1849379 1849384) (-1118 "SET.spad" 1845494 1845505 1846591 1846630) (-1117 "SETMN.spad" 1843944 1843961 1845484 1845489) (-1116 "SETCAT.spad" 1843266 1843275 1843934 1843939) (-1115 "SETCAT.spad" 1842586 1842597 1843256 1843261) (-1114 "SETAGG.spad" 1839135 1839146 1842566 1842581) (-1113 "SETAGG.spad" 1835692 1835705 1839125 1839130) (-1112 "SEQAST.spad" 1835395 1835404 1835682 1835687) (-1111 "SEGXCAT.spad" 1834551 1834564 1835385 1835390) (-1110 "SEG.spad" 1834364 1834375 1834470 1834475) (-1109 "SEGCAT.spad" 1833289 1833300 1834354 1834359) (-1108 "SEGBIND.spad" 1833047 1833058 1833236 1833241) (-1107 "SEGBIND2.spad" 1832745 1832758 1833037 1833042) (-1106 "SEGAST.spad" 1832459 1832468 1832735 1832740) (-1105 "SEG2.spad" 1831894 1831907 1832415 1832420) (-1104 "SDVAR.spad" 1831170 1831181 1831884 1831889) (-1103 "SDPOL.spad" 1828596 1828607 1828887 1829014) (-1102 "SCPKG.spad" 1826685 1826696 1828586 1828591) (-1101 "SCOPE.spad" 1825838 1825847 1826675 1826680) (-1100 "SCACHE.spad" 1824534 1824545 1825828 1825833) (-1099 "SASTCAT.spad" 1824443 1824452 1824524 1824529) (-1098 "SAOS.spad" 1824315 1824324 1824433 1824438) (-1097 "SAERFFC.spad" 1824028 1824048 1824305 1824310) (-1096 "SAE.spad" 1821982 1821998 1822593 1822728) (-1095 "SAEFACT.spad" 1821683 1821703 1821972 1821977) (-1094 "RURPK.spad" 1819342 1819358 1821673 1821678) (-1093 "RULESET.spad" 1818795 1818819 1819332 1819337) (-1092 "RULE.spad" 1817035 1817059 1818785 1818790) (-1091 "RULECOLD.spad" 1816887 1816900 1817025 1817030) (-1090 "RTVALUE.spad" 1816622 1816631 1816877 1816882) (-1089 "RSTRCAST.spad" 1816339 1816348 1816612 1816617) (-1088 "RSETGCD.spad" 1812717 1812737 1816329 1816334) (-1087 "RSETCAT.spad" 1802653 1802670 1812685 1812712) (-1086 "RSETCAT.spad" 1792609 1792628 1802643 1802648) (-1085 "RSDCMPK.spad" 1791061 1791081 1792599 1792604) (-1084 "RRCC.spad" 1789445 1789475 1791051 1791056) (-1083 "RRCC.spad" 1787827 1787859 1789435 1789440) (-1082 "RPTAST.spad" 1787529 1787538 1787817 1787822) (-1081 "RPOLCAT.spad" 1766889 1766904 1787397 1787524) (-1080 "RPOLCAT.spad" 1745962 1745979 1766472 1766477) (-1079 "ROUTINE.spad" 1741845 1741854 1744609 1744636) (-1078 "ROMAN.spad" 1741173 1741182 1741711 1741840) (-1077 "ROIRC.spad" 1740253 1740285 1741163 1741168) (-1076 "RNS.spad" 1739156 1739165 1740155 1740248) (-1075 "RNS.spad" 1738145 1738156 1739146 1739151) (-1074 "RNG.spad" 1737880 1737889 1738135 1738140) (-1073 "RNGBIND.spad" 1737040 1737054 1737835 1737840) (-1072 "RMODULE.spad" 1736805 1736816 1737030 1737035) (-1071 "RMCAT2.spad" 1736225 1736282 1736795 1736800) (-1070 "RMATRIX.spad" 1735049 1735068 1735392 1735431) (-1069 "RMATCAT.spad" 1730628 1730659 1735005 1735044) (-1068 "RMATCAT.spad" 1726097 1726130 1730476 1730481) (-1067 "RLINSET.spad" 1725652 1725663 1726087 1726092) (-1066 "RINTERP.spad" 1725540 1725560 1725642 1725647) (-1065 "RING.spad" 1725010 1725019 1725520 1725535) (-1064 "RING.spad" 1724488 1724499 1725000 1725005) (-1063 "RIDIST.spad" 1723880 1723889 1724478 1724483) (-1062 "RGCHAIN.spad" 1722463 1722479 1723365 1723392) (-1061 "RGBCSPC.spad" 1722244 1722256 1722453 1722458) (-1060 "RGBCMDL.spad" 1721774 1721786 1722234 1722239) (-1059 "RF.spad" 1719416 1719427 1721764 1721769) (-1058 "RFFACTOR.spad" 1718878 1718889 1719406 1719411) (-1057 "RFFACT.spad" 1718613 1718625 1718868 1718873) (-1056 "RFDIST.spad" 1717609 1717618 1718603 1718608) (-1055 "RETSOL.spad" 1717028 1717041 1717599 1717604) (-1054 "RETRACT.spad" 1716456 1716467 1717018 1717023) (-1053 "RETRACT.spad" 1715882 1715895 1716446 1716451) (-1052 "RETAST.spad" 1715694 1715703 1715872 1715877) (-1051 "RESULT.spad" 1713754 1713763 1714341 1714368) (-1050 "RESRING.spad" 1713101 1713148 1713692 1713749) (-1049 "RESLATC.spad" 1712425 1712436 1713091 1713096) (-1048 "REPSQ.spad" 1712156 1712167 1712415 1712420) (-1047 "REP.spad" 1709710 1709719 1712146 1712151) (-1046 "REPDB.spad" 1709417 1709428 1709700 1709705) (-1045 "REP2.spad" 1699075 1699086 1709259 1709264) (-1044 "REP1.spad" 1693271 1693282 1699025 1699030) (-1043 "REGSET.spad" 1691068 1691085 1692917 1692944) (-1042 "REF.spad" 1690403 1690414 1691023 1691028) (-1041 "REDORDER.spad" 1689609 1689626 1690393 1690398) (-1040 "RECLOS.spad" 1688392 1688412 1689096 1689189) (-1039 "REALSOLV.spad" 1687532 1687541 1688382 1688387) (-1038 "REAL.spad" 1687404 1687413 1687522 1687527) (-1037 "REAL0Q.spad" 1684702 1684717 1687394 1687399) (-1036 "REAL0.spad" 1681546 1681561 1684692 1684697) (-1035 "RDUCEAST.spad" 1681267 1681276 1681536 1681541) (-1034 "RDIV.spad" 1680922 1680947 1681257 1681262) (-1033 "RDIST.spad" 1680489 1680500 1680912 1680917) (-1032 "RDETRS.spad" 1679353 1679371 1680479 1680484) (-1031 "RDETR.spad" 1677492 1677510 1679343 1679348) (-1030 "RDEEFS.spad" 1676591 1676608 1677482 1677487) (-1029 "RDEEF.spad" 1675601 1675618 1676581 1676586) (-1028 "RCFIELD.spad" 1672787 1672796 1675503 1675596) (-1027 "RCFIELD.spad" 1670059 1670070 1672777 1672782) (-1026 "RCAGG.spad" 1667987 1667998 1670049 1670054) (-1025 "RCAGG.spad" 1665842 1665855 1667906 1667911) (-1024 "RATRET.spad" 1665202 1665213 1665832 1665837) (-1023 "RATFACT.spad" 1664894 1664906 1665192 1665197) (-1022 "RANDSRC.spad" 1664213 1664222 1664884 1664889) (-1021 "RADUTIL.spad" 1663969 1663978 1664203 1664208) (-1020 "RADIX.spad" 1660890 1660904 1662436 1662529) (-1019 "RADFF.spad" 1659047 1659084 1659166 1659322) (-1018 "RADCAT.spad" 1658642 1658651 1659037 1659042) (-1017 "RADCAT.spad" 1658235 1658246 1658632 1658637) (-1016 "QUEUE.spad" 1657583 1657594 1657842 1657869) (-1015 "QUAT.spad" 1655984 1655995 1656327 1656392) (-1014 "QUATCT2.spad" 1655604 1655623 1655974 1655979) (-1013 "QUATCAT.spad" 1653774 1653785 1655534 1655599) (-1012 "QUATCAT.spad" 1651695 1651708 1653457 1653462) (-1011 "QUAGG.spad" 1650522 1650533 1651663 1651690) (-1010 "QQUTAST.spad" 1650290 1650299 1650512 1650517) (-1009 "QFORM.spad" 1649908 1649923 1650280 1650285) (-1008 "QFCAT.spad" 1648610 1648621 1649810 1649903) (-1007 "QFCAT.spad" 1646903 1646916 1648105 1648110) (-1006 "QFCAT2.spad" 1646595 1646612 1646893 1646898) (-1005 "QEQUAT.spad" 1646153 1646162 1646585 1646590) (-1004 "QCMPACK.spad" 1640899 1640919 1646143 1646148) (-1003 "QALGSET.spad" 1636977 1637010 1640813 1640818) (-1002 "QALGSET2.spad" 1634972 1634991 1636967 1636972) (-1001 "PWFFINTB.spad" 1632387 1632409 1634962 1634967) (-1000 "PUSHVAR.spad" 1631725 1631745 1632377 1632382) (-999 "PTRANFN.spad" 1627853 1627863 1631715 1631720) (-998 "PTPACK.spad" 1624941 1624951 1627843 1627848) (-997 "PTFUNC2.spad" 1624764 1624778 1624931 1624936) (-996 "PTCAT.spad" 1624019 1624029 1624732 1624759) (-995 "PSQFR.spad" 1623326 1623350 1624009 1624014) (-994 "PSEUDLIN.spad" 1622212 1622222 1623316 1623321) (-993 "PSETPK.spad" 1607645 1607661 1622090 1622095) (-992 "PSETCAT.spad" 1601565 1601588 1607625 1607640) (-991 "PSETCAT.spad" 1595459 1595484 1601521 1601526) (-990 "PSCURVE.spad" 1594442 1594450 1595449 1595454) (-989 "PSCAT.spad" 1593225 1593254 1594340 1594437) (-988 "PSCAT.spad" 1592098 1592129 1593215 1593220) (-987 "PRTITION.spad" 1590796 1590804 1592088 1592093) (-986 "PRTDAST.spad" 1590515 1590523 1590786 1590791) (-985 "PRS.spad" 1580077 1580094 1590471 1590476) (-984 "PRQAGG.spad" 1579512 1579522 1580045 1580072) (-983 "PROPLOG.spad" 1579084 1579092 1579502 1579507) (-982 "PROPFUN2.spad" 1578707 1578720 1579074 1579079) (-981 "PROPFUN1.spad" 1578105 1578116 1578697 1578702) (-980 "PROPFRML.spad" 1576673 1576684 1578095 1578100) (-979 "PROPERTY.spad" 1576161 1576169 1576663 1576668) (-978 "PRODUCT.spad" 1573843 1573855 1574127 1574182) (-977 "PR.spad" 1572235 1572247 1572934 1573061) (-976 "PRINT.spad" 1571987 1571995 1572225 1572230) (-975 "PRIMES.spad" 1570240 1570250 1571977 1571982) (-974 "PRIMELT.spad" 1568321 1568335 1570230 1570235) (-973 "PRIMCAT.spad" 1567948 1567956 1568311 1568316) (-972 "PRIMARR.spad" 1566953 1566963 1567131 1567158) (-971 "PRIMARR2.spad" 1565720 1565732 1566943 1566948) (-970 "PREASSOC.spad" 1565102 1565114 1565710 1565715) (-969 "PPCURVE.spad" 1564239 1564247 1565092 1565097) (-968 "PORTNUM.spad" 1564014 1564022 1564229 1564234) (-967 "POLYROOT.spad" 1562863 1562885 1563970 1563975) (-966 "POLY.spad" 1560198 1560208 1560713 1560840) (-965 "POLYLIFT.spad" 1559463 1559486 1560188 1560193) (-964 "POLYCATQ.spad" 1557581 1557603 1559453 1559458) (-963 "POLYCAT.spad" 1551051 1551072 1557449 1557576) (-962 "POLYCAT.spad" 1543859 1543882 1550259 1550264) (-961 "POLY2UP.spad" 1543311 1543325 1543849 1543854) (-960 "POLY2.spad" 1542908 1542920 1543301 1543306) (-959 "POLUTIL.spad" 1541849 1541878 1542864 1542869) (-958 "POLTOPOL.spad" 1540597 1540612 1541839 1541844) (-957 "POINT.spad" 1539435 1539445 1539522 1539549) (-956 "PNTHEORY.spad" 1536137 1536145 1539425 1539430) (-955 "PMTOOLS.spad" 1534912 1534926 1536127 1536132) (-954 "PMSYM.spad" 1534461 1534471 1534902 1534907) (-953 "PMQFCAT.spad" 1534052 1534066 1534451 1534456) (-952 "PMPRED.spad" 1533531 1533545 1534042 1534047) (-951 "PMPREDFS.spad" 1532985 1533007 1533521 1533526) (-950 "PMPLCAT.spad" 1532065 1532083 1532917 1532922) (-949 "PMLSAGG.spad" 1531650 1531664 1532055 1532060) (-948 "PMKERNEL.spad" 1531229 1531241 1531640 1531645) (-947 "PMINS.spad" 1530809 1530819 1531219 1531224) (-946 "PMFS.spad" 1530386 1530404 1530799 1530804) (-945 "PMDOWN.spad" 1529676 1529690 1530376 1530381) (-944 "PMASS.spad" 1528686 1528694 1529666 1529671) (-943 "PMASSFS.spad" 1527653 1527669 1528676 1528681) (-942 "PLOTTOOL.spad" 1527433 1527441 1527643 1527648) (-941 "PLOT.spad" 1522356 1522364 1527423 1527428) (-940 "PLOT3D.spad" 1518820 1518828 1522346 1522351) (-939 "PLOT1.spad" 1517977 1517987 1518810 1518815) (-938 "PLEQN.spad" 1505267 1505294 1517967 1517972) (-937 "PINTERP.spad" 1504889 1504908 1505257 1505262) (-936 "PINTERPA.spad" 1504673 1504689 1504879 1504884) (-935 "PI.spad" 1504282 1504290 1504647 1504668) (-934 "PID.spad" 1503252 1503260 1504208 1504277) (-933 "PICOERCE.spad" 1502909 1502919 1503242 1503247) (-932 "PGROEB.spad" 1501510 1501524 1502899 1502904) (-931 "PGE.spad" 1493127 1493135 1501500 1501505) (-930 "PGCD.spad" 1492017 1492034 1493117 1493122) (-929 "PFRPAC.spad" 1491166 1491176 1492007 1492012) (-928 "PFR.spad" 1487829 1487839 1491068 1491161) (-927 "PFOTOOLS.spad" 1487087 1487103 1487819 1487824) (-926 "PFOQ.spad" 1486457 1486475 1487077 1487082) (-925 "PFO.spad" 1485876 1485903 1486447 1486452) (-924 "PF.spad" 1485450 1485462 1485681 1485774) (-923 "PFECAT.spad" 1483132 1483140 1485376 1485445) (-922 "PFECAT.spad" 1480842 1480852 1483088 1483093) (-921 "PFBRU.spad" 1478730 1478742 1480832 1480837) (-920 "PFBR.spad" 1476290 1476313 1478720 1478725) (-919 "PERM.spad" 1472097 1472107 1476120 1476135) (-918 "PERMGRP.spad" 1466867 1466877 1472087 1472092) (-917 "PERMCAT.spad" 1465528 1465538 1466847 1466862) (-916 "PERMAN.spad" 1464060 1464074 1465518 1465523) (-915 "PENDTREE.spad" 1463401 1463411 1463689 1463694) (-914 "PDSPC.spad" 1462214 1462224 1463391 1463396) (-913 "PDSPC.spad" 1461025 1461037 1462204 1462209) (-912 "PDRING.spad" 1460867 1460877 1461005 1461020) (-911 "PDEPROB.spad" 1459882 1459890 1460857 1460862) (-910 "PDEPACK.spad" 1453922 1453930 1459872 1459877) (-909 "PDECOMP.spad" 1453392 1453409 1453912 1453917) (-908 "PDECAT.spad" 1451748 1451756 1453382 1453387) (-907 "PDDOM.spad" 1451186 1451199 1451738 1451743) (-906 "PDDOM.spad" 1450622 1450637 1451176 1451181) (-905 "PCOMP.spad" 1450475 1450488 1450612 1450617) (-904 "PBWLB.spad" 1449063 1449080 1450465 1450470) (-903 "PATTERN.spad" 1443602 1443612 1449053 1449058) (-902 "PATTERN2.spad" 1443340 1443352 1443592 1443597) (-901 "PATTERN1.spad" 1441676 1441692 1443330 1443335) (-900 "PATRES.spad" 1439251 1439263 1441666 1441671) (-899 "PATRES2.spad" 1438923 1438937 1439241 1439246) (-898 "PATMATCH.spad" 1437120 1437151 1438631 1438636) (-897 "PATMAB.spad" 1436549 1436559 1437110 1437115) (-896 "PATLRES.spad" 1435635 1435649 1436539 1436544) (-895 "PATAB.spad" 1435399 1435409 1435625 1435630) (-894 "PARTPERM.spad" 1433407 1433415 1435389 1435394) (-893 "PARSURF.spad" 1432841 1432869 1433397 1433402) (-892 "PARSU2.spad" 1432638 1432654 1432831 1432836) (-891 "script-parser.spad" 1432158 1432166 1432628 1432633) (-890 "PARSCURV.spad" 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-802) T) ((-227 . -804) T) ((-227 . -801) T) ((-59 . -624) 178423) ((-59 . -623) 178335) ((-227 . -736) T) ((-526 . -624) 178296) ((-526 . -623) 178208) ((-507 . -623) 178140) ((-506 . -624) 178101) ((-506 . -623) 178013) ((-1095 . -372) 177964) ((-40 . -421) 177941) ((-77 . -1233) T) ((-881 . -922) NIL) ((-368 . -337) 177925) ((-368 . -372) T) ((-362 . -337) 177909) ((-362 . -372) T) ((-354 . -337) 177893) ((-354 . -372) T) ((-324 . -292) 177872) ((-108 . -372) T) ((-70 . -1233) T) ((-1247 . -347) 177824) ((-881 . -658) 177769) ((-1247 . -386) 177721) ((-977 . -132) 177576) ((-825 . -132) 177466) ((-971 . -661) 177450) ((-1102 . -174) 177361) ((-971 . -382) 177345) ((-1077 . -804) T) ((-1077 . -801) T) ((-882 . -626) 177243) ((-792 . -174) 177134) ((-790 . -174) 177045) ((-826 . -47) 177007) ((-1077 . -736) T) ((-335 . -499) 176991) ((-965 . -736) T) ((-1296 . -317) 176929) ((-464 . -174) 176840) ((-251 . -294) 176792) ((-1275 . -913) 176705) ((-1268 . -913) 176611) ((-1267 . -1071) 176446) ((-491 . -736) T) ((-1247 . -913) 176279) ((-1246 . -1071) 176087) ((-1227 . -298) 176066) ((-1202 . -1233) T) ((-1199 . -377) T) ((-1198 . -377) T) ((-1161 . -152) 176050) ((-1135 . -102) T) ((-1133 . -1115) T) ((-1095 . -23) T) ((-1095 . -1127) T) ((-1090 . -102) T) ((-1072 . -623) 176017) ((-940 . -968) T) ((-747 . -317) 175955) ((-75 . -1233) T) ((-674 . -391) 175927) ((-171 . -922) 175880) ((-30 . -968) T) ((-112 . -854) T) ((-1 . -623) 175862) ((-1018 . -419) 175834) ((-129 . -661) 175816) ((-50 . -630) 175800) ((-704 . -656) 175735) ((-605 . -913) 175648) ((-448 . -102) T) ((-129 . -382) 175630) ((-142 . -317) NIL) ((-882 . -1064) T) ((-843 . -860) 175609) ((-81 . -1233) T) ((-721 . -298) T) ((-40 . -1073) T) ((-591 . -174) T) ((-528 . -174) T) ((-521 . -623) 175591) ((-171 . -658) 175465) ((-517 . -623) 175447) ((-360 . -148) 175429) ((-360 . -146) T) ((-368 . -1127) T) ((-362 . -1127) T) ((-354 . -1127) T) ((-1019 . -315) T) ((-927 . -315) T) ((-882 . -249) T) ((-108 . -1127) T) ((-882 . -239) 175408) ((-1267 . -111) 175229) ((-1246 . -111) 175018) ((-251 . -1271) 175002) ((-574 . -858) T) ((-368 . -23) T) ((-363 . -358) T) ((-324 . -317) 174989) ((-321 . -317) 174930) ((-362 . -23) T) ((-327 . -132) T) ((-354 . -23) T) ((-1019 . -1037) T) ((-31 . -626) 174911) ((-108 . -23) T) ((-664 . -1066) 174895) ((-251 . -614) 174872) ((-341 . -1115) T) ((-664 . -650) 174842) ((-1269 . -38) 174734) ((-1256 . -922) 174713) ((-112 . -1115) T) ((-826 . -1233) 174692) ((-1050 . -102) T) ((-1256 . -658) 174581) ((-881 . -804) NIL) ((-865 . -658) 174555) ((-881 . -801) NIL) ((-826 . -897) NIL) ((-881 . -736) T) ((-1102 . -524) 174428) ((-792 . -524) 174375) ((-790 . -524) 174327) ((-581 . -658) 174314) ((-826 . -1053) 174142) ((-464 . -524) 174085) ((-398 . -399) T) ((-1267 . -626) 173898) ((-1246 . -626) 173646) ((-60 . -1233) T) ((-631 . -860) 173625) ((-510 . -671) T) ((-1161 . -991) 173594) ((-1039 . -656) 173531) ((-1018 . -462) T) ((-709 . -858) T) ((-520 . -802) T) ((-484 . -1071) 173366) ((-510 . -113) T) ((-352 . -1115) T) ((-321 . -1167) NIL) ((-297 . -132) T) ((-404 . -1115) T) ((-880 . -1073) T) ((-704 . -379) 173333) ((-363 . -656) 173263) ((-225 . -630) 173240) ((-335 . -294) 173192) ((-484 . -111) 173013) ((-1267 . -1064) T) ((-1246 . -1064) T) ((-826 . -386) 172997) ((-171 . -736) T) ((-664 . -102) T) ((-1267 . -249) 172976) ((-1267 . -239) 172928) ((-1246 . -239) 172833) ((-1246 . -249) 172812) ((-1018 . -412) NIL) ((-680 . -649) 172760) ((-324 . -38) 172670) ((-321 . -38) 172599) ((-69 . -623) 172581) ((-327 . -503) 172547) ((-48 . -656) 172497) ((-1205 . -296) 172476) ((-1241 . -860) T) ((-1128 . -1127) 172426) ((-83 . -1233) T) ((-61 . -623) 172408) ((-489 . -296) 172387) ((-1298 . -1053) 172364) ((-1180 . -1115) T) ((-1128 . -23) 172254) ((-826 . -913) 172190) ((-1256 . -736) T) ((-1117 . -1233) T) ((-484 . -626) 172016) ((-360 . -238) T) ((-1102 . -298) 171947) ((-979 . -1115) T) ((-904 . -102) T) ((-792 . -298) 171858) ((-335 . -19) 171842) ((-59 . -296) 171819) ((-790 . -298) 171750) ((-865 . -736) T) ((-118 . -858) NIL) ((-526 . -296) 171727) ((-335 . -614) 171704) ((-506 . -296) 171681) ((-464 . -298) 171612) ((-1050 . -317) 171463) ((-886 . -500) 171444) ((-886 . -623) 171410) ((-691 . -500) 171391) ((-581 . -736) T) ((-686 . -500) 171372) ((-691 . -623) 171322) ((-686 . -623) 171288) ((-672 . -623) 171270) ((-488 . -500) 171251) ((-488 . -623) 171217) ((-251 . -624) 171178) ((-251 . -500) 171155) ((-139 . -500) 171136) ((-138 . -500) 171117) ((-134 . -500) 171098) ((-251 . -623) 170990) ((-215 . -102) T) ((-139 . -623) 170956) ((-138 . -623) 170922) ((-134 . -623) 170888) ((-1162 . -34) T) ((-956 . -1233) T) ((-352 . -727) 170833) ((-680 . -25) T) ((-680 . -21) T) ((-1192 . -626) 170814) ((-484 . -1064) T) ((-645 . -427) 170779) ((-617 . -427) 170744) ((-1135 . -1167) T) ((-722 . -1066) 170567) ((-591 . -298) T) ((-528 . -298) T) ((-1268 . -315) 170546) ((-484 . -239) 170498) ((-484 . -249) 170477) ((-1247 . -315) 170456) ((-722 . -650) 170285) ((-1247 . -1037) NIL) ((-1095 . -132) T) ((-882 . -805) 170264) ((-145 . -102) T) ((-40 . -1115) T) ((-882 . -802) 170243) ((-654 . -1025) 170227) ((-590 . -1073) T) ((-574 . -1073) T) ((-505 . -1073) T) ((-417 . -462) T) ((-368 . -132) T) ((-324 . -410) 170211) ((-321 . -410) 170172) ((-362 . -132) T) ((-354 . -132) T) ((-1197 . -1115) T) ((-1135 . -38) 170159) ((-1109 . -623) 170126) ((-108 . -132) T) ((-967 . -1115) T) ((-934 . -1115) T) ((-781 . -1115) T) ((-682 . -1115) T) ((-711 . -148) T) ((-117 . -148) T) ((-1305 . -21) T) ((-1305 . -25) T) ((-1303 . -21) T) ((-1303 . -25) T) ((-674 . -1071) 170110) ((-541 . -860) T) ((-510 . -860) T) ((-364 . -1071) 170062) ((-361 . -1071) 170014) ((-353 . -1071) 169966) ((-258 . -1233) T) ((-257 . -1233) T) ((-271 . -1071) 169809) ((-253 . -1071) 169652) ((-674 . -111) 169631) ((-557 . -854) T) ((-364 . -111) 169569) ((-361 . -111) 169507) ((-353 . -111) 169445) ((-271 . -111) 169274) ((-253 . -111) 169103) ((-827 . -1237) 169082) ((-633 . -421) 169066) ((-44 . -21) T) ((-44 . -25) T) ((-825 . -649) 168972) ((-827 . -566) 168951) ((-258 . -1053) 168778) ((-257 . -1053) 168605) ((-127 . -120) 168589) ((-923 . -1071) 168554) ((-722 . -102) T) ((-709 . -1073) T) ((-607 . -626) 168535) ((-595 . -626) 168516) ((-546 . -628) 168419) ((-352 . -174) T) ((-88 . -623) 168401) ((-153 . -21) T) ((-153 . -25) T) ((-923 . -111) 168357) ((-40 . -727) 168302) ((-880 . -1115) T) ((-674 . -626) 168279) ((-655 . -626) 168260) ((-364 . -626) 168197) ((-361 . -626) 168134) ((-557 . -1115) T) ((-353 . -626) 168071) ((-335 . -624) 168032) ((-335 . -623) 167944) ((-271 . -626) 167697) ((-253 . -626) 167482) ((-1246 . -802) 167435) ((-1246 . -805) 167388) ((-258 . -386) 167357) ((-257 . -386) 167326) ((-664 . -38) 167296) ((-618 . -34) T) ((-492 . -1127) 167246) ((-485 . -34) T) ((-1128 . -132) 167136) ((-977 . -25) 166947) ((-923 . -626) 166897) ((-884 . -623) 166879) ((-977 . -21) 166834) ((-825 . -21) 166764) ((-825 . -25) 166635) ((-1239 . -377) T) ((-633 . -1073) T) ((-1194 . -566) 166614) ((-1188 . -47) 166591) ((-364 . -1064) T) ((-361 . -1064) T) ((-492 . -23) 166481) ((-353 . -1064) T) ((-271 . -1064) T) ((-253 . -1064) T) ((-1140 . -47) 166453) ((-118 . -1073) T) ((-1049 . -658) 166427) ((-971 . -34) T) ((-364 . -239) 166406) ((-364 . -249) T) ((-361 . -239) 166385) ((-361 . -249) T) ((-353 . -239) 166364) ((-353 . -249) T) ((-271 . -334) 166336) ((-253 . -334) 166293) ((-271 . -239) 166272) ((-1172 . -152) 166256) ((-258 . -913) 166188) ((-257 . -913) 166120) ((-1097 . -860) T) ((-424 . -1127) T) ((-1069 . -23) T) ((-1039 . -858) T) ((-923 . -1064) T) ((-330 . -658) 166102) ((-711 . -238) T) ((-680 . -235) 166075) ((-1227 . -1017) 166041) ((-1189 . -933) 166020) ((-1183 . -933) 165999) ((-1183 . -830) NIL) ((-1014 . -1066) 165895) ((-980 . -1233) T) ((-923 . -249) T) ((-827 . -372) 165874) ((-394 . -23) T) ((-128 . -1115) 165852) ((-122 . -1115) 165830) ((-923 . -239) T) ((-129 . -34) T) ((-388 . -658) 165795) ((-1014 . -650) 165743) ((-880 . -727) 165730) ((-1312 . -656) 165702) ((-1061 . -152) 165667) ((-1008 . -1233) T) ((-40 . -174) T) ((-704 . -421) 165649) ((-722 . -317) 165636) ((-846 . -658) 165596) ((-837 . -658) 165570) ((-327 . -25) T) ((-327 . -21) T) ((-668 . -294) 165549) ((-590 . -1115) T) ((-574 . -1115) T) ((-505 . -1115) T) ((-251 . -296) 165526) ((-1188 . -1233) T) ((-321 . -233) 165487) ((-1188 . -897) NIL) ((-55 . -1115) T) ((-1140 . -897) 165346) ((-130 . -860) T) ((-1188 . -1053) 165226) ((-1140 . -1053) 165109) ((-185 . -623) 165091) ((-864 . -1053) 164987) ((-792 . -294) 164914) ((-827 . -1127) T) ((-1049 . -736) T) ((-612 . -661) 164898) ((-1061 . -991) 164827) ((-1014 . -102) T) ((-827 . -23) T) ((-722 . -1167) 164805) ((-704 . -1073) T) ((-612 . -382) 164789) ((-360 . -462) T) ((-352 . -298) T) ((-1284 . -1115) T) ((-254 . -1115) T) ((-409 . -102) T) ((-297 . -21) T) ((-297 . -25) T) ((-370 . -736) T) ((-720 . -1115) T) ((-709 . -1115) T) ((-370 . -483) T) ((-1227 . -623) 164771) ((-1188 . -386) 164755) ((-1140 . -386) 164739) ((-1039 . -421) 164701) ((-142 . -231) 164683) ((-388 . -804) T) ((-388 . -801) T) ((-880 . -174) T) ((-388 . -736) T) ((-721 . -623) 164665) ((-722 . -38) 164494) ((-1283 . -1281) 164478) ((-360 . -412) T) ((-1283 . -1115) 164428) ((-1206 . -1115) T) ((-590 . -727) 164415) ((-574 . -727) 164402) ((-505 . -727) 164367) ((-1269 . -656) 164257) ((-324 . -639) 164236) ((-846 . -736) T) ((-837 . -736) T) ((-654 . -1233) T) ((-1095 . -649) 164184) ((-1188 . -913) 164127) ((-1140 . -913) 164111) ((-825 . -235) 164057) ((-672 . -1071) 164041) ((-108 . -649) 164023) ((-492 . -132) 163913) ((-1194 . -1127) T) ((-965 . -47) 163882) ((-633 . -1115) T) ((-672 . -111) 163861) ((-501 . -623) 163827) ((-335 . -296) 163804) ((-491 . -47) 163761) ((-1194 . -23) T) ((-118 . -1115) T) ((-103 . -102) 163739) ((-1295 . -1127) T) ((-558 . -860) T) ((-227 . -1233) T) ((-1069 . -132) T) 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-804) T) ((-103 . -317) 161178) ((-224 . -102) 161156) ((-709 . -174) T) ((-704 . -1115) T) ((-882 . -658) 161072) ((-65 . -393) T) ((-282 . -623) 161054) ((-65 . -405) T) ((-965 . -386) 161038) ((-880 . -298) T) ((-50 . -623) 161020) ((-1014 . -38) 160968) ((-1135 . -656) 160940) ((-591 . -623) 160922) ((-491 . -386) 160906) ((-591 . -624) 160888) ((-528 . -623) 160870) ((-923 . -1302) 160857) ((-881 . -1233) T) ((-711 . -462) T) ((-505 . -524) 160823) ((-497 . -372) T) ((-364 . -377) 160802) ((-361 . -377) 160781) ((-353 . -377) 160760) ((-724 . -736) T) ((-219 . -372) T) ((-117 . -462) T) ((-1306 . -1297) 160744) ((-881 . -895) 160721) ((-881 . -897) NIL) ((-977 . -860) 160620) ((-825 . -860) 160571) ((-1240 . -102) T) ((-664 . -666) 160555) ((-1219 . -34) T) ((-173 . -623) 160537) ((-1128 . -21) 160467) ((-1128 . -25) 160338) ((-881 . -1053) 160315) ((-965 . -913) 160296) ((-1256 . -47) 160273) ((-923 . -377) T) ((-59 . -661) 160257) ((-526 . -661) 160241) ((-491 . -913) 160218) 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-235) 158987) ((-362 . -235) 158960) ((-354 . -235) 158933) ((-225 . -623) 158915) ((-176 . -462) T) ((-224 . -317) 158853) ((-86 . -451) T) ((-86 . -405) T) ((-108 . -235) 158840) ((-219 . -23) T) ((-1307 . -1300) 158819) ((-687 . -1053) 158803) ((-590 . -298) T) ((-574 . -298) T) ((-505 . -298) T) ((-137 . -480) 158758) ((-1256 . -1233) T) ((-664 . -656) 158717) ((-48 . -1115) T) ((-722 . -233) 158701) ((-881 . -913) NIL) ((-1256 . -897) NIL) ((-900 . -102) T) ((-896 . -102) T) ((-398 . -1115) T) ((-171 . -386) 158685) ((-171 . -347) 158669) ((-1256 . -1053) 158549) ((-865 . -1053) 158445) ((-1157 . -102) T) ((-672 . -802) 158424) ((-663 . -132) T) ((-672 . -805) 158403) ((-118 . -524) 158311) ((-581 . -1053) 158293) ((-302 . -1290) 158263) ((-876 . -102) T) ((-976 . -566) 158242) ((-1227 . -1071) 158125) ((-1018 . -1066) 158070) ((-492 . -649) 157976) ((-917 . -1115) T) ((-1039 . -727) 157913) ((-721 . -1071) 157878) ((-1018 . -650) 157823) ((-627 . -102) T) ((-612 . -34) T) ((-1162 . -1233) T) ((-1227 . -111) 157692) ((-484 . -658) 157589) ((-363 . -727) 157534) ((-171 . -913) 157493) ((-709 . -298) T) ((-704 . -174) T) ((-721 . -111) 157449) ((-1312 . -1073) T) ((-1256 . -386) 157433) ((-428 . -1237) 157411) ((-1133 . -623) 157393) ((-321 . -858) NIL) ((-428 . -566) T) ((-227 . -315) T) ((-1246 . -801) 157346) ((-1246 . -804) 157299) ((-1267 . -736) T) ((-1246 . -736) T) ((-48 . -727) 157264) ((-227 . -1037) T) ((-1269 . -421) 157230) ((-360 . -1290) 157207) ((-1256 . -913) 157150) ((-728 . -736) T) ((-341 . -623) 157132) ((-1227 . -626) 157014) ((-1128 . -235) 156960) ((-112 . -623) 156942) ((-112 . -624) 156924) ((-728 . -483) T) ((-721 . -626) 156874) ((-1306 . -1066) 156858) ((-492 . -21) 156788) ((-128 . -499) 156772) ((-122 . -499) 156756) ((-492 . -25) 156627) ((-1306 . -650) 156597) ((-633 . -298) T) ((-596 . -1071) 156572) ((-447 . -1115) T) ((-1077 . -315) T) ((-118 . -298) T) ((-1119 . -102) T) ((-1018 . -102) T) ((-596 . -111) 156540) ((-1157 . -317) 156478) ((-1227 . -1064) T) ((-1077 . -1037) T) ((-66 . -1233) T) ((-1069 . -25) T) ((-1069 . -21) T) ((-721 . -1064) T) ((-394 . -21) T) ((-394 . -25) T) ((-704 . -524) NIL) ((-1039 . -174) T) ((-721 . -249) T) ((-1077 . -555) T) ((-722 . -656) 156388) ((-516 . -102) T) ((-512 . -102) T) ((-363 . -174) T) ((-352 . -623) 156370) ((-417 . -1066) 156322) ((-404 . -623) 156304) ((-1135 . -858) T) ((-484 . -736) T) ((-903 . -1053) 156272) ((-417 . -650) 156224) ((-108 . -860) T) ((-668 . -1071) 156208) ((-497 . -132) T) ((-1269 . -1073) T) ((-219 . -132) T) ((-1172 . -102) 156186) ((-99 . -1115) T) ((-251 . -676) 156170) ((-251 . -661) 156154) ((-668 . -111) 156133) ((-596 . -626) 156117) ((-324 . -421) 156101) ((-251 . -382) 156085) ((-1175 . -241) 156032) ((-1014 . -233) 156016) ((-74 . -1233) T) ((-48 . -174) T) ((-711 . -397) T) ((-711 . -144) T) ((-1306 . -102) T) ((-1213 . -626) 155998) ((-1103 . -1233) T) ((-1102 . -1071) 155841) ((-1091 . -1233) T) ((-271 . -922) 155820) ((-253 . -922) 155799) ((-792 . -1071) 155622) ((-790 . -1071) 155465) ((-618 . -1233) T) ((-1180 . -623) 155447) ((-1102 . -111) 155276) ((-1061 . -102) T) ((-485 . -1233) T) ((-471 . -1071) 155247) ((-464 . -1071) 155090) ((-674 . -658) 155074) ((-881 . -315) T) ((-792 . -111) 154883) ((-790 . -111) 154712) ((-364 . -658) 154664) ((-361 . -658) 154616) ((-353 . -658) 154568) ((-271 . -658) 154457) ((-253 . -658) 154346) ((-1174 . -860) T) ((-1103 . -1053) 154330) ((-471 . -111) 154291) ((-464 . -111) 154120) ((-1091 . -1053) 154097) ((-1015 . -34) T) ((-979 . -623) 154079) ((-971 . -1233) T) ((-127 . -1025) 154063) ((-976 . -1127) T) ((-881 . -1037) NIL) ((-745 . -1127) T) ((-725 . -1127) T) ((-668 . -626) 153981) ((-1283 . -499) 153965) ((-1157 . -38) 153925) ((-976 . -23) T) ((-923 . -658) 153890) ((-875 . -1115) T) ((-853 . -102) T) ((-827 . -21) T) ((-645 . -1066) 153874) ((-617 . -1066) 153858) ((-827 . -25) T) ((-745 . -23) T) ((-725 . -23) T) ((-645 . -650) 153842) ((-110 . -671) T) 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-860) T) ((-664 . -421) 150557) ((-680 . -238) 150536) ((-225 . -626) 150498) ((-110 . -860) T) ((-663 . -21) T) ((-663 . -25) T) ((-1306 . -38) 150468) ((-118 . -294) 150419) ((-1283 . -19) 150403) ((-1283 . -614) 150380) ((-1296 . -1115) T) ((-360 . -1066) 150325) ((-1092 . -1115) T) ((-1002 . -1115) T) ((-976 . -132) T) ((-827 . -235) 150312) ((-747 . -1115) T) ((-360 . -650) 150257) ((-745 . -132) T) ((-725 . -132) T) ((-521 . -803) T) ((-521 . -804) T) ((-463 . -132) T) ((-417 . -1167) 150235) ((-225 . -1064) T) ((-302 . -102) 150017) ((-142 . -1115) T) ((-709 . -1017) T) ((-1120 . -294) 149973) ((-91 . -1233) T) ((-128 . -623) 149905) ((-122 . -623) 149837) ((-1312 . -174) T) ((-1189 . -372) 149816) ((-1183 . -372) 149795) ((-324 . -1115) T) ((-428 . -132) T) ((-321 . -1115) T) ((-417 . -38) 149747) ((-1148 . -102) T) ((-1269 . -727) 149639) ((-664 . -1073) T) ((-1150 . -1278) T) ((-327 . -146) 149618) ((-327 . -148) 149597) ((-140 . -1115) T) ((-137 . -1115) T) ((-115 . -1115) T) ((-868 . -102) T) ((-590 . -623) 149579) ((-574 . -624) 149478) ((-574 . -623) 149460) ((-505 . -623) 149442) ((-505 . -624) 149387) ((-495 . -23) T) ((-492 . -860) 149338) ((-497 . -649) 149320) ((-978 . -623) 149302) ((-219 . -649) 149284) ((-227 . -414) T) ((-672 . -658) 149268) ((-55 . -623) 149250) ((-1188 . -933) 149229) ((-741 . -1127) T) ((-360 . -102) T) ((-1232 . -1098) T) ((-1135 . -854) T) ((-828 . -860) T) ((-741 . -23) T) ((-352 . -1071) 149174) ((-1174 . -1173) T) ((-1162 . -107) 149158) ((-1190 . -1127) T) ((-1189 . -1127) T) ((-525 . -1053) 149142) ((-1183 . -1127) T) ((-1141 . -1127) T) ((-352 . -111) 149071) ((-1019 . -1237) T) ((-127 . -1233) T) ((-927 . -1237) T) ((-704 . -294) NIL) ((-724 . -1233) T) ((-1284 . -623) 149053) ((-1190 . -23) T) ((-1189 . -23) T) ((-1183 . -23) T) ((-1157 . -233) 149037) ((-1019 . -566) T) ((-1141 . -23) T) ((-927 . -566) T) ((-1090 . -1115) T) ((-254 . -623) 149019) ((-825 . -238) 148971) ((-809 . -132) T) ((-720 . -623) 148953) 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-107) 146877) ((-495 . -132) T) ((-485 . -107) 146827) ((-246 . -1127) 146777) ((-882 . -386) 146761) ((-882 . -347) 146745) ((-246 . -23) 146635) ((-40 . -626) 146565) ((-1077 . -933) T) ((-1077 . -830) T) ((-591 . -377) T) ((-528 . -377) T) ((-1296 . -524) 146498) ((-1275 . -566) 146477) ((-1268 . -1237) 146456) ((-360 . -1167) T) ((-335 . -34) T) ((-44 . -427) 146440) ((-1197 . -626) 146376) ((-883 . -1233) T) ((-400 . -754) 146360) ((-1268 . -566) 146311) ((-1267 . -1233) T) ((-1157 . -656) 146270) ((-741 . -132) T) ((-682 . -626) 146254) ((-1247 . -1237) 146233) ((-1247 . -566) 146184) ((-1246 . -1233) T) ((-1246 . -897) 146057) ((-1246 . -895) 146027) ((-1190 . -132) T) ((-319 . -1098) T) ((-1189 . -132) T) ((-747 . -524) 145960) ((-1183 . -132) T) ((-1141 . -132) T) ((-904 . -1115) T) ((-145 . -854) T) ((-1039 . -1017) T) ((-701 . -623) 145942) ((-1019 . -23) T) ((-533 . -317) 145880) ((-1019 . -1127) T) ((-142 . -524) NIL) ((-876 . -656) 145825) ((-1018 . -358) NIL) ((-986 . -23) T) ((-927 . -1127) T) ((-360 . -38) 145790) ((-927 . -23) T) ((-882 . -913) 145749) ((-82 . -623) 145731) ((-40 . -1064) T) ((-880 . -1071) 145718) ((-880 . -111) 145703) ((-711 . -102) T) ((-704 . -623) 145685) ((-612 . -1233) T) ((-606 . -566) 145664) ((-437 . -1127) T) ((-348 . -1066) 145648) ((-215 . -1115) T) ((-176 . -1066) 145580) ((-484 . -47) 145550) ((-40 . -239) 145522) ((-40 . -249) T) ((-135 . -102) T) ((-117 . -102) T) ((-605 . -566) 145501) ((-348 . -650) 145485) ((-704 . -624) 145393) ((-324 . -524) 145359) ((-176 . -650) 145291) ((-321 . -524) 145183) ((-497 . -235) 145170) ((-1267 . -1053) 145154) ((-1246 . -1053) 144940) ((-1014 . -421) 144924) ((-219 . -235) 144911) ((-437 . -23) T) ((-1135 . -174) T) ((-1269 . -298) T) ((-664 . -727) 144881) ((-145 . -1115) T) ((-48 . -1017) T) ((-417 . -233) 144865) ((-303 . -241) 144815) ((-881 . -933) T) ((-881 . -830) NIL) ((-880 . -626) 144787) ((-874 . -860) T) ((-1246 . -347) 144757) ((-1246 . -386) 144727) ((-1095 . -238) 144652) ((-224 . -1136) 144636) ((-1283 . -296) 144613) ((-368 . -238) 144592) ((-362 . -238) 144571) ((-484 . -1233) T) ((-354 . -238) 144550) ((-108 . -238) T) ((-1227 . -658) 144475) ((-1018 . -656) 144405) ((-976 . -21) T) ((-976 . -25) T) ((-745 . -21) T) ((-745 . -25) T) ((-725 . -21) T) ((-725 . -25) T) ((-721 . -658) 144370) ((-463 . -21) T) ((-463 . -25) T) ((-348 . -102) T) ((-176 . -102) T) ((-1014 . -1073) T) ((-880 . -1064) T) ((-784 . -102) T) ((-1268 . -372) 144349) ((-1267 . -913) 144255) ((-1247 . -372) 144234) ((-1246 . -913) 144085) ((-1039 . -623) 144067) ((-417 . -838) 144020) ((-1190 . -503) 143986) ((-171 . -933) 143917) ((-1189 . -503) 143883) ((-1183 . -503) 143849) ((-722 . -1115) T) ((-1141 . -503) 143815) ((-590 . -1071) 143802) ((-574 . -1071) 143789) ((-505 . -1071) 143754) ((-324 . -298) 143733) ((-321 . -298) T) ((-363 . -623) 143715) ((-428 . -25) T) ((-428 . -21) T) ((-99 . -294) 143694) ((-590 . -111) 143679) ((-574 . -111) 143664) ((-505 . 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141418) ((-633 . -1071) 141405) ((-489 . -1233) T) ((-352 . -377) T) ((-142 . -499) 141387) ((-790 . -658) 141276) ((-1156 . -1233) T) ((-559 . -860) T) ((-471 . -658) 141247) ((-271 . -897) 141106) ((-253 . -897) NIL) ((-118 . -1071) 141051) ((-464 . -658) 140940) ((-674 . -1053) 140917) ((-633 . -111) 140902) ((-400 . -1066) 140886) ((-364 . -1053) 140870) ((-361 . -1053) 140854) ((-353 . -1053) 140838) ((-271 . -1053) 140682) ((-253 . -1053) 140558) ((-923 . -1233) T) ((-118 . -111) 140487) ((-59 . -1233) T) ((-400 . -650) 140471) ((-631 . -1066) 140455) ((-529 . -1233) T) ((-526 . -1233) T) ((-507 . -1233) T) ((-506 . -1233) T) ((-447 . -623) 140437) ((-444 . -623) 140419) ((-631 . -650) 140403) ((-3 . -102) T) ((-1042 . -1226) 140372) ((-843 . -102) T) ((-699 . -57) 140330) ((-709 . -1064) T) ((-645 . -656) 140299) ((-617 . -656) 140268) ((-50 . -658) 140242) ((-297 . -462) T) ((-486 . -1226) 140211) ((0 . -102) T) ((-591 . -658) 140176) ((-528 . -658) 140121) ((-49 . -102) T) 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-23) T) ((-741 . -25) T) ((-741 . -21) T) ((-1092 . -294) 139120) ((-78 . -406) T) ((-78 . -405) T) ((-543 . -777) 139102) ((-704 . -1071) 139052) ((-1308 . -102) T) ((-1275 . -132) T) ((-1268 . -132) T) ((-1247 . -132) T) ((-1190 . -25) T) ((-1157 . -421) 139036) ((-645 . -376) 138968) ((-617 . -376) 138900) ((-1172 . -1164) 138884) ((-103 . -1115) 138862) ((-1190 . -21) T) ((-1189 . -21) T) ((-875 . -623) 138844) ((-1014 . -727) 138792) ((-225 . -658) 138759) ((-704 . -111) 138693) ((-50 . -736) T) ((-1189 . -25) T) ((-360 . -358) T) ((-1183 . -21) T) ((-1095 . -462) 138644) ((-1183 . -25) T) ((-722 . -524) 138591) ((-591 . -736) T) ((-528 . -736) T) ((-1141 . -21) T) ((-1141 . -25) T) ((-606 . -132) T) ((-605 . -132) T) ((-302 . -656) 138326) ((-492 . -238) 138278) ((-368 . -462) T) ((-362 . -462) T) ((-354 . -462) T) ((-484 . -315) 138257) ((-1241 . -102) T) ((-321 . -294) 138192) ((-108 . -462) T) ((-79 . -451) T) ((-79 . -405) T) ((-487 . -102) T) ((-701 . -626) 138176) ((-1312 . -623) 138158) ((-1312 . -624) 138140) ((-1095 . -412) 138119) ((-1050 . -499) 138050) ((-137 . -294) 138027) ((-574 . -805) T) ((-574 . -802) T) ((-1078 . -241) 137973) ((-368 . -412) 137924) ((-362 . -412) 137875) ((-354 . -412) 137826) ((-1298 . -1127) T) ((-1307 . -1066) 137810) ((-390 . -1066) 137794) ((-1307 . -650) 137764) ((-828 . -238) T) ((-390 . -650) 137734) ((-704 . -626) 137669) ((-1298 . -23) T) ((-1285 . -102) T) ((-177 . -623) 137651) ((-1157 . -1073) T) ((-557 . -377) T) ((-680 . -754) 137635) ((-1194 . -146) 137614) ((-1194 . -148) 137593) ((-1161 . -1115) T) ((-1161 . -1086) 137562) ((-69 . -1233) T) ((-1039 . -1071) 137499) ((-360 . -656) 137429) ((-876 . -1073) T) ((-246 . -649) 137335) ((-704 . -1064) T) ((-363 . -1071) 137280) ((-61 . -1233) T) ((-1039 . -111) 137196) ((-914 . -623) 137107) ((-704 . -249) T) ((-704 . -239) NIL) ((-853 . -858) 137086) ((-709 . -805) T) ((-709 . -802) T) ((-1018 . -421) 137063) ((-363 . -111) 136992) ((-388 . -933) T) ((-417 . -858) 136971) ((-722 . -298) 136882) ((-225 . -736) T) ((-1275 . -503) 136848) ((-1268 . -503) 136814) ((-1247 . -503) 136780) ((-588 . -1115) T) ((-324 . -1017) 136759) ((-224 . -1115) 136737) ((-1240 . -854) T) ((-327 . -988) 136699) ((-105 . -102) T) ((-48 . -1071) 136664) ((-1307 . -102) T) ((-390 . -102) T) ((-48 . -111) 136620) ((-1019 . -649) 136602) ((-1269 . -623) 136584) ((-541 . -102) T) ((-510 . -102) T) ((-1148 . -1149) 136568) ((-153 . -1290) 136552) ((-251 . -1233) T) ((-1232 . -102) T) ((-1039 . -626) 136489) ((-827 . -238) T) ((-1188 . -1237) 136468) ((-363 . -626) 136398) ((-1140 . -1237) 136377) ((-246 . -21) 136307) ((-246 . -25) 136178) ((-128 . -120) 136162) ((-122 . -120) 136146) ((-44 . -754) 136130) ((-1188 . -566) 136041) ((-1140 . -566) 135972) ((-1240 . -1115) T) ((-1050 . -294) 135947) ((-1182 . -1098) T) ((-1009 . -1098) T) ((-826 . -132) T) ((-118 . -805) NIL) ((-118 . -802) NIL) ((-364 . -315) T) ((-361 . -315) T) ((-353 . -315) T) ((-258 . -1127) 135897) ((-257 . -1127) 135847) ((-1039 . -1064) T) ((-1018 . -1073) T) ((-48 . -626) 135780) ((-352 . -658) 135725) ((-631 . -38) 135709) ((-1296 . -623) 135671) ((-1296 . -624) 135632) ((-1092 . -623) 135614) ((-1039 . -249) T) ((-363 . -1064) T) ((-825 . -1290) 135584) ((-258 . -23) T) ((-257 . -23) T) ((-1002 . -623) 135566) ((-1190 . -235) 135519) ((-1189 . -235) 135465) ((-747 . -624) 135426) ((-747 . -623) 135408) ((-1183 . -235) 135289) ((-809 . -860) 135268) ((-1175 . -152) 135215) ((-1014 . -524) 135127) ((-363 . -239) T) ((-363 . -249) T) ((-398 . -626) 135108) ((-1019 . -25) T) ((-142 . -623) 135090) ((-142 . -624) 135049) ((-923 . -315) T) ((-1019 . -21) T) ((-986 . -25) T) ((-927 . -21) T) ((-927 . -25) T) ((-437 . -21) T) ((-437 . -25) T) ((-853 . -421) 135033) ((-48 . -1064) T) ((-1305 . -1297) 135017) ((-1303 . -1297) 135001) ((-1050 . -614) 134976) ((-324 . -624) 134837) ((-324 . -623) 134819) ((-321 . -624) NIL) ((-321 . -623) 134801) ((-48 . -249) T) ((-48 . -239) T) ((-664 . -294) 134762) ((-560 . -241) 134712) ((-140 . -623) 134679) ((-137 . -623) 134661) ((-115 . -623) 134643) ((-487 . -38) 134608) ((-1307 . -1304) 134587) ((-1298 . -132) T) ((-1306 . -1073) T) ((-1097 . -102) T) ((-88 . -1233) T) ((-510 . -317) NIL) ((-1015 . -107) 134571) ((-900 . -1115) T) ((-896 . -1115) T) ((-1283 . -661) 134555) ((-1283 . -382) 134539) ((-335 . -1233) T) ((-603 . -860) T) ((-1157 . -1115) T) ((-1157 . -1068) 134479) ((-103 . -524) 134412) ((-940 . -623) 134394) ((-352 . -736) T) ((-30 . -623) 134376) ((-876 . -1115) T) ((-853 . -1073) 134355) ((-40 . -658) 134262) ((-227 . -1237) T) ((-417 . -1073) T) ((-1174 . -152) 134244) ((-1014 . -298) 134195) ((-627 . -1115) T) ((-227 . -566) T) ((-327 . -1264) 134179) ((-327 . -1261) 134149) ((-711 . -656) 134121) ((-1205 . -1209) 134100) ((-1090 . -623) 134082) ((-1205 . -107) 134032) ((-657 . -152) 134016) ((-642 . -152) 133962) ((-117 . -656) 133934) ((-489 . -1209) 133913) ((-497 . -148) T) ((-497 . -146) NIL) ((-1135 . -624) 133828) ((-448 . -623) 133810) ((-219 . -148) T) ((-219 . -146) NIL) ((-1135 . -623) 133792) ((-130 . -102) T) ((-52 . -102) T) ((-1247 . -649) 133744) ((-489 . -107) 133694) ((-1008 . -23) T) ((-1307 . -38) 133664) ((-1188 . -1127) T) ((-1140 . -1127) T) ((-1077 . -1237) T) ((-246 . -235) 133610) ((-319 . -102) T) ((-864 . -1127) T) ((-965 . -1237) 133589) ((-491 . -1237) 133568) ((-1077 . -566) T) ((-965 . -566) 133499) ((-1188 . -23) T) ((-1166 . -1098) T) ((-1140 . -23) T) ((-864 . -23) T) ((-491 . -566) 133430) ((-1157 . -727) 133362) ((-680 . -1066) 133346) ((-1161 . -524) 133279) ((-680 . -650) 133263) ((-1050 . -624) NIL) ((-1050 . -623) 133245) ((-96 . -1098) T) ((-876 . -727) 133215) ((-1312 . -1071) 133202) ((-1227 . -47) 133171) ((-258 . -132) T) ((-257 . -132) T) ((-1119 . -1115) T) ((-1018 . -1115) T) ((-62 . -623) 133153) ((-1183 . -860) NIL) ((-1039 . -802) T) ((-1039 . -805) T) ((-1312 . -111) 133138) ((-1275 . -25) T) ((-1275 . -21) T) ((-1268 . -21) T) ((-880 . -658) 133125) ((-1268 . -25) T) ((-1247 . -21) T) ((-1247 . -25) T) ((-1042 . -152) 133109) ((-1019 . -235) 133096) ((-882 . -830) 133075) ((-882 . -933) T) ((-722 . -294) 133002) ((-606 . -21) T) ((-348 . -656) 132961) ((-606 . -25) T) ((-605 . -21) T) ((-176 . -656) 132878) ((-40 . -736) T) ((-224 . -524) 132811) ((-605 . -25) T) ((-486 . -152) 132795) ((-473 . -152) 132779) ((-934 . -804) T) ((-934 . -736) T) ((-781 . -803) T) ((-781 . -804) T) ((-516 . -1115) T) ((-512 . -1115) T) ((-781 . -736) T) ((-227 . -372) T) ((-1305 . -1066) 132763) ((-1303 . -1066) 132747) ((-1305 . -650) 132717) ((-1172 . -1115) 132695) ((-881 . -1237) T) ((-1303 . -650) 132665) ((-664 . -623) 132647) ((-881 . -566) T) ((-704 . -377) NIL) ((-44 . -1066) 132631) ((-1312 . -626) 132613) ((-1306 . -1115) T) ((-680 . -102) T) ((-368 . -1290) 132597) ((-362 . -1290) 132581) ((-44 . -650) 132565) ((-354 . -1290) 132549) ((-558 . -102) T) ((-530 . -860) 132528) ((-497 . -238) T) ((-219 . -238) T) ((-1061 . -1115) T) ((-827 . -462) 132507) ((-153 . -1066) 132491) ((-1061 . -1086) 132420) ((-1042 . -991) 132389) ((-829 . -1127) T) ((-1018 . -727) 132334) ((-153 . -650) 132318) ((-396 . -1127) T) ((-486 . -991) 132287) ((-473 . -991) 132256) ((-110 . -152) 132238) ((-73 . -623) 132220) ((-904 . -623) 132202) ((-1095 . -734) 132181) ((-1312 . -1064) T) ((-826 . -649) 132129) ((-302 . -1073) 132071) ((-171 . -1237) 131976) ((-227 . -1127) T) ((-332 . -23) T) ((-1183 . -1007) 131928) ((-853 . -1115) T) ((-1269 . -1071) 131833) ((-1141 . -750) 131812) ((-1267 . -933) 131791) ((-1246 . -933) 131770) ((-880 . -736) T) ((-171 . -566) 131681) ((-590 . -658) 131668) ((-574 . -658) 131640) ((-417 . -1115) T) ((-270 . -1115) T) ((-215 . -623) 131622) ((-505 . -658) 131572) ((-227 . -23) T) ((-1246 . -830) 131525) ((-1305 . -102) T) ((-363 . -1302) 131502) ((-1303 . -102) T) ((-1269 . -111) 131394) ((-825 . -1066) 131271) ((-825 . -650) 131193) ((-145 . -623) 131175) ((-1008 . -132) T) 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-235) 130200) ((-843 . -656) 130117) ((-484 . -933) 130096) ((-327 . -1066) 129931) ((-324 . -1071) 129841) ((-321 . -1071) 129770) ((-1014 . -294) 129728) ((-417 . -727) 129680) ((-327 . -650) 129521) ((-605 . -235) 129474) ((-711 . -858) T) ((-1269 . -1064) T) ((-324 . -111) 129370) ((-321 . -111) 129283) ((-977 . -102) T) ((-825 . -102) 129073) ((-722 . -624) NIL) ((-722 . -623) 129055) ((-1269 . -334) 128999) ((-668 . -1053) 128895) ((-1102 . -1233) 128874) ((-1050 . -296) 128849) ((-590 . -736) T) ((-574 . -804) T) ((-171 . -372) 128800) ((-574 . -801) T) ((-574 . -736) T) ((-505 . -736) T) ((-792 . -1233) T) ((-1161 . -499) 128784) ((-1102 . -897) NIL) ((-881 . -1127) T) ((-118 . -922) NIL) ((-1305 . -1304) 128760) ((-1303 . -1304) 128739) ((-792 . -897) NIL) ((-790 . -897) 128598) ((-1298 . -25) T) ((-1298 . -21) T) ((-1230 . -102) 128576) ((-1121 . -405) T) ((-633 . -658) 128563) ((-464 . -897) NIL) ((-685 . -102) 128541) ((-1102 . -1053) 128368) ((-881 . -23) T) ((-792 . -1053) 128227) ((-790 . -1053) 128084) ((-118 . -658) 128029) ((-464 . -1053) 127905) ((-324 . -626) 127469) ((-321 . -626) 127352) ((-400 . -656) 127321) ((-659 . -1053) 127305) ((-591 . -1233) T) ((-637 . -102) T) ((-528 . -1233) T) ((-224 . -499) 127289) ((-1283 . -34) T) ((-631 . -656) 127248) ((-297 . -1066) 127235) ((-137 . -626) 127219) ((-297 . -650) 127206) ((-645 . -727) 127190) ((-617 . -727) 127174) ((-680 . -38) 127134) ((-327 . -102) T) ((-85 . -623) 127116) ((-50 . -1053) 127100) ((-1135 . -1071) 127087) ((-1102 . -386) 127071) ((-792 . -386) 127055) ((-709 . -736) T) ((-709 . -804) T) ((-709 . -801) T) ((-591 . -1053) 127042) ((-528 . -1053) 127019) ((-60 . -57) 126981) ((-332 . -132) T) ((-324 . -1064) 126871) ((-321 . -1064) T) ((-171 . -1127) T) ((-790 . -386) 126855) ((-45 . -152) 126805) ((-1019 . -1007) 126787) ((-464 . -386) 126771) ((-417 . -174) T) ((-324 . -249) 126750) ((-321 . -249) T) ((-321 . -239) NIL) ((-302 . -1115) 126532) ((-227 . -132) T) ((-1135 . -111) 126517) ((-171 . -23) T) ((-809 . -148) 126496) ((-809 . -146) 126475) ((-258 . -649) 126381) ((-257 . -649) 126287) ((-327 . -292) 126253) ((-1172 . -524) 126186) ((-487 . -656) 126136) ((-1148 . -1115) T) ((-227 . -1075) T) ((-825 . -317) 126074) ((-1102 . -913) 126009) ((-792 . -913) 125952) ((-790 . -913) 125936) ((-1305 . -38) 125906) ((-1303 . -38) 125876) ((-1256 . -1127) T) ((-865 . -1127) T) ((-464 . -913) 125853) ((-868 . -1115) T) ((-1256 . -23) T) ((-1135 . -626) 125825) ((-1077 . -132) T) ((-581 . -1127) T) ((-865 . -23) T) ((-633 . -736) T) ((-364 . -933) T) ((-361 . -933) T) ((-297 . -102) T) ((-353 . -933) T) ((-985 . -1098) T) ((-965 . -132) T) ((-826 . -235) 125798) ((-118 . -804) NIL) ((-118 . -801) NIL) ((-118 . -736) T) ((-1061 . -524) 125699) ((-704 . -922) NIL) ((-581 . -23) T) ((-491 . -132) T) ((-428 . -238) 125678) ((-685 . -317) 125616) ((-645 . -771) T) ((-617 . -771) T) ((-1247 . -860) NIL) ((-1095 . -1066) 125526) ((-1018 . -298) T) ((-704 . -658) 125476) ((-258 . -21) T) ((-360 . -1115) T) ((-258 . -25) T) ((-257 . -21) T) ((-257 . -25) T) ((-153 . -38) 125460) ((-2 . -102) T) ((-923 . -933) T) ((-1095 . -650) 125328) ((-492 . -1290) 125298) ((-1135 . -1064) T) ((-721 . -315) T) ((-368 . -1066) 125250) ((-362 . -1066) 125202) ((-354 . -1066) 125154) ((-368 . -650) 125106) ((-225 . -1053) 125083) ((-362 . -650) 125035) ((-108 . -1066) 124985) ((-354 . -650) 124937) ((-302 . -727) 124879) ((-711 . -1073) T) ((-497 . -462) T) ((-417 . -524) 124791) ((-108 . -650) 124741) ((-219 . -462) T) ((-1135 . -239) T) ((-303 . -152) 124691) ((-1014 . -624) 124652) ((-1014 . -623) 124634) ((-1004 . -623) 124616) ((-117 . -1073) T) ((-664 . -1071) 124600) ((-227 . -503) T) ((-409 . -623) 124582) ((-409 . -624) 124559) ((-1069 . -1290) 124529) ((-664 . -111) 124508) ((-1157 . -499) 124492) ((-1307 . -656) 124451) ((-390 . -656) 124420) ((-825 . -38) 124390) ((-63 . -451) T) ((-63 . -405) T) ((-1175 . -102) T) ((-881 . -132) T) ((-494 . -102) 124368) ((-1312 . -377) T) ((-1095 . -102) T) ((-1076 . -102) T) ((-360 . -727) 124313) ((-741 . -148) 124292) ((-741 . -146) 124271) ((-664 . -626) 124189) ((-1039 . -658) 124126) ((-533 . -1115) 124104) ((-368 . -102) T) ((-362 . -102) T) ((-354 . -102) T) ((-108 . -102) T) ((-514 . -1115) T) ((-363 . -658) 124049) ((-1188 . -649) 123997) ((-1140 . -649) 123945) ((-394 . -519) 123924) ((-843 . -858) 123903) ((-388 . -1237) T) ((-704 . -736) T) ((-1247 . -1007) 123855) ((-348 . -1073) T) ((-112 . -1233) T) ((-176 . -1073) T) ((-103 . -623) 123787) ((-1190 . -146) 123766) ((-1190 . -148) 123745) ((-388 . -566) T) ((-1189 . -148) 123724) ((-1189 . -146) 123703) ((-1183 . -146) 123610) ((-417 . -298) T) ((-1183 . -148) 123517) ((-1141 . -148) 123496) ((-1141 . -146) 123475) ((-327 . -38) 123316) ((-171 . -132) T) ((-321 . -805) NIL) ((-321 . -802) NIL) ((-664 . -1064) T) ((-48 . -658) 123266) ((-1128 . -1066) 123143) ((-904 . -626) 123120) ((-1128 . -650) 123042) ((-1182 . -102) T) 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T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-363 . -736) T) ((-722 . -111) 121978) ((-680 . -233) 121962) ((-591 . -315) T) ((-528 . -315) T) ((-302 . -524) 121911) ((-108 . -317) NIL) ((-72 . -405) T) ((-1128 . -102) 121701) ((-843 . -421) 121685) ((-1135 . -805) T) ((-1135 . -802) T) ((-711 . -1115) T) ((-588 . -623) 121667) ((-388 . -372) T) ((-171 . -503) 121645) ((-224 . -623) 121577) ((-135 . -1115) T) ((-117 . -1115) T) ((-979 . -1233) T) ((-48 . -736) T) ((-1061 . -499) 121542) ((-142 . -435) 121524) ((-142 . -377) T) ((-1042 . -102) T) ((-522 . -519) 121503) ((-722 . -626) 121259) ((-1190 . -238) 121218) ((-486 . -102) T) ((-473 . -102) T) ((-1189 . -238) 121170) ((-1183 . -238) 121057) ((-1049 . -1127) T) ((-1240 . -623) 121039) ((-1197 . -1053) 120975) ((-1190 . -35) 120941) ((-1190 . -95) 120907) ((-1190 . -1221) 120873) ((-1190 . -1218) 120839) ((-1189 . -1218) 120805) ((-1189 . -1221) 120771) ((-1174 . -317) NIL) ((-89 . -406) T) ((-89 . -405) T) ((-1095 . -1167) 120750) ((-40 . -1233) 120722) ((-1189 . -95) 120688) ((-1049 . -23) T) ((-1189 . -35) 120654) ((-581 . -503) T) ((-1183 . -1218) 120620) ((-1183 . -1221) 120586) ((-1183 . -95) 120552) ((-1183 . -35) 120518) ((-370 . -1127) T) ((-368 . -1167) 120497) ((-362 . -1167) 120476) ((-354 . -1167) 120455) ((-1119 . -294) 120411) ((-1141 . -35) 120377) ((-1141 . -95) 120343) ((-108 . -1167) T) ((-1141 . -1221) 120309) ((-843 . -1073) 120288) ((-657 . -317) 120226) ((-642 . -317) 120077) ((-1141 . -1218) 120043) ((-722 . -1064) T) ((-1077 . -649) 120025) ((-1095 . -38) 119893) ((-965 . -649) 119841) ((-1019 . -148) T) ((-1019 . -146) NIL) ((-388 . -1127) T) ((-332 . -25) T) ((-330 . -23) T) ((-956 . -860) 119820) ((-722 . -334) 119797) ((-491 . -649) 119745) ((-40 . -1053) 119633) ((-722 . -239) T) ((-711 . -727) 119620) ((-348 . -1115) T) 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. -623) 118747) ((-533 . -524) 118680) ((-258 . -860) 118631) ((-257 . -860) 118582) ((-394 . -650) 118552) ((-881 . -649) 118529) ((-486 . -317) 118467) ((-473 . -317) 118405) ((-360 . -298) T) ((-1172 . -1271) 118389) ((-1157 . -623) 118351) ((-1157 . -624) 118312) ((-1155 . -102) T) ((-1014 . -1071) 118208) ((-40 . -913) 118160) ((-1172 . -614) 118137) ((-1312 . -658) 118124) ((-876 . -500) 118101) ((-1078 . -152) 118047) ((-882 . -1237) T) ((-1014 . -111) 117929) ((-348 . -727) 117913) ((-876 . -623) 117875) ((-176 . -727) 117807) ((-882 . -566) T) ((-417 . -294) 117765) ((-246 . -238) 117717) ((-108 . -410) 117699) ((-84 . -393) T) ((-84 . -405) T) ((-711 . -174) T) ((-627 . -623) 117681) ((-99 . -736) T) ((-492 . -102) 117471) ((-99 . -483) T) ((-117 . -174) T) ((-1305 . -656) 117430) ((-1303 . -656) 117389) ((-1128 . -38) 117359) ((-171 . -649) 117307) ((-1069 . -102) T) ((-1014 . -626) 117197) ((-881 . -25) T) ((-825 . -244) 117176) ((-881 . -21) T) ((-828 . -102) T) ((-44 . -656) 117119) ((-1019 . -238) T) ((-424 . -102) T) ((-394 . -102) T) ((-110 . -317) NIL) ((-229 . -102) 117097) ((-128 . -1233) T) ((-122 . -1233) T) ((-827 . -1066) 117048) ((-827 . -650) 116990) ((-1049 . -132) T) ((-680 . -376) 116974) ((-153 . -656) 116933) ((-645 . -294) 116891) ((-617 . -294) 116849) ((-1312 . -736) T) ((-1014 . -1064) T) ((-1256 . -649) 116797) ((-1119 . -623) 116779) ((-1018 . -623) 116761) ((-574 . -1233) T) ((-505 . -1233) T) ((-525 . -23) T) ((-520 . -23) T) ((-352 . -315) T) ((-518 . -23) T) ((-330 . -132) T) ((-3 . -1115) T) ((-1018 . -624) 116745) ((-1014 . -249) 116724) ((-1014 . -239) 116703) ((-1275 . -146) 116682) ((-1275 . -148) 116661) ((-843 . -1115) T) ((-1268 . -148) 116640) ((-1268 . -146) 116619) ((-1267 . -1237) 116598) ((-1247 . -146) 116505) ((-1247 . -148) 116412) ((-1246 . -1237) 116391) ((-388 . -132) T) ((-227 . -235) 116378) ((-574 . -897) 116360) ((0 . -1115) T) ((-176 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-49 . -1115) T) 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-1115) T) ((-533 . -499) 113785) ((-747 . -34) T) ((-663 . -1066) 113769) ((-492 . -38) 113739) ((-663 . -650) 113709) ((-881 . -235) NIL) ((-142 . -34) T) ((-118 . -895) 113686) ((-118 . -897) NIL) ((-633 . -1053) 113569) ((-1295 . -102) T) ((-1275 . -238) 113528) ((-654 . -860) 113507) ((-1268 . -238) 113459) ((-1247 . -238) 113346) ((-303 . -102) T) ((-722 . -377) 113325) ((-118 . -1053) 113302) ((-400 . -727) 113286) ((-605 . -238) 113245) ((-631 . -727) 113229) ((-1120 . -1233) T) ((-45 . -317) 113033) ((-826 . -146) 113012) ((-826 . -148) 112991) ((-297 . -656) 112963) ((-1306 . -391) 112942) ((-829 . -860) T) ((-1285 . -1115) T) ((-1175 . -231) 112889) ((-396 . -860) 112868) ((-1275 . -1221) 112834) ((-1275 . -1218) 112800) ((-1268 . -1218) 112766) ((-525 . -132) T) ((-1268 . -1221) 112732) ((-1247 . -1218) 112698) ((-1247 . -1221) 112664) ((-1275 . -35) 112630) ((-1275 . -95) 112596) ((-1268 . -95) 112562) ((-645 . -623) 112531) ((-617 . -623) 112500) ((-227 . -860) T) ((-1268 . -35) 112466) ((-1267 . -1127) T) ((-1247 . -95) 112432) ((-1135 . -658) 112404) ((-1247 . -35) 112370) ((-1246 . -1127) T) ((-603 . -152) 112352) ((-1095 . -358) 112331) ((-176 . -298) T) ((-118 . -386) 112308) ((-118 . -347) 112285) ((-171 . -235) 112230) ((-880 . -315) T) ((-321 . -804) NIL) ((-321 . -801) NIL) ((-324 . -736) 112079) ((-321 . -736) T) ((-484 . -372) 112058) ((-368 . -358) 112037) ((-362 . -358) 112016) ((-354 . -358) 111995) ((-324 . -483) 111974) ((-1267 . -23) T) ((-1246 . -23) T) ((-728 . -1127) T) ((-724 . -132) T) ((-663 . -102) T) ((-487 . -727) 111939) ((-45 . -290) 111889) ((-105 . -1115) T) ((-68 . -623) 111871) ((-985 . -102) T) ((-874 . -102) T) ((-633 . -913) 111830) ((-1307 . -1115) T) ((-390 . -1115) T) ((-1256 . -235) 111817) ((-82 . -1233) T) ((-1232 . -1115) T) ((-1077 . -860) T) ((-118 . -913) NIL) ((-792 . -933) 111796) ((-723 . -860) T) ((-541 . -1115) T) ((-510 . -1115) T) ((-364 . -1237) T) ((-361 . -1237) T) ((-353 . -1237) T) ((-271 . -1237) 111775) ((-253 . -1237) 111754) ((-543 . -870) T) ((-1128 . -233) 111723) ((-1174 . -838) T) ((-1157 . -1071) 111707) ((-400 . -771) T) ((-704 . -1233) T) ((-701 . -1053) 111691) ((-364 . -566) T) ((-361 . -566) T) ((-353 . -566) T) ((-271 . -566) 111622) ((-253 . -566) 111553) ((-535 . -1098) T) ((-1157 . -111) 111532) ((-463 . -754) 111502) ((-876 . -1071) 111472) ((-827 . -38) 111414) ((-704 . -895) 111396) ((-704 . -897) 111378) ((-303 . -317) 111182) ((-923 . -1237) T) ((-1172 . -296) 111159) ((-1095 . -656) 111054) ((-680 . -421) 111038) ((-876 . -111) 111003) ((-1019 . -462) T) ((-704 . -1053) 110948) ((-923 . -566) T) ((-543 . -623) 110930) ((-591 . -933) T) ((-497 . -1066) 110880) ((-484 . -1127) T) ((-528 . -933) T) ((-927 . -462) T) ((-65 . -623) 110862) ((-219 . -1066) 110812) ((-497 . -650) 110762) ((-368 . -656) 110699) ((-362 . -656) 110636) ((-354 . -656) 110573) ((-642 . -231) 110519) ((-219 . -650) 110469) ((-108 . -656) 110419) ((-484 . -23) T) ((-1135 . -804) T) ((-882 . -132) T) ((-1135 . -801) T) ((-1298 . -1300) 110398) ((-1135 . -736) T) ((-664 . -658) 110372) ((-302 . -623) 110113) ((-1157 . -626) 110031) ((-1050 . -34) T) ((-826 . -238) 110010) ((-590 . -315) T) ((-574 . -315) T) ((-505 . -315) T) ((-1307 . -727) 109980) ((-704 . -386) 109962) ((-704 . -347) 109944) ((-487 . -174) T) ((-390 . -727) 109914) ((-876 . -626) 109849) ((-881 . -860) NIL) ((-574 . -1037) T) ((-505 . -1037) T) ((-1148 . -623) 109831) ((-1128 . -244) 109810) ((-216 . -102) T) ((-1165 . -102) T) ((-71 . -623) 109792) ((-1157 . -1064) T) ((-1194 . -38) 109689) ((-868 . -623) 109671) ((-574 . -555) T) ((-680 . -1073) T) ((-741 . -962) 109624) ((-363 . -1233) T) ((-1157 . -239) 109603) ((-1097 . -1115) T) ((-1049 . -25) T) ((-1049 . -21) T) ((-1018 . -1071) 109548) ((-918 . -102) T) ((-876 . -1064) T) ((-704 . -913) NIL) ((-364 . -337) 109532) ((-364 . -372) T) ((-361 . -337) 109516) ((-361 . -372) T) ((-353 . -337) 109500) ((-353 . -372) T) ((-497 . -102) T) ((-1295 . -38) 109470) ((-556 . -860) T) ((-533 . -697) 109420) ((-219 . -102) T) ((-1039 . -1053) 109300) ((-1018 . -111) 109229) ((-1190 . -988) 109198) ((-1189 . -988) 109160) ((-530 . -152) 109144) ((-1095 . -379) 109123) ((-360 . -623) 109105) ((-330 . -21) T) ((-363 . -1053) 109082) ((-330 . -25) T) ((-1183 . -988) 109051) ((-48 . -1233) T) ((-76 . -623) 109033) ((-1141 . -988) 109000) ((-709 . -315) T) ((-130 . -854) T) ((-923 . -372) T) ((-388 . -25) T) ((-388 . -21) T) ((-923 . -337) 108987) ((-86 . -623) 108969) ((-709 . -1037) T) ((-687 . -860) T) ((-1267 . -132) T) ((-1246 . -132) T) ((-914 . -1025) 108953) ((-846 . -21) T) ((-48 . -1053) 108896) ((-846 . -25) T) ((-837 . -25) T) ((-837 . -21) T) ((-1128 . -656) 108666) ((-1305 . -1073) T) ((-559 . -102) T) ((-1303 . -1073) T) ((-664 . -736) T) ((-1119 . -628) 108569) ((-1018 . -626) 108499) ((-1306 . -1071) 108483) ((-825 . -421) 108452) ((-103 . -120) 108436) ((-130 . -1115) T) ((-52 . -1115) T) ((-939 . -623) 108418) ((-881 . -1007) 108395) ((-833 . -102) T) ((-1306 . -111) 108374) ((-663 . -38) 108344) ((-581 . -860) T) ((-364 . -1127) T) ((-361 . -1127) T) ((-353 . -1127) T) ((-271 . -1127) T) ((-253 . -1127) T) ((-1165 . -317) 108148) ((-633 . -315) 108127) ((-1103 . -235) 108114) ((-674 . -23) T) ((-534 . -1098) T) ((-319 . -1115) T) ((-492 . -233) 108083) ((-153 . -1073) T) ((-364 . -23) T) ((-361 . -23) T) ((-353 . -23) T) ((-118 . -315) T) ((-271 . -23) T) ((-253 . -23) T) ((-1018 . -1064) T) ((-722 . -922) 108062) ((-1172 . -626) 108039) ((-1018 . -239) 108011) ((-1018 . -249) T) ((-118 . -1037) NIL) ((-923 . -1127) T) ((-1268 . -462) 107990) ((-1247 . -462) 107969) ((-533 . -623) 107901) ((-722 . -658) 107790) ((-417 . -1071) 107742) ((-514 . -623) 107724) ((-923 . -23) T) ((-497 . -317) NIL) ((-1306 . -626) 107680) ((-484 . -132) T) ((-219 . -317) NIL) ((-417 . -111) 107618) ((-825 . -1073) 107568) ((-747 . -1113) 107552) ((-1267 . -503) 107518) ((-1246 . -503) 107484) ((-558 . -854) T) ((-142 . -1113) 107466) ((-487 . -298) T) ((-1306 . -1064) T) ((-258 . -238) 107418) ((-257 . -238) 107370) ((-1238 . -102) T) ((-1078 . -102) T) ((-853 . -626) 107238) ((-510 . -524) NIL) ((-492 . -244) 107217) ((-417 . -626) 107115) ((-976 . -1066) 106998) ((-745 . -1066) 106968) ((-976 . -650) 106865) ((-1188 . -146) 106844) ((-745 . -650) 106814) ((-463 . -1066) 106784) ((-1188 . -148) 106763) ((-1140 . -148) 106742) ((-1140 . -146) 106721) ((-645 . -1071) 106705) ((-617 . -1071) 106689) ((-463 . -650) 106659) ((-1190 . -1274) 106643) ((-1190 . -1261) 106620) ((-1189 . -1266) 106581) ((-680 . -1115) T) ((-680 . -1068) 106521) ((-1189 . -1261) 106491) ((-558 . -1115) T) ((-497 . -1167) T) ((-1189 . -1264) 106475) ((-1183 . -1245) 106436) ((-828 . -273) 106420) ((-219 . -1167) T) ((-352 . -933) T) ((-99 . -1233) T) ((-645 . -111) 106399) ((-617 . -111) 106378) ((-1183 . -1261) 106355) ((-853 . -1064) 106334) ((-1183 . -1243) 106318) ((-525 . -25) T) ((-505 . -310) T) ((-521 . -23) T) ((-520 . -25) T) ((-518 . -25) T) ((-517 . -23) T) ((-428 . -1066) 106292) ((-417 . -1064) T) ((-327 . -1073) T) ((-704 . -315) T) ((-428 . -650) 106266) ((-108 . -858) T) ((-722 . -736) T) ((-417 . -249) T) ((-417 . -239) 106245) ((-388 . -235) 106232) ((-497 . -38) 106182) ((-219 . -38) 106132) ((-484 . -503) 106098) ((-1240 . -377) T) ((-1174 . -1159) T) ((-1116 . -102) T) ((-837 . -235) 106071) ((-711 . -623) 106053) ((-711 . -624) 105968) ((-724 . -21) T) ((-724 . -25) T) ((-1150 . -102) T) ((-492 . -656) 105738) ((-135 . -623) 105720) ((-117 . -623) 105702) ((-158 . -25) T) ((-1305 . -1115) T) ((-882 . -649) 105650) ((-1303 . -1115) T) ((-976 . -102) T) ((-745 . -102) T) ((-725 . -102) T) ((-463 . -102) T) ((-826 . -462) 105601) ((-44 . -1115) T) ((-1103 . -860) T) ((-1078 . -317) 105452) ((-674 . -132) T) ((-1069 . -656) 105421) ((-680 . -727) 105405) ((-297 . -1073) T) ((-364 . -132) T) ((-361 . -132) T) ((-353 . -132) T) ((-271 . -132) T) ((-253 . -132) T) ((-394 . -656) 105374) ((-428 . -102) T) ((-153 . -1115) T) ((-45 . -231) 105324) ((-809 . -1066) 105308) ((-971 . -860) 105287) ((-1014 . -658) 105189) ((-809 . -650) 105173) ((-246 . -1290) 105143) ((-1039 . -315) T) ((-302 . -1071) 105064) ((-923 . -132) T) ((-40 . -933) T) ((-497 . -410) 105046) ((-363 . -315) T) ((-219 . -410) 105028) ((-1095 . -421) 105012) ((-302 . -111) 104928) ((-1199 . -860) T) ((-1198 . -860) T) ((-882 . -25) T) ((-882 . -21) T) ((-1269 . -47) 104872) ((-348 . -623) 104854) ((-1188 . -238) T) ((-227 . -148) T) ((-176 . -623) 104836) ((-784 . -623) 104818) ((-129 . -860) T) ((-618 . -241) 104765) ((-485 . -241) 104715) ((-1305 . -727) 104685) ((-48 . -315) T) ((-1303 . -727) 104655) ((-65 . -626) 104584) ((-977 . -1115) T) ((-825 . -1115) 104374) ((-320 . -102) T) ((-914 . -1233) T) ((-48 . -1037) T) ((-1246 . -649) 104282) ((-699 . -102) 104260) ((-44 . -727) 104244) ((-560 . -102) T) ((-302 . -626) 104175) ((-67 . -392) T) ((-67 . -405) T) ((-672 . -23) T) ((-827 . -656) 104111) ((-680 . -771) T) ((-1230 . -1115) 104089) ((-360 . -1071) 104034) ((-685 . -1115) 104012) ((-1077 . -148) T) ((-965 . -148) 103991) ((-965 . -146) 103970) ((-809 . -102) T) ((-153 . -727) 103954) ((-491 . -148) 103933) ((-491 . -146) 103912) ((-360 . -111) 103841) ((-1095 . -1073) T) ((-330 . -860) 103820) ((-1275 . -988) 103789) ((-637 . -1115) T) ((-1268 . -988) 103751) ((-521 . -132) T) ((-517 . -132) T) ((-303 . -231) 103701) ((-368 . -1073) T) ((-362 . -1073) T) ((-354 . -1073) T) ((-302 . -1064) 103643) ((-1247 . -988) 103612) ((-388 . -860) T) ((-108 . -1073) T) ((-1014 . -736) T) ((-880 . -933) T) ((-853 . -805) 103591) ((-853 . -802) 103570) ((-428 . -317) 103509) ((-478 . -102) T) ((-605 . -988) 103478) ((-327 . -1115) T) ((-417 . -805) 103457) ((-417 . -802) 103436) ((-510 . -499) 103418) ((-1269 . -1053) 103384) ((-1267 . -21) T) ((-1267 . -25) T) ((-1246 . -21) T) ((-1246 . -25) T) ((-825 . -727) 103326) ((-360 . -626) 103256) ((-709 . -414) T) ((-1296 . -1233) T) ((-1128 . -421) 103225) ((-616 . -102) T) ((-1092 . -1233) T) ((-1018 . -377) NIL) ((-681 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1194 . -656) 103135) ((-747 . -1233) T) ((-741 . -1066) 102978) ((-44 . -771) T) ((-741 . -650) 102827) ((-603 . -102) T) ((-663 . -666) 102811) ((-77 . -406) T) ((-77 . -405) T) ((-142 . -1233) T) ((-881 . -148) T) ((-881 . -146) NIL) ((-1232 . -93) T) ((-360 . -1064) T) ((-227 . -238) T) ((-70 . -392) T) ((-70 . -405) T) ((-1181 . -102) T) ((-680 . -524) 102744) ((-1295 . -656) 102689) ((-699 . -317) 102627) ((-976 . -38) 102524) ((-1196 . -623) 102506) ((-745 . -38) 102476) ((-560 . -317) 102280) ((-1190 . -1066) 102163) ((-324 . -1233) T) ((-360 . -239) T) ((-360 . -249) T) ((-321 . -1233) T) ((-297 . -1115) T) ((-1189 . -1066) 101998) ((-1183 . -1066) 101788) ((-1141 . -1066) 101671) ((-1190 . -650) 101568) ((-1189 . -650) 101409) ((-721 . -1237) T) ((-1183 . -650) 101205) ((-1172 . -661) 101189) 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-1083) 99061) ((-1135 . -897) 99043) ((-809 . -38) 99027) ((-271 . -649) 98975) ((-253 . -649) 98923) ((-711 . -1071) 98910) ((-605 . -1261) 98887) ((-1135 . -1053) 98869) ((-327 . -174) 98800) ((-368 . -1115) T) ((-362 . -1115) T) ((-354 . -1115) T) ((-510 . -19) 98782) ((-1117 . -152) 98766) ((-881 . -238) NIL) ((-108 . -1115) T) ((-117 . -1071) 98753) ((-721 . -372) T) ((-510 . -614) 98728) ((-711 . -111) 98713) ((-1267 . -235) 98659) ((-1246 . -235) 98558) ((-446 . -102) T) ((-886 . -1278) T) ((-256 . -102) T) ((-45 . -1164) 98508) ((-117 . -111) 98493) ((-1308 . -623) 98460) ((-1308 . -500) 98442) ((-1285 . -623) 98424) ((-1256 . -238) T) ((-645 . -730) T) ((-617 . -730) T) ((-1241 . -623) 98406) ((-1239 . -860) T) ((-1227 . -1127) T) ((-1227 . -23) T) ((-1188 . -462) 98337) ((-825 . -524) 98270) ((-1050 . -1233) T) ((-246 . -1066) 98147) ((-1183 . -317) 98032) ((-1182 . -1115) T) ((-956 . -152) 98016) ((-1174 . -1115) T) ((-1157 . -658) 97954) ((-246 . -650) 97876) ((-1141 . -317) 97863) ((-1140 . -462) 97814) ((-1102 . -566) 97745) ((-535 . -102) T) ((-530 . -102) 97695) ((-1102 . -1237) 97674) ((-1095 . -727) 97542) ((-1019 . -1066) 97492) ((-792 . -1237) 97471) ((-790 . -1237) 97450) ((-62 . -1233) T) ((-487 . -623) 97402) ((-487 . -624) 97324) ((-1009 . -1115) T) ((-792 . -566) 97235) ((-790 . -566) 97166) ((-741 . -317) 97153) ((-492 . -421) 97122) ((-633 . -933) 97101) ((-464 . -1237) 97080) ((-711 . -626) 97052) ((-685 . -524) 96985) ((-408 . -623) 96967) ((-674 . -25) T) ((-674 . -21) T) ((-464 . -566) 96898) ((-364 . -25) T) ((-364 . -21) T) ((-361 . -25) T) ((-118 . -933) T) ((-118 . -830) NIL) ((-361 . -21) T) ((-353 . -25) T) ((-353 . -21) T) ((-271 . -25) T) ((-271 . -21) T) ((-253 . -25) T) ((-253 . -21) T) ((-171 . -238) 96849) ((-83 . -393) T) ((-83 . -405) T) ((-135 . -626) 96831) ((-117 . -626) 96803) ((-1019 . -650) 96753) ((-956 . -995) 96737) ((-927 . -650) 96689) ((-927 . -1066) 96641) ((-923 . -21) T) ((-923 . -25) T) ((-882 . -860) 96592) ((-876 . -658) 96552) ((-721 . -1127) T) ((-721 . -23) T) ((-711 . -1064) T) ((-711 . -239) T) ((-297 . -174) T) ((-664 . -1233) T) ((-319 . -93) T) ((-657 . -1115) 96530) ((-642 . -620) 96505) ((-642 . -1115) T) ((-591 . -1237) T) ((-591 . -566) T) ((-528 . -1237) T) ((-528 . -566) T) ((-497 . -656) 96455) ((-484 . -235) 96401) ((-437 . -1066) 96385) ((-437 . -650) 96369) ((-368 . -727) 96321) ((-362 . -727) 96273) ((-348 . -1071) 96257) ((-354 . -727) 96209) ((-348 . -111) 96188) ((-176 . -1071) 96120) ((-219 . -656) 96070) ((-176 . -111) 95981) ((-108 . -727) 95931) ((-281 . -1115) T) ((-280 . -1115) T) ((-279 . -1115) T) ((-278 . -1115) T) ((-277 . -1115) T) ((-276 . -1115) T) ((-275 . -1115) T) ((-214 . -1115) T) ((-213 . -1115) T) ((-171 . -1221) 95909) ((-171 . -1218) 95887) ((-211 . -1115) T) ((-210 . -1115) T) ((-117 . -1064) T) ((-209 . -1115) T) ((-208 . -1115) T) ((-205 . -1115) T) ((-204 . -1115) T) ((-203 . -1115) T) ((-202 . -1115) T) ((-201 . -1115) T) ((-200 . -1115) T) ((-199 . -1115) T) ((-198 . -1115) T) ((-197 . -1115) T) ((-196 . -1115) T) ((-195 . -1115) T) ((-246 . -102) 95677) ((-171 . -35) 95655) ((-171 . -95) 95633) ((-664 . -1053) 95529) ((-492 . -1073) 95479) ((-1128 . -1115) 95269) ((-1157 . -34) T) ((-680 . -499) 95253) ((-73 . -1233) T) ((-105 . -623) 95235) ((-1307 . -623) 95217) ((-390 . -623) 95199) ((-348 . -626) 95151) ((-176 . -626) 95068) ((-1232 . -500) 95049) ((-741 . -38) 94898) ((-581 . -1221) T) ((-581 . -1218) T) ((-541 . -623) 94880) ((-530 . -317) 94818) ((-510 . -623) 94800) ((-510 . -624) 94782) ((-1232 . -623) 94748) ((-1183 . -1167) NIL) ((-1042 . -1086) 94717) ((-1042 . -1115) T) ((-1019 . -102) T) ((-986 . -102) T) ((-927 . -102) T) ((-904 . -1053) 94694) ((-1157 . -736) T) ((-1018 . -658) 94601) ((-486 . -1115) T) ((-473 . -1115) T) ((-596 . -23) T) ((-581 . -35) T) ((-581 . -95) T) ((-437 . -102) T) ((-1078 . -231) 94547) ((-1190 . -38) 94444) ((-876 . -736) T) ((-704 . -933) T) ((-521 . -25) T) ((-517 . -21) T) ((-517 . -25) T) ((-1189 . -38) 94285) ((-348 . -1064) T) ((-1183 . -38) 94081) ((-1095 . -174) T) ((-176 . -1064) T) ((-1141 . -38) 93978) ((-722 . -47) 93955) ((-368 . -174) T) ((-362 . -174) T) ((-529 . -57) 93929) ((-507 . -57) 93879) ((-360 . -1302) 93856) ((-227 . -462) T) ((-327 . -298) 93807) ((-354 . -174) T) ((-176 . -249) T) ((-1246 . -860) 93706) ((-108 . -174) T) ((-882 . -1007) 93690) ((-668 . -1127) T) ((-591 . -372) T) ((-591 . -337) 93677) ((-528 . -337) 93654) ((-528 . -372) T) ((-324 . -315) 93633) ((-321 . -315) T) ((-612 . -860) 93612) ((-1128 . -727) 93554) ((-530 . -290) 93538) ((-668 . -23) T) ((-428 . -233) 93522) ((-321 . -1037) NIL) ((-345 . -23) T) ((-103 . -1025) 93506) ((-45 . -36) 93485) ((-622 . -1115) T) ((-360 . -377) T) ((-534 . -102) T) ((-505 . -27) T) ((-246 . -317) 93423) ((-1102 . -1127) T) ((-1306 . -658) 93397) ((-792 . -1127) T) ((-790 . -1127) T) ((-1194 . -421) 93381) ((-464 . -1127) T) ((-1077 . -462) T) ((-1166 . -1115) T) ((-965 . -462) 93332) ((-1130 . -1098) T) ((-110 . -1115) T) ((-1102 . -23) T) ((-1175 . -524) 93115) ((-827 . -1073) T) ((-792 . -23) T) ((-790 . -23) T) ((-491 . -462) 93066) ((-471 . -23) T) ((-390 . -391) 93045) ((-364 . -235) 93018) ((-361 . -235) 92991) ((-353 . -235) 92964) ((-464 . -23) T) ((-271 . -235) 92937) ((-96 . -1115) T) ((-722 . -1233) T) ((-680 . -294) 92914) ((-494 . -524) 92847) ((-1275 . -1066) 92730) ((-1275 . -650) 92627) ((-1268 . -650) 92468) ((-1268 . -1066) 92303) ((-1247 . -650) 92099) ((-297 . -298) T) ((-1247 . -1066) 91889) ((-1097 . -623) 91871) ((-1097 . -624) 91852) ((-417 . -922) 91831) ((-1227 . -132) T) ((-50 . -1127) T) ((-1183 . -410) 91783) ((-1039 . -933) T) ((-1018 . -736) T) ((-853 . -658) 91756) ((-722 . -897) NIL) ((-606 . -1066) 91716) ((-591 . -1127) T) ((-528 . -1127) T) ((-605 . -1066) 91599) ((-1172 . -34) T) ((-1019 . -317) NIL) ((-825 . -499) 91583) ((-606 . -650) 91556) ((-363 . -933) T) ((-605 . -650) 91453) ((-923 . -235) 91440) ((-417 . -658) 91356) ((-50 . -23) T) ((-721 . -132) T) ((-722 . -1053) 91236) ((-591 . -23) T) ((-108 . -524) NIL) ((-528 . -23) T) ((-171 . -419) 91207) ((-1155 . -1115) T) ((-1298 . -1297) 91191) ((-711 . -805) T) ((-711 . -802) T) ((-1135 . -315) T) ((-388 . -148) T) ((-288 . -623) 91173) ((-287 . -623) 91155) ((-1246 . -1007) 91125) ((-48 . -933) T) ((-685 . -499) 91109) ((-258 . -1290) 91079) ((-257 . -1290) 91049) ((-1192 . -860) T) ((-1103 . -238) T) ((-1128 . -174) 91028) ((-1135 . -1037) T) ((-1061 . -34) T) ((-846 . -148) 91007) ((-846 . -146) 90986) ((-747 . -107) 90970) ((-622 . -133) T) ((-492 . -1115) 90760) ((-1194 . -1073) T) ((-881 . -462) T) ((-85 . -1233) T) ((-246 . -38) 90730) ((-142 . -107) 90712) ((-722 . -386) 90696) ((-843 . -626) 90564) ((-1306 . -736) T) ((-1295 . -1073) T) ((-1275 . -102) T) ((-1135 . -555) T) ((-589 . -102) T) ((-130 . -500) 90546) ((-1268 . -102) T) ((-400 . -1071) 90530) ((-1188 . -962) 90499) ((-44 . -294) 90476) ((-130 . -623) 90443) ((-52 . -623) 90425) ((-1140 . -962) 90392) ((-663 . -421) 90376) ((-1247 . -102) T) ((-1174 . -524) NIL) ((-672 . -25) T) ((-631 . -1071) 90360) ((-672 . -21) T) ((-976 . -656) 90270) ((-745 . -656) 90215) ((-725 . -656) 90187) ((-400 . -111) 90166) ((-224 . -261) 90150) ((-1069 . -1068) 90090) ((-1069 . -1115) T) ((-1019 . -1167) T) ((-828 . -1115) T) ((-463 . -656) 90005) ((-352 . -1237) T) ((-645 . -658) 89989) ((-631 . -111) 89968) ((-617 . -658) 89952) ((-606 . -102) T) ((-319 . -500) 89933) ((-596 . -132) T) ((-605 . -102) T) ((-424 . -1115) T) ((-394 . -1115) T) ((-319 . -623) 89899) ((-229 . -1115) 89877) ((-657 . -524) 89810) ((-642 . -524) 89654) ((-843 . -1064) 89633) ((-654 . -152) 89617) ((-352 . -566) T) ((-722 . -913) 89560) ((-560 . -231) 89510) ((-1275 . -292) 89476) ((-1268 . -292) 89442) ((-1095 . -298) 89393) ((-497 . -858) T) ((-225 . -1127) T) ((-1247 . -292) 89359) ((-1227 . -503) 89325) ((-1019 . -38) 89275) ((-219 . -858) T) ((-428 . -656) 89234) ((-927 . -38) 89186) 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87919) ((-45 . -620) 87898) ((-324 . -310) T) ((-837 . -238) 87877) ((-487 . -626) 87827) ((-1247 . -317) 87712) ((-680 . -623) 87674) ((-59 . -860) 87653) ((-1019 . -410) 87635) ((-558 . -623) 87617) ((-809 . -656) 87576) ((-825 . -614) 87553) ((-526 . -860) 87532) ((-506 . -860) 87511) ((-40 . -1237) T) ((-1014 . -1053) 87407) ((-50 . -132) T) ((-591 . -132) T) ((-528 . -132) T) ((-302 . -658) 87267) ((-352 . -337) 87244) ((-352 . -372) T) ((-330 . -331) 87221) ((-327 . -294) 87179) ((-40 . -566) T) ((-388 . -1218) T) ((-388 . -1221) T) ((-1050 . -1209) 87154) ((-1205 . -241) 87104) ((-1183 . -233) 87056) ((-338 . -1115) T) ((-388 . -95) T) ((-388 . -35) T) ((-1050 . -107) 87002) ((-487 . -1064) T) ((-1307 . -1071) 86986) ((-489 . -241) 86936) ((-1175 . -499) 86870) ((-1298 . -1066) 86854) ((-390 . -1071) 86838) ((-1298 . -650) 86808) ((-487 . -249) T) ((-826 . -102) T) ((-724 . -148) 86787) ((-724 . -146) 86766) ((-494 . -499) 86750) ((-495 . -344) 86719) ((-1307 . -111) 86698) 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-1017) 85400) ((-79 . -623) 85382) ((-722 . -315) 85361) ((-302 . -736) 85263) ((-834 . -102) T) ((-874 . -854) T) ((-302 . -483) 85242) ((-1298 . -102) T) ((-40 . -372) T) ((-882 . -148) 85221) ((-495 . -656) 85203) ((-882 . -146) 85182) ((-1174 . -499) 85164) ((-1307 . -1064) T) ((-492 . -524) 85097) ((-1161 . -1233) T) ((-977 . -623) 85079) ((-657 . -499) 85063) ((-642 . -499) 84994) ((-825 . -623) 84725) ((-48 . -27) T) ((-1194 . -727) 84622) ((-663 . -1115) T) ((-871 . -870) T) ((-446 . -373) 84596) ((-741 . -656) 84506) ((-1117 . -102) T) ((-985 . -1115) T) ((-874 . -1115) T) ((-826 . -317) 84493) ((-543 . -537) T) ((-543 . -586) T) ((-1303 . -391) 84465) ((-1069 . -524) 84398) ((-1175 . -294) 84374) ((-246 . -233) 84343) ((-258 . -1066) 84220) ((-257 . -1066) 84097) ((-1295 . -727) 84067) ((-1182 . -93) T) ((-1009 . -93) T) ((-827 . -174) 84046) ((-258 . -650) 83968) ((-257 . -650) 83890) ((-1230 . -500) 83867) ((-229 . -524) 83800) ((-631 . -805) 83779) ((-631 . -802) 83758) 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-860) 82504) ((-1194 . -174) 82455) ((-374 . -102) T) ((-246 . -244) 82434) ((-258 . -102) T) ((-257 . -102) T) ((-1256 . -962) 82403) ((-251 . -860) 82382) ((-826 . -38) 82231) ((-45 . -524) 82023) ((-1174 . -294) 81973) ((-216 . -1115) T) ((-1165 . -1115) T) ((-882 . -238) 81952) ((-1165 . -620) 81931) ((-596 . -25) T) ((-596 . -21) T) ((-1117 . -317) 81869) ((-976 . -421) 81853) ((-709 . -1237) T) ((-642 . -294) 81806) ((-1102 . -649) 81754) ((-792 . -649) 81702) ((-790 . -649) 81650) ((-352 . -132) T) ((-297 . -623) 81632) ((-918 . -1115) T) ((-709 . -566) T) ((-130 . -626) 81614) ((-880 . -1127) T) ((-464 . -649) 81562) ((-918 . -916) 81546) ((-388 . -462) T) ((-497 . -1115) T) ((-956 . -317) 81484) ((-711 . -658) 81456) ((-559 . -854) T) ((-219 . -1115) T) ((-324 . -933) 81435) ((-321 . -933) T) ((-321 . -830) NIL) ((-400 . -730) T) ((-880 . -23) T) ((-117 . -658) 81422) ((-484 . -146) 81401) ((-428 . -421) 81385) ((-484 . -148) 81364) ((-110 . -499) 81346) ((-319 . -626) 81327) 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-624) 76762) ((-642 . -624) NIL) ((-642 . -623) 76744) ((-497 . -174) T) ((-227 . -650) 76709) ((-225 . -21) T) ((-219 . -174) T) ((-225 . -25) T) ((-484 . -1221) 76675) ((-484 . -1218) 76641) ((-281 . -623) 76623) ((-280 . -623) 76605) ((-279 . -623) 76587) ((-278 . -623) 76569) ((-277 . -623) 76551) ((-510 . -661) 76533) ((-276 . -623) 76515) ((-348 . -736) T) ((-275 . -623) 76497) ((-110 . -19) 76479) ((-176 . -736) T) ((-510 . -382) 76461) ((-214 . -623) 76443) ((-530 . -1164) 76427) ((-510 . -124) T) ((-110 . -614) 76402) ((-213 . -623) 76384) ((-484 . -35) 76350) ((-484 . -95) 76316) ((-211 . -623) 76298) ((-210 . -623) 76280) ((-209 . -623) 76262) ((-208 . -623) 76244) ((-205 . -623) 76226) ((-204 . -623) 76208) ((-203 . -623) 76190) ((-202 . -623) 76172) ((-201 . -623) 76154) ((-200 . -623) 76136) ((-199 . -623) 76118) ((-546 . -1118) 76070) ((-198 . -623) 76052) ((-197 . -623) 76034) ((-45 . -499) 75971) ((-196 . -623) 75953) ((-195 . -623) 75935) ((-153 . -626) 75904) ((-1130 . -102) T) ((-825 . -111) 75794) ((-654 . -102) 75744) ((-492 . -294) 75721) ((-1306 . -1053) 75705) ((-1128 . -623) 75436) ((-1116 . -1115) T) ((-1061 . -1233) T) ((-1188 . -317) 75423) ((-1077 . -1066) 75410) ((-1150 . -1115) T) ((-965 . -1066) 75253) ((-1140 . -317) 75240) ((-1111 . -1098) T) ((-633 . -1127) T) ((-1077 . -650) 75227) ((-1105 . -1098) T) ((-965 . -650) 75076) ((-1102 . -235) 75049) ((-491 . -1066) 74892) ((-1088 . -1098) T) ((-1081 . -1098) T) ((-1051 . -1098) T) ((-1034 . -1098) T) ((-118 . -1127) T) ((-491 . -650) 74741) ((-792 . -235) 74728) ((-829 . -102) T) ((-636 . -1098) T) ((-633 . -23) T) ((-1165 . -524) 74520) ((-493 . -1098) T) ((-396 . -102) T) ((-332 . -102) T) ((-220 . -1098) T) ((-976 . -1115) T) ((-153 . -1064) T) ((-741 . -421) 74504) ((-118 . -23) T) ((-1018 . -913) 74456) ((-745 . -1115) T) ((-725 . -1115) T) ((-463 . -1115) T) ((-417 . -1233) T) ((-324 . -440) 74440) ((-602 . -93) T) ((-1275 . -656) 74350) ((-1042 . -624) 74311) ((-1039 . -1237) T) ((-227 . -102) T) ((-1042 . -623) 74273) ((-1268 . -656) 74155) ((-826 . -233) 74139) ((-825 . -626) 73889) ((-1247 . -656) 73726) ((-1039 . -566) T) ((-843 . -658) 73699) ((-363 . -1237) T) ((-486 . -623) 73661) ((-486 . -624) 73622) ((-473 . -624) 73583) ((-473 . -623) 73545) ((-606 . -656) 73504) ((-417 . -895) 73488) ((-327 . -1071) 73323) ((-417 . -897) 73248) ((-605 . -656) 73158) ((-853 . -1053) 73054) ((-497 . -524) NIL) ((-492 . -614) 73031) ((-591 . -235) 73018) ((-363 . -566) T) ((-528 . -235) 73005) ((-219 . -524) NIL) ((-882 . -462) T) ((-428 . -1115) T) ((-417 . -1053) 72869) ((-327 . -111) 72690) ((-704 . -372) T) ((-227 . -292) T) ((-1230 . -626) 72667) ((-48 . -1237) T) ((-1188 . -1167) 72645) ((-1175 . -296) 72621) ((-825 . -1064) 72571) ((-590 . -132) T) ((-574 . -132) T) ((-505 . -132) T) ((-364 . -238) 72550) ((-361 . -238) 72529) ((-353 . -238) 72508) ((-48 . -566) T) ((-1077 . -102) T) ((-271 . -238) 72487) ((-965 . -102) T) ((-324 . -27) 72466) ((-881 . 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. -656) 69319) ((-581 . -1066) 69306) ((-492 . -623) 69037) ((-246 . -421) 69006) ((-965 . -317) 68993) ((-581 . -650) 68980) ((-65 . -1233) T) ((-1078 . -524) 68824) ((-681 . -1115) T) ((-633 . -132) T) ((-491 . -317) 68811) ((-616 . -1115) T) ((-556 . -102) T) ((-118 . -132) T) ((-297 . -1064) T) ((-182 . -1115) T) ((-162 . -1115) T) ((-157 . -1115) T) ((-155 . -1115) T) ((-463 . -771) T) ((-31 . -1098) T) ((-976 . -174) 68762) ((-985 . -93) T) ((-1095 . -1071) 68672) ((-631 . -804) 68651) ((-603 . -1115) T) ((-631 . -801) 68630) ((-631 . -736) T) ((-303 . -294) 68609) ((-302 . -1233) T) ((-1069 . -623) 68571) ((-1069 . -624) 68532) ((-1039 . -1127) T) ((-171 . -102) T) ((-282 . -860) T) ((-1181 . -1115) T) ((-828 . -623) 68514) ((-1128 . -296) 68491) ((-1117 . -231) 68475) ((-1018 . -315) T) ((-809 . -727) 68459) ((-368 . -1071) 68411) ((-363 . -1127) T) ((-362 . -1071) 68363) ((-424 . -623) 68345) ((-394 . -623) 68327) ((-354 . -1071) 68279) ((-229 . -623) 68211) ((-1095 . -111) 68107) ((-1039 . -23) T) ((-108 . -1071) 68057) ((-911 . -102) T) ((-851 . -102) T) ((-818 . -102) T) ((-779 . -102) T) ((-687 . -102) T) ((-484 . -462) 68036) ((-428 . -174) T) ((-368 . -111) 67974) ((-362 . -111) 67912) ((-354 . -111) 67850) ((-258 . -233) 67819) ((-257 . -233) 67788) ((-363 . -23) T) ((-71 . -1233) T) ((-227 . -38) 67753) ((-108 . -111) 67687) ((-40 . -25) T) ((-40 . -21) T) ((-680 . -730) T) ((-171 . -292) 67665) ((-48 . -1127) T) ((-934 . -25) T) ((-781 . -25) T) ((-1307 . -658) 67639) ((-1165 . -499) 67576) ((-495 . -1115) T) ((-1298 . -656) 67535) ((-1256 . -102) T) ((-1077 . -1167) T) ((-865 . -102) T) ((-246 . -1073) 67485) ((-977 . -802) 67438) ((-977 . -805) 67391) ((-390 . -658) 67375) ((-48 . -23) T) ((-825 . -805) 67354) ((-825 . -802) 67333) ((-558 . -377) T) ((-303 . -614) 67312) ((-487 . -736) T) ((-581 . -102) T) ((-1095 . -626) 67130) ((-255 . -187) T) ((-189 . -187) T) ((-881 . -317) 67087) ((-663 . -294) 67066) ((-112 . -671) T) ((-360 . -1233) T) 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. -317) 42100) ((-219 . -805) T) ((-219 . -802) T) ((-1014 . -23) T) ((-722 . -132) T) ((-1246 . -410) 42070) ((-846 . -656) 42015) ((-837 . -656) 41974) ((-324 . -25) 41826) ((-171 . -421) 41810) ((-324 . -21) 41681) ((-321 . -25) T) ((-321 . -21) T) ((-874 . -377) T) ((-976 . -626) 41534) ((-110 . -34) T) ((-745 . -626) 41490) ((-725 . -626) 41472) ((-492 . -658) 41277) ((-881 . -1073) T) ((-603 . -296) 41252) ((-590 . -148) T) ((-574 . -148) T) ((-505 . -148) T) ((-1188 . -727) 41081) ((-1072 . -102) 41059) ((-1140 . -727) 40908) ((-1135 . -649) 40890) ((-864 . -727) 40860) ((-680 . -1233) T) ((-1 . -102) T) ((-428 . -626) 40768) ((-246 . -623) 40499) ((-1130 . -1115) T) ((-1256 . -421) 40483) ((-1205 . -317) 40287) ((-976 . -1064) T) ((-745 . -1064) T) ((-725 . -1064) T) ((-654 . -1115) 40237) ((-1069 . -658) 40221) ((-865 . -421) 40205) ((-521 . -102) T) ((-517 . -102) T) ((-271 . -317) 40192) ((-253 . -317) 40179) ((-976 . -334) 40158) ((-394 . -658) 40142) ((-680 . -1053) 40038) 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. -1115) 18463) ((-724 . -1115) T) ((-668 . -38) 18433) ((-492 . -913) 18365) ((-255 . -1115) T) ((-189 . -1115) T) ((-363 . -412) T) ((-324 . -148) 18344) ((-324 . -146) 18323) ((-129 . -524) NIL) ((-117 . -566) T) ((-321 . -148) 18279) ((-321 . -146) 18235) ((-48 . -462) T) ((-163 . -1115) T) ((-158 . -1115) T) ((-1175 . -107) 18182) ((-792 . -1167) 18160) ((-699 . -34) T) ((-1298 . -111) 18139) ((-560 . -34) T) ((-494 . -107) 18123) ((-258 . -296) 18100) ((-257 . -296) 18077) ((-881 . -294) 18028) ((-45 . -1233) T) ((-1239 . -854) T) ((-827 . -1233) T) ((-826 . -1064) T) ((-672 . -656) 17997) ((-1194 . -47) 17974) ((-826 . -334) 17936) ((-1102 . -38) 17785) ((-826 . -239) 17764) ((-792 . -38) 17593) ((-790 . -38) 17442) ((-1130 . -500) 17423) ((-464 . -38) 17272) ((-1130 . -623) 17238) ((-1133 . -102) T) ((-654 . -624) 17199) ((-654 . -623) 17111) ((-591 . -1167) T) ((-528 . -1167) T) ((-1162 . -499) 17095) ((-352 . -1066) 17040) ((-1219 . -1115) 17018) ((-1157 . -25) T) ((-1157 . 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196480) ((-1035 . -500) 196461) ((-826 . -736) T) ((-741 . -47) 196426) ((-633 . -38) 196413) ((-364 . -298) T) ((-361 . -298) T) ((-353 . -298) T) ((-271 . -298) 196344) ((-253 . -298) 196275) ((-1052 . -623) 196241) ((-1040 . -102) T) ((-1035 . -623) 196207) ((-636 . -500) 196188) ((-423 . -736) T) ((-118 . -38) 196133) ((-493 . -500) 196114) ((-636 . -623) 196080) ((-423 . -483) T) ((-220 . -500) 196061) ((-493 . -623) 196027) ((-363 . -102) T) ((-220 . -623) 195993) ((-1228 . -1074) T) ((-352 . -656) 195923) ((-721 . -1074) T) ((-1191 . -47) 195900) ((-1190 . -47) 195870) ((-1184 . -47) 195847) ((-129 . -296) 195822) ((-1051 . -152) 195768) ((-924 . -298) T) ((-1142 . -47) 195740) ((-704 . -317) NIL) ((-525 . -623) 195722) ((-520 . -623) 195704) ((-518 . -623) 195686) ((-335 . -1116) 195636) ((-324 . -907) 195600) ((-321 . -907) NIL) ((-722 . -462) 195531) ((-48 . -102) T) ((-1268 . -294) 195489) ((-1247 . -294) 195389) ((-654 . -676) 195373) ((-654 . -661) 195357) ((-348 . -21) T) 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194297) ((-1184 . -897) NIL) ((-1184 . -895) 194249) ((-612 . -614) 194226) ((-1220 . -623) 194158) ((-1192 . -623) 194140) ((-62 . -405) T) ((-1190 . -1054) 194075) ((-1184 . -1054) 194041) ((-704 . -38) 193991) ((-40 . -656) 193921) ((-484 . -294) 193879) ((-1240 . -623) 193861) ((-741 . -386) 193845) ((-848 . -623) 193827) ((-668 . -1074) T) ((-633 . -914) 193786) ((-1268 . -1018) 193752) ((-1247 . -1018) 193718) ((-256 . -1234) T) ((-1104 . -626) 193702) ((-1079 . -1210) 193677) ((-1092 . -626) 193654) ((-882 . -624) 193461) ((-882 . -623) 193443) ((-118 . -914) NIL) ((-711 . -235) 193430) ((-1206 . -499) 193367) ((-428 . -1038) 193345) ((-48 . -317) 193332) ((-1079 . -107) 193278) ((-489 . -499) 193215) ((-530 . -1234) T) ((-1184 . -347) 193167) ((-1157 . -499) 193138) ((-1184 . -386) 193090) ((-1103 . -1074) T) ((-447 . -102) T) ((-185 . -1116) T) ((-258 . -34) T) ((-257 . -34) T) ((-792 . -1074) T) ((-790 . -1074) T) ((-741 . -912) 193067) ((-464 . -1074) T) ((-59 . -499) 193051) ((-1050 . -1072) 193025) ((-529 . -499) 193009) ((-526 . -499) 192993) ((-507 . -499) 192977) ((-506 . -499) 192961) ((-251 . -524) 192894) ((-1050 . -111) 192861) ((-1191 . -912) 192774) ((-1190 . -912) 192680) ((-680 . -1128) T) ((-1184 . -912) 192513) ((-655 . -93) T) ((-1142 . -912) 192497) ((-363 . -1168) T) ((-330 . -1072) 192479) ((-31 . -500) 192460) ((-258 . -804) 192439) ((-258 . -803) 192418) ((-257 . -804) 192397) ((-257 . -803) 192376) ((-31 . -623) 192342) ((-50 . -1074) T) ((-258 . -736) 192292) ((-257 . -736) 192242) ((-1228 . -1116) T) ((-680 . -23) T) ((-591 . -1074) T) ((-528 . -1074) T) ((-388 . -1072) 192207) ((-330 . -111) 192182) ((-73 . -392) T) ((-73 . -405) T) ((-1040 . -38) 192119) ((-704 . -410) 192101) ((-99 . -102) T) ((-721 . -1116) T) ((-1313 . -1067) 192088) ((-1019 . -146) 192060) ((-1019 . -148) 192032) ((-880 . -656) 192004) ((-388 . -111) 191960) ((-327 . -1238) 191939) ((-484 . -1018) 191905) ((-363 . -38) 191870) ((-40 . -379) 191842) ((-883 . -623) 191714) ((-128 . -126) 191698) ((-122 . -126) 191682) ((-846 . -1072) 191652) ((-843 . -21) 191604) ((-837 . -1072) 191588) ((-843 . -25) 191540) ((-327 . -566) 191491) ((-527 . -626) 191472) ((-574 . -838) T) ((-246 . -1234) T) ((-1050 . -626) 191441) ((-846 . -111) 191406) ((-837 . -111) 191385) ((-1268 . -623) 191367) ((-1247 . -623) 191349) ((-1247 . -624) 191020) ((-1189 . -923) 190999) ((-1141 . -923) 190978) ((-48 . -38) 190943) ((-1306 . -1128) T) ((-546 . -294) 190899) ((-612 . -623) 190811) ((-612 . -624) 190772) ((-1304 . -1128) T) ((-370 . -626) 190756) ((-330 . -626) 190740) ((-1158 . -238) 190719) ((-246 . -1054) 190546) ((-1189 . -658) 190435) ((-1141 . -658) 190324) ((-864 . -658) 190298) ((-728 . -623) 190280) ((-556 . -377) T) ((-1306 . -23) T) ((-704 . -914) NIL) ((-1304 . -23) T) ((-501 . -1116) T) ((-388 . -626) 190230) ((-388 . -628) 190212) ((-1050 . -1065) T) ((-875 . -102) T) ((-1206 . -294) 190191) ((-171 . -377) 190142) ((-1020 . -1234) T) ((-846 . -626) 190096) ((-837 . -626) 190051) ((-44 . -23) T) ((-489 . -294) 190030) ((-596 . -1116) T) ((-1162 . -1125) 189999) ((-1120 . -1119) 189951) ((-400 . -21) T) ((-400 . -25) T) ((-153 . -1128) T) ((-1313 . -102) T) ((-1020 . -895) 189933) ((-1020 . -897) 189915) ((-1228 . -727) 189812) ((-633 . -233) 189796) ((-631 . -21) T) ((-297 . -566) T) ((-631 . -25) T) ((-1214 . -1116) T) ((-721 . -727) 189761) ((-246 . -386) 189730) ((-1020 . -1054) 189690) ((-388 . -1065) T) ((-225 . -1074) T) ((-118 . -233) 189667) ((-59 . -294) 189619) ((-153 . -23) T) ((-526 . -294) 189571) ((-335 . -524) 189504) ((-506 . -294) 189456) ((-388 . -249) T) ((-388 . -239) T) ((-846 . -1065) T) ((-837 . -1065) T) ((-722 . -963) 189425) ((-711 . -860) T) ((-484 . -623) 189407) ((-1270 . -1067) 189312) ((-590 . -656) 189284) ((-574 . -656) 189256) ((-505 . -656) 189206) ((-837 . -239) 189185) ((-135 . -860) T) ((-1270 . -650) 189077) ((-668 . -1116) T) ((-1206 . -614) 189056) ((-560 . -1210) 189035) ((-345 . -1116) T) ((-327 . -372) 189014) ((-417 . -148) 188993) ((-417 . -146) 188972) ((-978 . -1128) 188871) ((-246 . -912) 188803) ((-825 . -1128) 188753) ((-664 . -862) 188737) ((-489 . -614) 188716) ((-560 . -107) 188666) ((-1020 . -386) 188648) ((-1020 . -347) 188630) ((-1193 . -623) 188612) ((-97 . -1116) T) ((-978 . -23) 188423) ((-487 . -21) T) ((-487 . -25) T) ((-825 . -23) 188313) ((-1193 . -624) 188235) ((-59 . -19) 188219) ((-1189 . -736) T) ((-1141 . -736) T) ((-1103 . -1116) T) ((-526 . -19) 188203) ((-506 . -19) 188187) ((-59 . -614) 188164) ((-1019 . -238) 188136) ((-915 . -102) 188114) ((-864 . -736) T) ((-792 . -1116) T) ((-526 . -614) 188091) ((-506 . -614) 188068) ((-790 . -1116) T) ((-790 . -1081) 188035) ((-471 . -1116) T) ((-464 . -1116) T) ((-596 . -727) 188010) ((-659 . -1116) T) ((-1276 . -47) 187987) ((-1270 . -102) T) ((-1269 . -47) 187957) ((-1248 . -47) 187934) ((-1228 . -174) 187885) ((-1190 . -315) 187864) ((-1184 . -315) 187843) ((-1112 . -626) 187824) ((-1106 . -626) 187805) ((-1096 . -566) 187756) ((-1096 . -1238) 187707) ((-1020 . -912) NIL) ((-1089 . -626) 187688) ((-680 . -132) T) ((-637 . -1128) T) ((-1082 . -626) 187669) ((-1052 . -626) 187650) ((-1035 . -626) 187631) ((-724 . -1072) 187601) ((-709 . -656) 187551) ((-282 . -1116) T) ((-85 . -451) T) ((-85 . -405) T) ((-722 . -907) 187490) ((-721 . -174) T) ((-50 . -1116) T) ((-605 . -47) 187467) ((-227 . -658) 187432) ((-591 . -1116) T) ((-528 . -1116) T) ((-497 . -830) T) ((-497 . -934) T) ((-368 . -1238) T) ((-362 . -1238) T) ((-354 . -1238) T) ((-327 . -1128) T) ((-324 . -1067) 187342) ((-321 . -1067) 187271) ((-108 . -1238) T) ((-636 . -626) 187252) ((-368 . -566) T) ((-219 . -934) T) ((-219 . -830) T) ((-324 . -650) 187162) ((-321 . -650) 187091) ((-362 . -566) T) ((-354 . -566) T) ((-493 . -626) 187072) ((-108 . -566) T) ((-668 . -727) 187042) ((-1184 . -1038) NIL) ((-220 . -626) 187023) ((-327 . -23) T) ((-67 . -1234) T) ((-1016 . -623) 186955) ((-704 . -233) 186937) ((-724 . -111) 186902) ((-654 . -34) T) ((-251 . -499) 186886) ((-1313 . -1168) T) ((-1308 . -21) T) ((-1308 . -25) T) ((-1306 . -132) T) ((-1118 . -1114) 186870) ((-173 . -1116) T) ((-1304 . -132) T) ((-1297 . -102) T) ((-1280 . -623) 186836) ((-1276 . -1234) T) ((-1269 . -1234) T) ((-966 . -923) 186815) ((-1269 . -1054) 186750) ((-1248 . -1234) T) ((-1248 . -897) NIL) ((-525 . -626) 186734) ((-1248 . -895) 186686) ((-1248 . -1054) 186652) ((-1228 . -524) 186619) ((-491 . -923) 186598) ((-1206 . -624) NIL) ((-1206 . -623) 186580) ((-1103 . -727) 186429) ((-1078 . -658) 186401) ((-966 . -658) 186290) ((-607 . -500) 186271) ((-595 . -500) 186252) ((-792 . -727) 186081) ((-607 . -623) 186047) ((-595 . -623) 186013) ((-546 . -623) 185995) ((-546 . -624) 185976) ((-790 . -727) 185825) ((-1093 . -102) T) ((-390 . -25) T) ((-633 . -656) 185797) ((-390 . -21) T) ((-491 . -658) 185686) ((-471 . -727) 185657) ((-464 . -727) 185506) ((-1003 . -102) T) ((-1158 . -1139) 185451) ((-1062 . -1227) 185380) ((-915 . -317) 185318) ((-747 . -102) T) ((-118 . -656) 185248) ((-615 . -626) 185230) ((-886 . -93) T) ((-724 . -626) 185184) ((-541 . -25) T) ((-691 . -93) T) ((-686 . -93) T) ((-674 . -623) 185166) ((-655 . -500) 185147) ((-142 . -102) T) ((-44 . -132) T) ((-655 . -623) 185100) ((-605 . -1234) T) ((-352 . -1074) T) ((-297 . -1128) T) ((-488 . -93) T) ((-417 . -238) 185079) ((-364 . -623) 185061) ((-361 . -623) 185043) ((-353 . -623) 185025) ((-271 . -624) 184773) ((-271 . -623) 184755) ((-253 . -623) 184737) ((-253 . -624) 184598) ((-134 . -93) T) ((-139 . -93) T) ((-138 . -93) T) ((-1157 . -623) 184580) ((-1136 . -650) 184567) ((-1136 . -1067) 184554) ((-829 . -736) T) ((-829 . -867) T) ((-612 . -296) 184531) ((-591 . -727) 184496) ((-489 . -624) NIL) ((-489 . -623) 184478) ((-528 . -727) 184423) ((-324 . -102) T) ((-321 . -102) T) ((-297 . -23) T) ((-153 . -132) T) ((-924 . -623) 184405) ((-924 . -624) 184387) ((-396 . -736) T) ((-882 . -1072) 184339) ((-882 . -111) 184277) ((-724 . -1065) T) ((-722 . -1260) 184261) ((-704 . -358) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-529 . -623) 184193) ((-388 . -805) T) ((-225 . -1116) T) ((-169 . -1234) T) ((-388 . -802) T) ((-227 . -804) T) ((-227 . -801) T) ((-59 . -624) 184154) ((-59 . -623) 184066) ((-227 . -736) T) ((-526 . -624) 184027) ((-526 . -623) 183939) ((-507 . -623) 183871) ((-506 . -624) 183832) ((-506 . -623) 183744) ((-1096 . -372) 183695) ((-40 . -421) 183672) ((-77 . -1234) T) ((-881 . -923) NIL) ((-368 . -337) 183656) ((-368 . -372) T) ((-362 . -337) 183640) ((-362 . -372) T) ((-354 . -337) 183624) ((-354 . -372) T) ((-324 . -292) 183603) ((-108 . -372) T) ((-70 . -1234) T) ((-1248 . -347) 183555) ((-881 . -658) 183500) ((-1248 . -386) 183452) ((-978 . -132) 183307) ((-825 . -132) 183197) ((-972 . -661) 183181) ((-1103 . -174) 183092) ((-972 . -382) 183076) ((-1078 . -804) T) ((-1078 . -801) T) ((-882 . -626) 182974) ((-792 . -174) 182865) ((-790 . -174) 182776) ((-826 . -47) 182738) ((-1078 . -736) T) ((-335 . -499) 182722) ((-966 . -736) T) ((-1297 . -317) 182660) ((-1276 . -912) 182573) ((-464 . -174) 182484) ((-251 . -294) 182436) ((-1269 . -912) 182342) ((-1268 . -1072) 182177) ((-1248 . -912) 182010) ((-491 . -736) T) ((-1247 . -1072) 181818) ((-1228 . -298) 181797) ((-1203 . -1234) T) ((-1200 . -377) T) ((-1199 . -377) T) ((-1162 . -152) 181781) ((-1136 . -102) T) ((-1134 . -1116) T) ((-1096 . -23) T) ((-1096 . -1128) T) ((-1091 . -102) T) ((-1073 . -623) 181748) ((-1019 . -419) 181720) ((-941 . -969) T) ((-747 . -317) 181658) ((-75 . -1234) T) ((-674 . -391) 181630) ((-171 . -923) 181583) ((-30 . -969) T) ((-112 . -854) T) ((-1 . -623) 181565) ((-1015 . -907) 181522) ((-129 . -661) 181504) ((-50 . -630) 181488) ((-704 . -656) 181423) ((-605 . -912) 181336) ((-448 . -102) T) ((-129 . -382) 181318) ((-142 . -317) NIL) ((-882 . -1065) T) ((-843 . -860) 181297) ((-81 . -1234) T) ((-721 . -298) T) ((-40 . -1074) T) ((-591 . -174) T) ((-528 . -174) T) ((-521 . -623) 181279) ((-171 . -658) 181153) ((-517 . -623) 181135) ((-360 . -148) 181117) ((-360 . -146) T) ((-368 . -1128) T) ((-362 . -1128) T) ((-354 . -1128) T) ((-1020 . -315) T) ((-928 . -315) T) ((-882 . -249) T) ((-108 . -1128) T) ((-882 . -239) 181096) ((-1268 . -111) 180917) ((-1247 . -111) 180706) ((-251 . -1272) 180690) ((-574 . -858) T) ((-368 . -23) T) ((-363 . -358) T) ((-324 . -317) 180677) ((-321 . -317) 180618) ((-362 . -23) T) ((-327 . -132) T) ((-354 . -23) T) ((-1020 . -1038) T) ((-31 . -626) 180599) ((-108 . -23) T) ((-664 . -1067) 180583) ((-251 . -614) 180560) ((-341 . -1116) T) ((-664 . -650) 180530) ((-1270 . -38) 180422) ((-1257 . -923) 180401) ((-112 . -1116) T) ((-826 . -1234) T) ((-1051 . -102) T) ((-1257 . -658) 180290) ((-881 . -804) NIL) ((-865 . -658) 180264) ((-881 . -801) NIL) ((-826 . -897) NIL) ((-881 . -736) T) ((-1103 . -524) 180137) ((-792 . -524) 180084) ((-790 . -524) 180036) ((-581 . -658) 180023) ((-826 . -1054) 179851) ((-464 . -524) 179794) ((-398 . -399) T) ((-1268 . -626) 179607) ((-1247 . -626) 179355) ((-60 . -1234) T) ((-631 . -860) 179334) ((-510 . -671) T) ((-1162 . -992) 179303) ((-1040 . -656) 179240) ((-1019 . -462) T) ((-709 . -858) T) ((-520 . -802) T) ((-484 . -1072) 179075) ((-510 . -113) T) ((-352 . -1116) T) ((-321 . -1168) NIL) ((-297 . -132) T) ((-404 . -1116) T) ((-880 . -1074) T) ((-704 . -379) 179042) ((-363 . -656) 178972) ((-225 . -630) 178949) ((-335 . -294) 178901) ((-484 . -111) 178722) ((-1268 . -1065) T) ((-1247 . -1065) T) ((-826 . -386) 178706) ((-171 . -736) T) ((-664 . -102) T) ((-1268 . -249) 178685) ((-1268 . -239) 178637) ((-1247 . -239) 178542) ((-1247 . -249) 178521) ((-1019 . -412) NIL) ((-680 . -649) 178469) ((-324 . -38) 178379) ((-321 . -38) 178308) ((-69 . -623) 178290) ((-327 . -503) 178256) ((-48 . -656) 178206) ((-1206 . -296) 178185) ((-1242 . -860) T) ((-1129 . -1128) 178135) ((-83 . -1234) T) ((-61 . -623) 178117) ((-489 . -296) 178096) ((-1299 . -1054) 178073) ((-1181 . -1116) T) ((-1129 . -23) 177963) ((-826 . -912) 177899) ((-1257 . -736) T) ((-1118 . -1234) T) ((-484 . -626) 177725) ((-360 . -238) T) ((-1103 . -298) 177656) ((-980 . -1116) T) ((-904 . -102) T) ((-792 . -298) 177567) ((-335 . -19) 177551) ((-59 . -296) 177528) ((-790 . -298) 177459) ((-865 . -736) T) ((-118 . -858) NIL) ((-526 . -296) 177436) ((-335 . -614) 177413) ((-506 . -296) 177390) ((-464 . -298) 177321) ((-1051 . -317) 177172) ((-886 . -500) 177153) ((-886 . -623) 177119) ((-691 . -500) 177100) ((-581 . -736) T) ((-686 . -500) 177081) ((-691 . -623) 177031) ((-686 . -623) 176997) ((-672 . -623) 176979) ((-488 . -500) 176960) ((-488 . -623) 176926) ((-251 . -624) 176887) ((-251 . -500) 176864) ((-139 . -500) 176845) ((-138 . -500) 176826) ((-134 . -500) 176807) ((-251 . -623) 176699) ((-215 . -102) T) ((-139 . -623) 176665) ((-138 . -623) 176631) ((-134 . -623) 176597) ((-1163 . -34) T) ((-957 . -1234) T) ((-352 . -727) 176542) ((-680 . -25) T) ((-680 . -21) T) ((-1193 . -626) 176523) ((-484 . -1065) T) ((-645 . -427) 176488) ((-617 . -427) 176453) ((-1136 . -1168) T) ((-722 . -1067) 176276) ((-591 . -298) T) ((-528 . -298) T) ((-1269 . -315) 176255) ((-484 . -239) 176207) ((-484 . -249) 176186) ((-1248 . -315) 176165) ((-722 . -650) 175994) ((-1248 . -1038) NIL) ((-1096 . -132) T) ((-882 . -805) 175973) ((-145 . -102) T) ((-40 . -1116) T) ((-882 . -802) 175952) ((-654 . -1026) 175936) ((-590 . -1074) T) ((-574 . -1074) T) ((-505 . -1074) T) ((-417 . -462) T) ((-368 . -132) T) ((-324 . -410) 175920) ((-321 . -410) 175881) ((-362 . -132) T) ((-354 . -132) T) ((-1198 . -1116) T) ((-1136 . -38) 175868) ((-1110 . -623) 175835) ((-108 . -132) T) ((-968 . -1116) T) ((-935 . -1116) T) ((-781 . -1116) T) ((-682 . -1116) T) ((-711 . -148) T) ((-117 . -148) T) ((-1306 . -21) T) ((-1306 . -25) T) ((-1304 . -21) T) ((-1304 . -25) T) ((-674 . -1072) 175819) ((-541 . -860) T) ((-510 . -860) T) ((-364 . -1072) 175771) ((-361 . -1072) 175723) ((-353 . -1072) 175675) ((-258 . -1234) T) ((-257 . -1234) T) ((-271 . -1072) 175518) ((-253 . -1072) 175361) ((-674 . -111) 175340) ((-827 . -1238) 175319) ((-557 . -854) T) ((-324 . -914) 175285) ((-364 . -111) 175223) ((-361 . -111) 175161) ((-353 . -111) 175099) ((-271 . -111) 174928) ((-253 . -111) 174757) ((-321 . -914) NIL) ((-633 . -421) 174741) ((-44 . -21) T) ((-44 . -25) T) ((-825 . -649) 174647) ((-827 . -566) 174626) ((-258 . -1054) 174453) ((-257 . -1054) 174280) ((-127 . -120) 174264) ((-924 . -1072) 174229) ((-722 . -102) T) ((-709 . -1074) T) ((-607 . -626) 174210) ((-595 . -626) 174191) ((-546 . -628) 174094) ((-352 . -174) T) ((-88 . -623) 174076) ((-153 . -21) T) ((-153 . -25) T) ((-924 . -111) 174032) ((-40 . -727) 173977) ((-880 . -1116) T) ((-674 . -626) 173954) ((-655 . -626) 173935) ((-364 . -626) 173872) ((-361 . -626) 173809) ((-557 . -1116) T) ((-353 . -626) 173746) ((-335 . -624) 173707) ((-335 . -623) 173619) ((-271 . -626) 173372) ((-253 . -626) 173157) ((-1247 . -802) 173110) ((-1247 . -805) 173063) ((-258 . -386) 173032) ((-257 . -386) 173001) ((-664 . -38) 172971) ((-618 . -34) T) ((-492 . -1128) 172921) ((-485 . -34) T) ((-1129 . -132) 172811) ((-978 . -25) 172622) ((-924 . -626) 172572) ((-884 . -623) 172554) ((-978 . -21) 172509) ((-825 . -21) 172439) ((-825 . -25) 172310) ((-1240 . -377) T) ((-633 . -1074) T) ((-1195 . -566) 172289) ((-1189 . -47) 172266) ((-364 . -1065) T) ((-361 . -1065) T) ((-492 . -23) 172156) ((-353 . -1065) T) ((-271 . -1065) T) ((-253 . -1065) T) ((-1141 . -47) 172128) ((-118 . -1074) T) ((-1050 . -658) 172102) ((-972 . -34) T) ((-364 . -239) 172081) ((-364 . -249) T) ((-361 . -239) 172060) ((-361 . -249) T) ((-353 . -239) 172039) ((-353 . -249) T) ((-271 . -334) 172011) ((-253 . -334) 171968) ((-271 . -239) 171947) ((-1173 . -152) 171931) ((-258 . -912) 171863) ((-257 . -912) 171795) ((-1158 . -907) 171752) ((-1098 . -860) T) ((-424 . -1128) T) ((-1070 . -23) T) ((-1040 . -858) T) ((-924 . -1065) T) ((-330 . -658) 171734) ((-711 . -238) T) ((-680 . -235) 171707) ((-1228 . -1018) 171673) ((-1190 . -934) 171652) ((-1184 . -934) 171631) ((-1184 . -830) NIL) ((-1015 . -1067) 171527) ((-981 . -1234) T) ((-924 . -249) T) ((-827 . -372) 171506) ((-394 . -23) T) ((-128 . -1116) 171484) ((-122 . -1116) 171462) ((-924 . -239) T) ((-129 . -34) T) ((-388 . -658) 171427) ((-1015 . -650) 171375) ((-880 . -727) 171362) ((-1313 . -656) 171334) ((-1062 . -152) 171299) ((-1009 . -1234) T) ((-40 . -174) T) ((-704 . -421) 171281) ((-722 . -317) 171268) ((-846 . -658) 171228) ((-837 . -658) 171202) ((-327 . -25) T) ((-327 . -21) T) ((-668 . -294) 171181) ((-590 . -1116) T) ((-574 . -1116) T) ((-505 . -1116) T) ((-251 . -296) 171158) ((-1189 . -1234) T) ((-1141 . -1234) T) ((-321 . -233) 171119) ((-1189 . -897) NIL) ((-55 . -1116) T) ((-1141 . -897) 170978) ((-130 . -860) T) ((-1189 . -1054) 170858) ((-1141 . -1054) 170741) ((-185 . -623) 170723) ((-864 . -1054) 170619) ((-792 . -294) 170546) ((-827 . -1128) T) 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169623) ((-108 . -649) 169605) ((-492 . -132) 169495) ((-1195 . -1128) T) ((-966 . -47) 169464) ((-633 . -1116) T) ((-672 . -111) 169443) ((-501 . -623) 169409) ((-335 . -296) 169386) ((-491 . -47) 169343) ((-1195 . -23) T) ((-118 . -1116) T) ((-103 . -102) 169321) ((-1296 . -1128) T) ((-558 . -860) T) ((-227 . -1234) T) ((-1070 . -132) T) ((-1040 . -1074) T) ((-1296 . -23) T) ((-829 . -1054) 169305) ((-1214 . -623) 169287) ((-1019 . -734) 169259) ((-1136 . -838) T) ((-709 . -727) 169224) ((-596 . -623) 169206) ((-396 . -1054) 169190) ((-363 . -1074) T) ((-394 . -132) T) ((-332 . -1054) 169174) ((-1121 . -1116) T) ((-1096 . -21) T) ((-1096 . -25) T) ((-227 . -897) 169156) ((-1020 . -934) T) ((-91 . -34) T) ((-1020 . -830) T) ((-928 . -934) T) ((-1015 . -317) 169121) ((-886 . -626) 169102) ((-497 . -1238) T) ((-724 . -658) 169062) ((-691 . -626) 169043) ((-686 . -626) 169024) ((-219 . -1238) T) ((-417 . -907) 168981) ((-227 . -1054) 168941) ((-40 . -298) T) ((-497 . -566) T) ((-488 . -626) 168922) ((-368 . -25) T) ((-324 . -656) 168577) ((-321 . -656) 168491) ((-368 . -21) T) ((-362 . -25) T) ((-362 . -21) T) ((-219 . -566) T) ((-354 . -25) T) ((-354 . -21) T) ((-327 . -235) 168437) ((-251 . -626) 168414) ((-139 . -626) 168395) ((-138 . -626) 168376) ((-134 . -626) 168357) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1074) T) ((-590 . -174) T) ((-574 . -174) T) ((-505 . -174) T) ((-1078 . -1234) T) ((-966 . -1234) T) ((-668 . -623) 168339) ((-491 . -1234) T) ((-747 . -746) 168323) ((-345 . -623) 168305) ((-68 . -392) T) ((-68 . -405) T) ((-1118 . -107) 168289) ((-1078 . -897) 168271) ((-966 . -897) 168196) ((-663 . -1128) T) ((-633 . -727) 168183) ((-491 . -897) NIL) ((-1162 . -102) T) ((-1110 . -628) 168167) ((-1078 . -1054) 168149) ((-97 . -623) 168131) ((-487 . -148) T) ((-966 . -1054) 168011) ((-118 . -727) 167956) ((-722 . -914) 167899) ((-663 . -23) T) ((-491 . -1054) 167775) ((-1103 . -624) NIL) ((-1103 . -623) 167757) ((-792 . -624) NIL) ((-792 . -623) 167718) ((-790 . -624) 167352) ((-790 . -623) 167266) ((-1129 . -649) 167172) ((-471 . -623) 167154) ((-464 . -623) 167136) ((-464 . -624) 166997) ((-1051 . -231) 166943) ((-882 . -923) 166922) ((-127 . -34) T) ((-827 . -132) T) ((-659 . -623) 166904) ((-588 . -102) T) ((-364 . -1303) 166888) ((-361 . -1303) 166872) ((-353 . -1303) 166856) ((-128 . -524) 166789) ((-122 . -524) 166722) ((-521 . -802) T) ((-521 . -805) T) ((-520 . -804) T) ((-103 . -317) 166660) ((-224 . -102) 166638) ((-709 . -174) T) ((-704 . -1116) T) ((-882 . -658) 166554) ((-65 . -393) T) ((-282 . -623) 166536) ((-65 . -405) T) ((-966 . -386) 166520) ((-880 . -298) T) ((-50 . -623) 166502) ((-1015 . -38) 166450) ((-1136 . -656) 166422) ((-591 . -623) 166404) ((-491 . -386) 166388) ((-591 . -624) 166370) ((-528 . -623) 166352) ((-924 . -1303) 166339) ((-881 . -1234) T) ((-711 . -462) T) ((-505 . -524) 166305) ((-497 . -372) T) ((-364 . -377) 166284) ((-361 . -377) 166263) ((-353 . -377) 166242) ((-724 . -736) T) ((-219 . -372) T) ((-117 . -462) T) ((-1307 . -1298) 166226) ((-881 . -895) 166203) ((-881 . -897) NIL) ((-978 . -860) 166102) ((-825 . -860) 166053) ((-1241 . -102) T) ((-664 . -666) 166037) ((-1220 . -34) T) ((-173 . -623) 166019) ((-1129 . -21) 165949) ((-1129 . -25) 165820) ((-881 . -1054) 165797) ((-966 . -912) 165778) ((-1257 . -47) 165755) ((-924 . -377) T) ((-59 . -661) 165739) ((-526 . -661) 165723) ((-491 . -912) 165700) ((-71 . -451) T) ((-71 . -405) T) ((-506 . -661) 165684) ((-59 . -382) 165668) ((-633 . -174) T) ((-526 . -382) 165652) ((-506 . -382) 165636) ((-837 . -718) 165620) ((-1189 . -315) 165599) ((-1195 . -132) T) ((-1158 . -1067) 165583) ((-118 . -174) T) ((-1158 . -650) 165515) ((-1162 . -317) 165453) ((-171 . -1234) T) ((-1296 . -132) T) ((-876 . -1067) 165423) ((-645 . -754) 165407) ((-617 . -754) 165391) ((-1269 . -934) 165370) ((-1248 . -934) 165349) ((-1248 . -830) NIL) ((-876 . -650) 165319) ((-704 . -727) 165269) ((-1247 . -923) 165222) ((-1040 . -1116) T) ((-881 . -386) 165199) ((-881 . -347) 165176) ((-919 . -1128) T) ((-171 . -895) 165160) ((-171 . -897) 165085) ((-1284 . -524) 165018) ((-1268 . -658) 164915) ((-1096 . -235) 164834) ((-497 . -1128) T) ((-363 . -1116) T) ((-219 . -1128) T) ((-76 . -451) T) ((-76 . -405) T) ((-171 . -1054) 164730) ((-302 . -907) 164687) ((-327 . -860) T) ((-1247 . -658) 164495) ((-882 . -804) 164474) ((-882 . -801) 164453) ((-882 . -736) T) ((-497 . -23) T) ((-368 . -235) 164426) ((-362 . -235) 164399) ((-354 . -235) 164372) ((-225 . -623) 164354) ((-176 . -462) T) ((-224 . -317) 164292) ((-86 . -451) T) ((-86 . -405) T) ((-108 . -235) 164279) ((-219 . -23) T) ((-1308 . -1301) 164258) ((-687 . -1054) 164242) ((-590 . -298) T) ((-574 . -298) T) ((-505 . -298) T) ((-137 . -480) 164197) ((-1257 . -1234) T) ((-664 . -656) 164156) ((-48 . -1116) T) ((-722 . -233) 164140) ((-881 . -912) NIL) ((-1257 . -897) NIL) ((-900 . -102) T) ((-896 . -102) T) ((-398 . -1116) T) ((-171 . -386) 164124) ((-171 . -347) 164108) ((-1257 . -1054) 163988) ((-865 . -1054) 163884) ((-1158 . -102) T) ((-1015 . -914) 163843) ((-672 . -802) 163822) ((-663 . -132) T) ((-672 . -805) 163801) ((-118 . -524) 163709) ((-581 . -1054) 163691) ((-302 . -1291) 163661) ((-876 . -102) T) ((-977 . -566) 163640) ((-1228 . -1072) 163523) ((-1019 . -1067) 163468) ((-492 . -649) 163374) ((-918 . -1116) T) ((-1040 . -727) 163311) ((-721 . -1072) 163276) ((-1019 . -650) 163221) ((-627 . -102) T) ((-612 . -34) T) ((-1163 . -1234) T) ((-1228 . -111) 163090) ((-484 . -658) 162987) ((-363 . -727) 162932) ((-171 . -912) 162891) ((-709 . -298) T) ((-704 . -174) T) ((-721 . -111) 162847) ((-1313 . -1074) T) ((-1257 . -386) 162831) ((-428 . -1238) 162809) ((-1134 . -623) 162791) ((-321 . -858) NIL) ((-428 . -566) T) ((-227 . -315) T) ((-1247 . -801) 162744) ((-1247 . -804) 162697) ((-1268 . -736) T) ((-1247 . -736) T) ((-48 . -727) 162662) ((-227 . -1038) T) ((-1270 . -421) 162628) ((-360 . -1291) 162605) ((-1257 . -912) 162548) ((-728 . -736) T) ((-341 . -623) 162530) ((-1228 . -626) 162412) ((-1129 . -235) 162358) ((-112 . -623) 162340) ((-112 . -624) 162322) ((-728 . -483) T) ((-721 . -626) 162272) ((-1307 . -1067) 162256) ((-492 . -21) 162186) ((-128 . -499) 162170) ((-122 . -499) 162154) ((-492 . -25) 162025) ((-1307 . -650) 161995) ((-633 . -298) T) ((-596 . -1072) 161970) ((-447 . -1116) T) ((-1078 . -315) T) ((-118 . -298) T) ((-1120 . -102) T) ((-1019 . -102) T) ((-596 . -111) 161938) ((-1158 . -317) 161876) ((-1228 . -1065) T) ((-1078 . -1038) T) ((-66 . -1234) T) ((-1070 . -25) T) ((-1070 . -21) T) ((-721 . -1065) T) ((-394 . -21) T) ((-394 . -25) T) ((-704 . -524) NIL) ((-1040 . -174) T) ((-721 . -249) T) ((-1078 . -555) T) ((-722 . -656) 161786) ((-516 . -102) T) ((-512 . -102) T) ((-363 . -174) T) ((-352 . -623) 161768) ((-417 . -1067) 161720) ((-404 . -623) 161702) ((-1136 . -858) T) ((-484 . -736) T) ((-903 . -1054) 161670) ((-417 . -650) 161622) ((-108 . -860) T) ((-668 . -1072) 161606) ((-497 . -132) T) ((-1270 . -1074) T) ((-219 . -132) T) ((-1173 . -102) 161584) ((-99 . -1116) T) ((-251 . -676) 161568) ((-251 . -661) 161552) ((-668 . -111) 161531) ((-596 . -626) 161515) ((-324 . -421) 161499) ((-251 . -382) 161483) ((-1176 . -241) 161430) ((-1015 . -233) 161414) ((-74 . -1234) T) ((-48 . -174) T) ((-711 . -397) T) ((-711 . -144) T) ((-1307 . -102) T) ((-1214 . -626) 161396) ((-1104 . -1234) T) ((-1103 . -1072) 161239) ((-1092 . -1234) T) ((-271 . -923) 161218) ((-253 . -923) 161197) ((-792 . -1072) 161020) ((-790 . -1072) 160863) ((-618 . -1234) T) ((-1181 . -623) 160845) ((-1103 . -111) 160674) ((-1062 . -102) T) ((-485 . -1234) T) ((-471 . -1072) 160645) ((-464 . -1072) 160488) ((-674 . -658) 160472) ((-881 . -315) T) ((-792 . -111) 160281) ((-790 . -111) 160110) ((-364 . -658) 160062) ((-361 . -658) 160014) ((-353 . -658) 159966) ((-271 . -658) 159855) ((-253 . -658) 159744) ((-1175 . -860) T) ((-1104 . -1054) 159728) ((-471 . -111) 159689) ((-464 . -111) 159518) ((-1092 . -1054) 159495) ((-1016 . -34) T) ((-980 . -623) 159477) ((-972 . -1234) T) ((-127 . -1026) 159461) ((-977 . -1128) T) ((-881 . -1038) NIL) ((-745 . -1128) T) ((-725 . -1128) T) ((-668 . -626) 159379) ((-1284 . -499) 159363) ((-1158 . -38) 159323) ((-977 . -23) T) ((-924 . -658) 159288) ((-875 . -1116) T) ((-853 . -102) T) ((-827 . -21) T) ((-645 . -1067) 159272) ((-617 . -1067) 159256) ((-827 . -25) T) ((-745 . -23) T) ((-725 . -23) T) ((-645 . -650) 159240) ((-110 . -671) T) ((-617 . -650) 159224) ((-591 . -1072) 159189) ((-528 . -1072) 159134) ((-229 . -57) 159092) ((-463 . -23) T) ((-417 . -102) T) ((-270 . -102) T) ((-110 . -113) T) ((-704 . -298) T) ((-876 . -38) 159062) ((-591 . -111) 159018) ((-528 . -111) 158947) ((-1103 . -626) 158683) ((-428 . -1128) T) ((-324 . -1074) 158573) ((-321 . -1074) T) ((-129 . -1234) T) ((-792 . -626) 158321) ((-790 . -626) 158087) ((-668 . -1065) T) ((-1313 . -1116) T) ((-464 . -626) 157872) ((-171 . -315) 157803) ((-428 . -23) T) ((-40 . -623) 157785) ((-40 . -624) 157769) ((-108 . -1008) 157751) ((-117 . -879) 157735) ((-659 . -626) 157719) ((-48 . -524) 157685) ((-1220 . -1026) 157669) ((-1198 . -623) 157636) ((-1206 . -34) T) ((-968 . -623) 157602) ((-935 . -623) 157584) ((-1129 . -860) 157535) ((-781 . -623) 157517) ((-682 . -623) 157499) ((-1173 . -317) 157437) ((-489 . -34) T) ((-1108 . -1234) T) ((-487 . -462) T) ((-1157 . -34) T) ((-1103 . -1065) T) ((-50 . -626) 157406) ((-792 . -1065) T) ((-790 . -1065) T) ((-657 . -241) 157390) ((-642 . -241) 157336) ((-591 . -626) 157286) ((-528 . -626) 157216) ((-492 . -235) 157162) ((-1257 . -315) 157141) ((-1103 . -334) 157102) ((-464 . -1065) T) ((-1195 . -21) T) ((-1103 . -239) 157081) ((-792 . -334) 157058) ((-792 . -239) T) ((-790 . -334) 157030) ((-741 . -1238) 157009) ((-335 . -661) 156993) ((-1195 . -25) T) ((-59 . -34) T) ((-529 . -34) T) ((-526 . -34) T) ((-464 . -334) 156972) ((-335 . -382) 156956) ((-507 . -34) T) ((-506 . -34) T) ((-1019 . -1168) NIL) ((-741 . -566) 156887) ((-645 . -102) T) ((-617 . -102) T) ((-364 . -736) T) ((-361 . -736) T) ((-353 . -736) T) ((-271 . -736) T) ((-253 . -736) T) ((-388 . -1234) T) ((-1062 . -317) 156795) ((-1296 . -21) T) ((-915 . -1116) 156773) ((-828 . -235) 156760) ((-50 . -1065) T) ((-1296 . -25) T) ((-1191 . -566) 156739) ((-1190 . -1238) 156718) ((-1190 . -566) 156669) ((-1184 . -1238) 156648) ((-1184 . -566) 156599) ((-591 . -1065) T) ((-528 . -1065) T) ((-1040 . -298) T) ((-370 . -1054) 156583) ((-330 . -1054) 156567) ((-1019 . -38) 156512) ((-388 . -897) 156494) ((-1015 . -656) 156417) ((-846 . -1234) T) ((-837 . -1234) 156396) ((-809 . -1128) T) ((-924 . -736) T) ((-591 . -249) T) ((-591 . -239) T) ((-528 . -239) T) ((-528 . -249) T) ((-1142 . -566) 156375) ((-363 . -298) T) ((-657 . -705) 156359) ((-388 . -1054) 156319) ((-302 . -1067) 156240) ((-348 . -907) 156219) ((-1136 . -1074) T) ((-103 . -126) 156203) ((-302 . -650) 156145) ((-809 . -23) T) ((-1306 . -1301) 156121) ((-1304 . -1301) 156100) ((-1284 . -294) 156052) ((-417 . -317) 156017) ((-1270 . -1116) T) ((-1158 . -914) 155976) ((-880 . -623) 155958) ((-846 . -1054) 155927) ((-205 . -797) T) ((-204 . -797) T) ((-203 . -797) T) ((-202 . -797) T) ((-201 . -797) T) ((-200 . -797) T) ((-199 . -797) T) ((-198 . -797) T) ((-197 . -797) T) ((-196 . -797) T) ((-557 . -623) 155909) ((-505 . -1018) T) ((-281 . -849) T) ((-280 . -849) T) ((-279 . -849) T) ((-278 . -849) T) ((-48 . -298) T) ((-277 . -849) T) ((-276 . -849) T) ((-275 . -849) T) ((-195 . -797) T) ((-622 . -860) T) ((-664 . -421) 155893) ((-680 . -238) 155872) ((-225 . -626) 155834) ((-110 . -860) T) ((-663 . -21) T) ((-663 . -25) T) ((-1307 . -38) 155804) ((-118 . -294) 155755) ((-1284 . -19) 155739) ((-1284 . -614) 155716) ((-1297 . -1116) T) ((-360 . -1067) 155661) ((-1093 . -1116) T) ((-1003 . -1116) T) ((-977 . -132) T) ((-827 . -235) 155648) ((-747 . -1116) T) ((-360 . -650) 155593) ((-745 . -132) T) ((-725 . -132) T) ((-521 . -803) T) ((-521 . -804) T) ((-463 . -132) T) ((-417 . -1168) 155571) ((-225 . -1065) T) ((-302 . -102) 155353) ((-142 . -1116) T) ((-709 . -1018) T) ((-1121 . -294) 155309) ((-91 . -1234) T) ((-128 . -623) 155241) ((-122 . -623) 155173) ((-1313 . -174) T) ((-1190 . -372) 155152) ((-1184 . -372) 155131) ((-324 . -1116) T) ((-428 . -132) T) ((-321 . -1116) T) ((-417 . -38) 155083) ((-1149 . -102) T) ((-1270 . -727) 154975) ((-664 . -1074) T) ((-1151 . -1279) T) ((-327 . -146) 154954) ((-327 . -148) 154933) ((-140 . -1116) T) ((-137 . -1116) T) ((-115 . -1116) T) ((-868 . -102) T) ((-590 . -623) 154915) ((-574 . -624) 154814) ((-574 . -623) 154796) ((-505 . -623) 154778) ((-505 . -624) 154723) ((-495 . -23) T) ((-492 . -860) 154674) ((-497 . -649) 154656) ((-979 . -623) 154638) ((-1019 . -914) 154590) ((-219 . -649) 154572) ((-227 . -414) T) ((-672 . -658) 154556) ((-55 . -623) 154538) ((-1189 . -934) 154517) ((-741 . -1128) T) ((-360 . -102) T) ((-1233 . -1099) T) ((-1136 . -854) T) ((-828 . -860) T) ((-741 . -23) T) ((-352 . -1072) 154462) ((-1175 . -1174) T) ((-1163 . -107) 154446) ((-1191 . -1128) T) ((-1190 . -1128) T) ((-525 . -1054) 154430) ((-1184 . -1128) T) ((-1142 . -1128) T) ((-352 . -111) 154359) ((-1020 . -1238) T) ((-127 . -1234) T) ((-928 . -1238) T) ((-704 . -294) NIL) ((-724 . -1234) T) ((-1285 . -623) 154341) ((-1191 . -23) T) ((-1190 . -23) T) ((-1184 . -23) T) ((-1158 . -233) 154325) ((-1020 . -566) T) ((-1142 . -23) T) ((-928 . -566) T) ((-1091 . -1116) T) ((-254 . -623) 154307) ((-825 . -238) 154259) ((-809 . -132) T) ((-720 . -623) 154241) ((-324 . -727) 154151) ((-321 . -727) 154080) ((-709 . -623) 154062) ((-709 . -624) 154007) ((-417 . -410) 153991) ((-448 . -1116) T) ((-497 . -25) T) ((-497 . -21) T) ((-1136 . -1116) T) ((-219 . -25) T) ((-219 . -21) T) ((-722 . -421) 153975) ((-724 . -1054) 153944) ((-1284 . -623) 153856) ((-1284 . -624) 153817) ((-1270 . -174) T) ((-1207 . -623) 153799) ((-251 . -34) T) ((-352 . -626) 153729) ((-404 . -626) 153711) ((-940 . -990) T) 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141785) ((-825 . -907) 141715) ((-1020 . -649) 141697) ((-1270 . -623) 141679) ((-541 . -102) T) ((-510 . -102) T) ((-1149 . -1150) 141663) ((-153 . -1291) 141647) ((-251 . -1234) T) ((-1233 . -102) T) ((-1040 . -626) 141584) ((-827 . -238) T) ((-1189 . -1238) 141563) ((-363 . -626) 141493) ((-1141 . -1238) 141472) ((-246 . -21) 141402) ((-246 . -25) 141273) ((-128 . -120) 141257) ((-122 . -120) 141241) ((-44 . -754) 141225) ((-1189 . -566) 141136) ((-1141 . -566) 141067) ((-1241 . -1116) T) ((-1051 . -294) 141042) ((-1183 . -1099) T) ((-1010 . -1099) T) ((-826 . -132) T) ((-118 . -805) NIL) ((-118 . -802) NIL) ((-364 . -315) T) ((-361 . -315) T) ((-353 . -315) T) ((-258 . -1128) 140992) ((-257 . -1128) 140942) ((-1040 . -1065) T) ((-1019 . -1074) T) ((-48 . -626) 140875) ((-352 . -658) 140820) ((-1297 . -623) 140782) ((-631 . -38) 140766) ((-1297 . -624) 140727) ((-1191 . -235) 140680) ((-1093 . -623) 140662) ((-1040 . -249) T) ((-363 . -1065) T) ((-825 . -1291) 140632) ((-258 . -23) 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-1238) T) ((-246 . -235) 138609) ((-319 . -102) T) ((-864 . -1128) T) ((-966 . -1238) 138588) ((-491 . -1238) 138567) ((-1078 . -566) T) ((-966 . -566) 138498) ((-1189 . -23) T) ((-1167 . -1099) T) ((-1141 . -23) T) ((-864 . -23) T) ((-491 . -566) 138429) ((-1158 . -727) 138361) ((-680 . -1067) 138345) ((-1162 . -524) 138278) ((-680 . -650) 138262) ((-1051 . -624) NIL) ((-1051 . -623) 138244) ((-96 . -1099) T) ((-1313 . -1072) 138231) ((-876 . -727) 138201) ((-1313 . -111) 138186) ((-1228 . -47) 138155) ((-1184 . -860) NIL) ((-258 . -132) T) ((-257 . -132) T) ((-1120 . -1116) T) ((-1019 . -1116) T) ((-62 . -623) 138137) ((-1096 . -907) 138068) ((-1040 . -802) T) ((-1040 . -805) T) ((-1276 . -25) T) ((-1276 . -21) T) ((-1269 . -21) T) ((-1269 . -25) T) ((-880 . -658) 138055) ((-1248 . -21) T) ((-1248 . -25) T) ((-1043 . -152) 138039) ((-1020 . -235) 138026) ((-882 . -830) 138005) ((-882 . -934) T) ((-722 . -294) 137932) ((-606 . -21) T) ((-348 . -656) 137891) ((-108 . -907) NIL) ((-606 . -25) T) ((-605 . -21) T) ((-176 . -656) 137808) ((-40 . -736) T) ((-224 . -524) 137741) ((-605 . -25) T) ((-486 . -152) 137725) ((-473 . -152) 137709) ((-935 . -804) T) ((-935 . -736) T) ((-781 . -803) T) ((-781 . -804) T) ((-516 . -1116) T) ((-512 . -1116) T) ((-781 . -736) T) ((-227 . -372) T) ((-1306 . -1067) 137693) ((-1304 . -1067) 137677) ((-1306 . -650) 137647) ((-1173 . -1116) 137625) ((-881 . -1238) T) ((-1304 . -650) 137595) ((-664 . -623) 137577) ((-881 . -566) T) ((-704 . -377) NIL) ((-44 . -1067) 137561) ((-1313 . -626) 137543) ((-1307 . -1116) T) ((-680 . -102) T) ((-368 . -1291) 137527) ((-362 . -1291) 137511) ((-44 . -650) 137495) ((-354 . -1291) 137479) ((-558 . -102) T) ((-1228 . -1234) T) ((-530 . -860) 137458) ((-497 . -238) T) ((-219 . -238) T) ((-1062 . -1116) T) ((-827 . -462) 137437) ((-153 . -1067) 137421) ((-1062 . -1087) 137350) ((-1043 . -992) 137319) ((-829 . -1128) T) ((-1019 . -727) 137264) ((-153 . -650) 137248) ((-396 . -1128) T) ((-486 . -992) 137217) ((-473 . -992) 137186) ((-110 . -152) 137168) ((-73 . -623) 137150) ((-904 . -623) 137132) ((-1096 . -734) 137111) ((-1313 . -1065) T) ((-826 . -649) 137059) ((-302 . -1074) 137001) ((-171 . -1238) 136906) ((-227 . -1128) T) ((-332 . -23) T) ((-1184 . -1008) 136858) ((-853 . -1116) T) ((-1270 . -1072) 136763) ((-1142 . -750) 136742) ((-1268 . -934) 136721) ((-1247 . -934) 136700) ((-880 . -736) T) ((-171 . -566) 136611) ((-590 . -658) 136598) ((-574 . -658) 136570) ((-417 . -1116) T) ((-270 . -1116) T) ((-215 . -623) 136552) ((-505 . -658) 136502) ((-227 . -23) T) ((-1247 . -830) 136455) ((-1306 . -102) T) ((-363 . -1303) 136432) ((-1304 . -102) T) ((-1270 . -111) 136324) ((-1129 . -907) 136254) ((-825 . -1067) 136131) ((-825 . -650) 136053) ((-145 . -623) 136035) ((-1009 . -132) T) ((-44 . -102) T) ((-246 . -860) 135986) ((-1257 . -1238) 135965) ((-103 . -499) 135949) ((-1307 . -727) 135919) ((-1103 . -47) 135880) ((-1078 . -1128) T) ((-966 . -1128) T) ((-128 . -34) T) ((-122 . -34) T) ((-792 . -47) 135857) ((-790 . -47) 135829) ((-1257 . -566) 135740) ((-363 . -377) T) ((-491 . -1128) T) ((-1189 . -132) T) ((-1141 . -132) T) ((-464 . -47) 135719) ((-881 . -372) T) ((-864 . -132) T) ((-153 . -102) T) ((-1078 . -23) T) ((-966 . -23) T) ((-581 . -566) T) ((-826 . -25) T) ((-826 . -21) T) ((-1158 . -524) 135652) ((-602 . -1099) T) ((-596 . -1054) 135636) ((-1270 . -626) 135510) ((-491 . -23) T) ((-360 . -1074) T) ((-1228 . -912) 135491) ((-680 . -317) 135429) ((-1129 . -1291) 135399) ((-709 . -658) 135364) ((-1020 . -860) T) ((-1019 . -174) T) ((-977 . -146) 135343) ((-645 . -1116) T) ((-617 . -1116) T) ((-977 . -148) 135322) ((-745 . -148) 135301) ((-745 . -146) 135280) ((-668 . -1234) T) ((-987 . -860) T) ((-1276 . -235) 135233) ((-1269 . -235) 135179) ((-1248 . -235) 135060) ((-843 . -656) 134977) ((-484 . -934) 134956) ((-327 . -1067) 134791) ((-324 . -1072) 134701) ((-321 . -1072) 134630) ((-1015 . -294) 134588) ((-417 . -727) 134540) ((-327 . -650) 134381) ((-605 . -235) 134334) ((-711 . -858) T) ((-1270 . -1065) T) ((-324 . -111) 134230) ((-321 . -111) 134143) ((-978 . -102) T) ((-825 . -102) 133933) ((-722 . -624) NIL) ((-722 . -623) 133915) ((-1270 . -334) 133859) ((-668 . -1054) 133755) ((-1103 . -1234) T) ((-1051 . -296) 133730) ((-590 . -736) T) ((-574 . -804) T) ((-171 . -372) 133681) ((-574 . -801) T) ((-574 . -736) T) ((-505 . -736) T) ((-792 . -1234) T) ((-790 . -1234) T) ((-1162 . -499) 133665) ((-464 . -1234) T) ((-1103 . -897) NIL) ((-881 . -1128) T) ((-118 . -923) NIL) ((-1306 . -1305) 133641) ((-1304 . -1305) 133620) ((-792 . -897) NIL) ((-790 . -897) 133479) ((-1299 . -25) T) ((-1299 . -21) T) ((-1231 . -102) 133457) ((-1122 . -405) T) ((-633 . -658) 133444) ((-464 . -897) NIL) ((-685 . -102) 133422) ((-1103 . -1054) 133249) ((-881 . -23) T) ((-792 . -1054) 133108) ((-790 . -1054) 132965) ((-118 . -658) 132910) ((-464 . -1054) 132786) ((-324 . -626) 132350) ((-321 . -626) 132233) ((-400 . -656) 132202) ((-659 . -1054) 132186) ((-591 . -1234) T) ((-637 . -102) T) ((-528 . -1234) T) ((-224 . -499) 132170) ((-1284 . -34) T) ((-631 . -656) 132129) ((-297 . -1067) 132116) ((-137 . -626) 132100) ((-297 . -650) 132087) ((-645 . -727) 132071) ((-617 . -727) 132055) ((-680 . -38) 132015) ((-327 . -102) T) ((-85 . -623) 131997) ((-50 . -1054) 131981) ((-1136 . -1072) 131968) ((-1103 . -386) 131952) ((-792 . -386) 131936) ((-709 . -736) T) ((-709 . -804) T) ((-709 . -801) T) ((-591 . -1054) 131923) ((-528 . -1054) 131900) ((-60 . -57) 131862) ((-332 . -132) T) ((-324 . -1065) 131752) ((-321 . -1065) T) ((-171 . -1128) T) ((-790 . -386) 131736) ((-45 . -152) 131686) ((-1020 . -1008) 131668) ((-464 . -386) 131652) ((-417 . -174) T) ((-324 . -249) 131631) ((-321 . -249) T) ((-321 . -239) NIL) ((-302 . -1116) 131413) ((-227 . -132) T) ((-1136 . -111) 131398) ((-171 . -23) T) ((-809 . -148) 131377) ((-809 . -146) 131356) ((-258 . -649) 131262) ((-257 . -649) 131168) ((-327 . -292) 131134) ((-1173 . -524) 131067) ((-487 . -656) 131017) ((-492 . -907) 130947) ((-1149 . -1116) T) ((-227 . -1076) T) ((-825 . -317) 130885) ((-1103 . -912) 130820) ((-792 . -912) 130763) ((-790 . -912) 130747) ((-1306 . -38) 130717) ((-1304 . -38) 130687) ((-1257 . -1128) T) ((-865 . -1128) T) ((-464 . -912) 130664) ((-868 . -1116) T) ((-1257 . -23) T) ((-1136 . -626) 130636) ((-1078 . -132) T) ((-581 . -1128) T) ((-865 . -23) T) ((-633 . -736) T) ((-364 . -934) T) ((-361 . -934) T) ((-297 . -102) T) ((-353 . -934) T) ((-986 . -1099) T) ((-966 . -132) T) ((-826 . -235) 130609) ((-118 . -804) NIL) ((-118 . -801) NIL) ((-118 . -736) T) ((-1062 . -524) 130510) ((-704 . -923) NIL) ((-581 . -23) T) ((-491 . -132) T) ((-428 . -238) 130489) ((-685 . -317) 130427) ((-645 . -771) T) ((-617 . -771) T) ((-1248 . -860) NIL) ((-1096 . -1067) 130337) ((-1019 . -298) T) ((-704 . -658) 130287) ((-258 . -21) T) ((-360 . -1116) T) ((-258 . -25) T) ((-257 . -21) T) ((-257 . -25) T) ((-153 . -38) 130271) ((-2 . -102) T) ((-924 . -934) T) ((-1096 . -650) 130139) ((-492 . -1291) 130109) ((-1136 . -1065) T) ((-721 . -315) T) ((-368 . -1067) 130061) ((-362 . -1067) 130013) ((-354 . -1067) 129965) ((-368 . -650) 129917) ((-225 . -1054) 129894) ((-362 . -650) 129846) ((-108 . -1067) 129796) ((-354 . -650) 129748) ((-302 . -727) 129690) ((-711 . -1074) T) ((-497 . -462) T) ((-417 . -524) 129602) ((-108 . -650) 129552) ((-219 . -462) T) ((-1136 . -239) T) ((-303 . -152) 129502) ((-1015 . -624) 129463) ((-1015 . -623) 129445) ((-1005 . -623) 129427) ((-117 . -1074) T) ((-664 . -1072) 129411) ((-227 . -503) T) ((-409 . -623) 129393) ((-409 . -624) 129370) ((-1070 . -1291) 129340) ((-664 . -111) 129319) ((-680 . -914) 129278) ((-1158 . -499) 129262) ((-1308 . -656) 129221) ((-390 . -656) 129190) ((-825 . -38) 129160) ((-63 . -451) T) ((-63 . -405) T) ((-1176 . -102) T) ((-881 . -132) T) ((-494 . -102) 129138) ((-1313 . -377) T) ((-1096 . -102) T) ((-1077 . -102) T) ((-360 . -727) 129083) ((-741 . -148) 129062) ((-741 . -146) 129041) ((-664 . -626) 128959) ((-1040 . -658) 128896) ((-533 . -1116) 128874) ((-368 . -102) T) ((-362 . -102) T) ((-354 . -102) T) ((-108 . -102) T) ((-514 . -1116) T) ((-363 . -658) 128819) ((-1189 . -649) 128767) ((-1141 . -649) 128715) ((-394 . -519) 128694) ((-843 . -858) 128673) ((-388 . -1238) T) ((-704 . -736) T) ((-1248 . -1008) 128625) ((-348 . -1074) T) ((-112 . -1234) T) ((-176 . -1074) T) ((-103 . -623) 128557) ((-1191 . -146) 128536) ((-1191 . -148) 128515) ((-388 . -566) T) ((-1190 . -148) 128494) ((-1190 . -146) 128473) ((-1184 . -146) 128380) ((-417 . -298) T) ((-1184 . -148) 128287) ((-1142 . -148) 128266) ((-1142 . -146) 128245) ((-327 . -38) 128086) ((-171 . -132) T) ((-321 . -805) NIL) ((-321 . -802) NIL) ((-664 . -1065) T) ((-48 . -658) 128036) ((-1129 . -1067) 127913) ((-904 . -626) 127890) ((-1129 . -650) 127812) ((-1183 . -102) T) ((-1010 . -102) T) ((-1009 . -21) T) ((-128 . -1026) 127796) ((-122 . -1026) 127780) ((-1009 . -25) T) ((-915 . -120) 127764) 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-102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-363 . -736) T) ((-722 . -111) 126680) ((-680 . -233) 126664) ((-591 . -315) T) ((-528 . -315) T) ((-302 . -524) 126613) ((-108 . -317) NIL) ((-72 . -405) T) ((-1129 . -102) 126403) ((-843 . -421) 126387) ((-1136 . -805) T) ((-1136 . -802) T) ((-711 . -1116) T) ((-588 . -623) 126369) ((-388 . -372) T) ((-171 . -503) 126347) ((-224 . -623) 126279) ((-135 . -1116) T) ((-117 . -1116) T) ((-980 . -1234) T) ((-48 . -736) T) ((-1062 . -499) 126244) ((-142 . -435) 126226) ((-142 . -377) T) ((-1043 . -102) T) ((-522 . -519) 126205) ((-722 . -626) 125961) ((-1191 . -238) 125920) ((-486 . -102) T) ((-473 . -102) T) ((-1190 . -238) 125872) ((-1184 . -238) 125759) ((-1050 . -1128) T) ((-327 . -914) 125665) ((-1241 . -623) 125647) ((-1198 . -1054) 125583) ((-1191 . -35) 125549) ((-1191 . -95) 125515) ((-1191 . -1222) 125481) ((-1191 . -1219) 125447) ((-1190 . -1219) 125413) ((-1190 . -1222) 125379) ((-1175 . -317) NIL) ((-89 . -406) T) ((-89 . -405) T) ((-1096 . -1168) 125358) ((-40 . -1234) 125287) ((-1190 . -95) 125253) ((-1050 . -23) T) ((-1190 . -35) 125219) ((-581 . -503) T) ((-1184 . -1219) 125185) ((-1184 . -1222) 125151) ((-1184 . -95) 125117) ((-1184 . -35) 125083) ((-370 . -1128) T) ((-368 . -1168) 125062) ((-362 . -1168) 125041) ((-354 . -1168) 125020) ((-1120 . -294) 124976) ((-1142 . -35) 124942) ((-1142 . -95) 124908) ((-108 . -1168) T) ((-1142 . -1222) 124874) ((-843 . -1074) 124853) ((-657 . -317) 124791) ((-642 . -317) 124642) ((-1142 . -1219) 124608) ((-722 . -1065) T) ((-1078 . -649) 124590) ((-1096 . -38) 124458) ((-966 . -649) 124406) ((-1020 . -148) T) ((-1020 . -146) NIL) ((-388 . -1128) T) ((-332 . -25) T) ((-330 . -23) T) ((-957 . -860) 124385) ((-722 . -334) 124362) ((-491 . -649) 124310) ((-40 . -1054) 124198) ((-722 . -239) T) ((-711 . -727) 124185) ((-348 . -1116) T) ((-176 . -1116) T) ((-339 . -860) T) ((-428 . -462) 124135) ((-388 . -23) T) ((-368 . -38) 124100) ((-362 . -38) 124065) ((-354 . -38) 124030) ((-80 . -451) T) ((-80 . -405) T) ((-227 . -25) T) ((-227 . -21) T) ((-846 . -1128) T) ((-108 . -38) 123980) ((-837 . -1128) T) ((-784 . -1116) T) ((-117 . -727) 123967) ((-682 . -1054) 123951) ((-622 . -102) T) ((-846 . -23) T) ((-837 . -23) T) ((-1173 . -294) 123903) ((-1129 . -317) 123841) ((-492 . -1067) 123718) ((-1118 . -241) 123702) ((-64 . -406) T) ((-64 . -405) T) ((-1167 . -102) T) ((-110 . -102) T) ((-492 . -650) 123624) ((-40 . -386) 123601) ((-96 . -102) T) ((-663 . -862) 123585) ((-1189 . -235) 123572) ((-1151 . -1099) T) ((-1078 . -21) T) ((-1078 . -25) T) ((-1070 . -1067) 123556) ((-825 . -233) 123525) ((-966 . -25) T) ((-966 . -21) T) ((-1070 . -650) 123467) ((-631 . -1074) T) ((-1136 . -377) T) ((-1043 . -317) 123405) ((-680 . -656) 123364) ((-491 . -25) T) ((-491 . -21) T) ((-394 . -1067) 123348) ((-900 . -623) 123330) ((-896 . -623) 123312) ((-533 . -524) 123245) ((-258 . -860) 123196) ((-257 . -860) 123147) 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-238) T) ((-424 . -102) T) ((-394 . -102) T) ((-110 . -317) NIL) ((-229 . -102) 121595) ((-128 . -1234) T) ((-122 . -1234) T) ((-108 . -914) NIL) ((-827 . -1067) 121546) ((-827 . -650) 121488) ((-1050 . -132) T) ((-680 . -376) 121472) ((-153 . -656) 121431) ((-645 . -294) 121389) ((-617 . -294) 121347) ((-1313 . -736) T) ((-1015 . -1065) T) ((-1257 . -649) 121295) ((-1120 . -623) 121277) ((-1019 . -623) 121259) ((-574 . -1234) T) ((-505 . -1234) T) ((-525 . -23) T) ((-520 . -23) T) ((-352 . -315) T) ((-518 . -23) T) ((-330 . -132) T) ((-3 . -1116) T) ((-1019 . -624) 121243) ((-1015 . -249) 121222) ((-1015 . -239) 121201) ((-1276 . -146) 121180) ((-1276 . -148) 121159) ((-843 . -1116) T) ((-1269 . -148) 121138) ((-1269 . -146) 121117) ((-1268 . -1238) 121096) ((-1248 . -146) 121003) ((-1248 . -148) 120910) ((-1247 . -1238) 120889) ((-388 . -132) T) ((-227 . -235) 120876) ((-574 . -897) 120858) ((0 . -1116) T) ((-176 . -174) T) ((-171 . -21) T) ((-171 . -25) T) ((-49 . -1116) T) ((-1270 . -658) 120763) ((-1268 . -566) 120714) ((-724 . -1128) T) ((-1247 . -566) 120665) ((-574 . -1054) 120647) ((-605 . -148) 120626) ((-605 . -146) 120605) ((-505 . -1054) 120548) ((-1151 . -1153) T) ((-87 . -393) T) ((-87 . -405) T) ((-882 . -372) T) ((-846 . -132) T) ((-837 . -132) T) ((-978 . -656) 120492) ((-724 . -23) T) ((-516 . -623) 120458) ((-512 . -623) 120440) ((-825 . -656) 120210) ((-1308 . -1074) T) ((-388 . -1076) T) ((-1042 . -1116) 120188) ((-55 . -1054) 120170) ((-915 . -34) T) ((-492 . -317) 120108) ((-602 . -102) T) ((-1173 . -624) 120069) ((-1173 . -623) 120001) ((-1195 . -1067) 119884) ((-45 . -102) T) ((-827 . -102) T) ((-1195 . -650) 119781) ((-1257 . -25) T) ((-1257 . -21) T) ((-1078 . -235) 119768) ((-865 . -25) T) ((-44 . -376) 119752) ((-865 . -21) T) ((-741 . -462) 119703) ((-1307 . -623) 119685) ((-1296 . -1067) 119655) ((-1070 . -317) 119593) ((-681 . -1099) T) ((-616 . -1099) T) ((-400 . -1116) T) ((-581 . -25) T) ((-581 . -21) T) ((-182 . -1099) T) ((-162 . -1099) T) ((-157 . -1099) T) ((-155 . -1099) T) ((-1296 . -650) 119563) ((-631 . -1116) T) ((-709 . -897) 119545) ((-1284 . -1234) T) ((-229 . -317) 119483) ((-145 . -377) T) ((-1062 . -624) 119425) ((-1062 . -623) 119368) ((-321 . -923) NIL) ((-1242 . -854) T) ((-1129 . -914) 119300) ((-709 . -1054) 119245) ((-721 . -934) T) ((-484 . -1238) 119224) ((-1190 . -462) 119203) ((-1184 . -462) 119182) ((-338 . -102) T) ((-882 . -1128) T) ((-327 . -656) 119064) ((-324 . -658) 118793) ((-321 . -658) 118722) ((-484 . -566) 118673) ((-348 . -524) 118639) ((-560 . -152) 118589) ((-40 . -315) T) ((-853 . -623) 118571) ((-711 . -298) T) ((-882 . -23) T) ((-388 . -503) T) ((-1096 . -233) 118541) ((-522 . -102) T) ((-417 . -624) 118348) ((-417 . -623) 118330) ((-270 . -623) 118312) ((-117 . -298) T) ((-1270 . -736) T) ((-633 . -1234) 118255) ((-1309 . -1116) T) ((-1268 . -372) 118234) ((-1247 . -372) 118213) ((-1297 . -34) T) ((-1242 . -1116) T) ((-118 . -1234) T) ((-108 . -233) 118195) ((-1195 . -102) T) ((-487 . -1116) T) ((-533 . -499) 118179) ((-747 . -34) T) ((-663 . -1067) 118163) ((-492 . -38) 118133) ((-663 . -650) 118103) ((-881 . -235) NIL) ((-142 . -34) T) ((-118 . -895) 118080) ((-118 . -897) NIL) ((-633 . -1054) 117963) ((-1296 . -102) T) ((-1276 . -238) 117922) ((-654 . -860) 117901) ((-1269 . -238) 117853) ((-1248 . -238) 117740) ((-303 . -102) T) ((-722 . -377) 117719) ((-118 . -1054) 117696) ((-400 . -727) 117680) ((-605 . -238) 117639) ((-631 . -727) 117623) ((-1121 . -1234) T) ((-45 . -317) 117427) ((-826 . -146) 117406) ((-826 . -148) 117385) ((-297 . -656) 117357) ((-1307 . -391) 117336) ((-829 . -860) T) ((-1286 . -1116) T) ((-1176 . -231) 117283) ((-396 . -860) 117262) ((-1276 . -35) 117228) ((-1276 . -1222) 117194) ((-1276 . -1219) 117160) ((-1269 . -1219) 117126) ((-525 . -132) T) ((-1269 . -1222) 117092) ((-1248 . -1219) 117058) ((-1248 . -1222) 117024) ((-1276 . -95) 116990) ((-1269 . -95) 116956) ((-428 . -907) 116913) ((-645 . -623) 116882) ((-617 . -623) 116851) ((-227 . -860) T) ((-1269 . -35) 116817) ((-1268 . -1128) T) ((-1248 . -95) 116783) ((-1136 . -658) 116755) ((-1248 . -35) 116721) ((-1247 . -1128) T) ((-603 . -152) 116703) ((-1096 . -358) 116682) ((-176 . -298) T) ((-118 . -386) 116659) ((-118 . -347) 116636) ((-171 . -235) 116581) ((-880 . -315) T) ((-321 . -804) NIL) ((-321 . -801) NIL) ((-324 . -736) 116430) ((-321 . -736) T) ((-484 . -372) 116409) ((-368 . -358) 116388) ((-362 . -358) 116367) ((-354 . -358) 116346) ((-324 . -483) 116325) ((-1268 . -23) T) ((-1247 . -23) T) ((-728 . -1128) T) ((-724 . -132) T) ((-663 . -102) T) ((-487 . -727) 116290) ((-45 . -290) 116240) ((-105 . -1116) T) ((-68 . -623) 116222) ((-986 . -102) T) ((-874 . -102) T) ((-633 . -912) 116181) ((-1308 . -1116) T) ((-390 . -1116) T) ((-1257 . -235) 116168) ((-82 . -1234) T) ((-1233 . -1116) T) ((-1078 . -860) T) ((-118 . -912) NIL) ((-792 . -934) 116147) ((-723 . -860) T) ((-541 . -1116) T) ((-510 . -1116) T) ((-364 . -1238) T) ((-361 . -1238) T) ((-353 . -1238) T) ((-271 . -1238) 116126) ((-253 . -1238) 116105) ((-543 . -870) T) ((-1129 . -233) 116074) ((-1175 . -838) T) ((-1158 . -1072) 116058) ((-400 . -771) T) ((-704 . -1234) T) ((-701 . -1054) 116042) ((-364 . -566) T) ((-361 . -566) T) ((-353 . -566) T) ((-271 . -566) 115973) ((-253 . -566) 115904) ((-535 . -1099) T) ((-1158 . -111) 115883) ((-463 . -754) 115853) ((-876 . -1072) 115823) ((-827 . -38) 115765) ((-704 . -895) 115747) ((-704 . -897) 115729) ((-303 . -317) 115533) ((-1173 . -296) 115510) ((-924 . -1238) T) ((-1096 . -656) 115405) ((-1020 . -462) T) ((-680 . -421) 115389) ((-876 . -111) 115354) ((-928 . -462) T) ((-704 . -1054) 115299) ((-924 . -566) T) ((-543 . -623) 115281) ((-591 . -934) T) ((-497 . -1067) 115231) ((-484 . -1128) T) ((-528 . -934) T) ((-492 . -914) 115163) ((-65 . -623) 115145) ((-219 . -1067) 115095) ((-497 . -650) 115045) ((-368 . -656) 114982) ((-362 . -656) 114919) ((-354 . -656) 114856) ((-642 . -231) 114802) ((-219 . -650) 114752) ((-108 . -656) 114702) ((-484 . -23) T) ((-1136 . -804) T) ((-882 . -132) T) ((-1136 . -801) T) ((-1299 . -1301) 114681) ((-1136 . -736) T) ((-664 . -658) 114655) ((-302 . -623) 114396) ((-1158 . -626) 114314) ((-1051 . -34) T) ((-826 . -238) 114293) ((-590 . -315) T) ((-574 . -315) T) ((-505 . -315) T) ((-1308 . -727) 114263) ((-704 . -386) 114245) ((-704 . -347) 114227) ((-487 . -174) T) ((-390 . -727) 114197) ((-876 . -626) 114132) ((-881 . -860) NIL) ((-574 . -1038) T) ((-505 . -1038) T) ((-1149 . -623) 114114) ((-1129 . -244) 114093) ((-216 . -102) T) ((-1166 . -102) T) ((-71 . -623) 114075) ((-1158 . -1065) T) ((-1195 . -38) 113972) ((-868 . -623) 113954) ((-574 . -555) T) ((-680 . -1074) T) ((-741 . -963) 113907) ((-363 . -1234) T) ((-1158 . -239) 113886) ((-1098 . -1116) T) ((-1050 . -25) T) ((-1050 . -21) T) ((-1019 . -1072) 113831) ((-919 . -102) T) ((-876 . -1065) T) ((-704 . -912) NIL) ((-364 . -337) 113815) ((-364 . -372) T) ((-361 . -337) 113799) ((-361 . -372) T) 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111566) ((-484 . -132) T) ((-219 . -317) NIL) ((-417 . -111) 111504) ((-825 . -1074) 111454) ((-747 . -1114) 111438) ((-1268 . -503) 111404) ((-1247 . -503) 111370) ((-558 . -854) T) ((-142 . -1114) 111352) ((-487 . -298) T) ((-1307 . -1065) T) ((-258 . -238) 111304) ((-257 . -238) 111256) ((-1239 . -102) T) ((-1079 . -102) T) ((-853 . -626) 111124) ((-510 . -524) NIL) ((-492 . -244) 111103) ((-417 . -626) 111001) ((-977 . -1067) 110884) ((-745 . -1067) 110854) ((-977 . -650) 110751) ((-1189 . -146) 110730) ((-745 . -650) 110700) ((-463 . -1067) 110670) ((-1189 . -148) 110649) ((-1141 . -148) 110628) ((-1141 . -146) 110607) ((-645 . -1072) 110591) ((-617 . -1072) 110575) ((-463 . -650) 110545) ((-1191 . -1275) 110529) ((-1191 . -1262) 110506) ((-1190 . -1267) 110467) ((-680 . -1116) T) ((-680 . -1069) 110407) ((-1190 . -1262) 110377) ((-558 . -1116) T) ((-497 . -1168) T) ((-1190 . -1265) 110361) ((-1184 . -1246) 110322) ((-828 . -273) 110306) ((-219 . -1168) T) ((-352 . -934) T) ((-99 . -1234) T) ((-645 . -111) 110285) ((-617 . -111) 110264) ((-1184 . -1262) 110241) ((-853 . -1065) 110220) ((-1184 . -1244) 110204) ((-525 . -25) T) ((-505 . -310) T) ((-521 . -23) T) ((-520 . -25) T) ((-518 . -25) T) ((-517 . -23) T) ((-428 . -1067) 110178) ((-417 . -1065) T) ((-327 . -1074) T) ((-704 . -315) T) ((-428 . -650) 110152) ((-108 . -858) T) ((-722 . -736) T) ((-417 . -249) T) ((-417 . -239) 110131) ((-388 . -235) 110118) ((-497 . -38) 110068) ((-219 . -38) 110018) ((-484 . -503) 109984) ((-1241 . -377) T) ((-1175 . -1160) T) ((-1117 . -102) T) ((-837 . -235) 109957) ((-711 . -623) 109939) ((-711 . -624) 109854) ((-724 . -21) T) ((-724 . -25) T) ((-1151 . -102) T) ((-492 . -656) 109624) ((-246 . -907) 109554) ((-135 . -623) 109536) ((-117 . -623) 109518) ((-158 . -25) T) ((-1306 . -1116) T) ((-882 . -649) 109466) ((-1304 . -1116) T) ((-977 . -102) T) ((-745 . -102) T) ((-725 . -102) T) ((-463 . -102) T) ((-826 . -462) 109417) ((-44 . -1116) T) ((-1104 . -860) T) ((-1079 . -317) 109268) ((-674 . -132) T) ((-1070 . -656) 109237) ((-680 . -727) 109221) ((-297 . -1074) T) ((-364 . -132) T) ((-361 . -132) T) ((-353 . -132) T) ((-271 . -132) T) ((-253 . -132) T) ((-394 . -656) 109190) ((-428 . -102) T) ((-153 . -1116) T) ((-45 . -231) 109140) ((-1020 . -907) NIL) ((-809 . -1067) 109124) ((-972 . -860) 109103) ((-1015 . -658) 109005) ((-809 . -650) 108989) ((-246 . -1291) 108959) ((-1040 . -315) T) ((-302 . -1072) 108880) ((-924 . -132) T) ((-40 . -934) T) ((-497 . -410) 108862) ((-363 . -315) T) ((-219 . -410) 108844) ((-1096 . -421) 108828) ((-302 . -111) 108744) ((-1200 . -860) T) ((-1199 . -860) T) ((-882 . -25) T) ((-882 . -21) T) ((-1270 . -47) 108688) ((-348 . -623) 108670) ((-1189 . -238) T) ((-227 . -148) T) ((-176 . -623) 108652) ((-784 . -623) 108634) ((-129 . -860) T) ((-618 . -241) 108581) ((-485 . -241) 108531) ((-1306 . -727) 108501) ((-48 . -315) T) ((-1304 . -727) 108471) ((-65 . -626) 108400) ((-978 . -1116) T) ((-825 . -1116) 108190) ((-320 . -102) T) ((-915 . -1234) T) ((-48 . -1038) T) ((-1247 . -649) 108098) ((-699 . -102) 108076) ((-44 . -727) 108060) ((-560 . -102) T) ((-302 . -626) 107991) ((-67 . -392) T) ((-497 . -914) NIL) ((-67 . -405) T) ((-219 . -914) NIL) ((-672 . -23) T) ((-827 . -656) 107927) ((-680 . -771) T) ((-1231 . -1116) 107905) ((-360 . -1072) 107850) ((-685 . -1116) 107828) ((-1078 . -148) T) ((-966 . -148) 107807) ((-966 . -146) 107786) ((-809 . -102) T) ((-153 . -727) 107770) ((-491 . -148) 107749) ((-491 . -146) 107728) ((-360 . -111) 107657) ((-1096 . -1074) T) ((-330 . -860) 107636) ((-1276 . -989) 107605) ((-637 . -1116) T) ((-1269 . -989) 107567) ((-521 . -132) T) ((-517 . -132) T) ((-303 . -231) 107517) ((-368 . -1074) T) ((-362 . -1074) T) ((-354 . -1074) T) ((-302 . -1065) 107459) ((-1248 . -989) 107428) ((-388 . -860) T) ((-108 . -1074) T) ((-1015 . -736) T) ((-880 . -934) T) ((-853 . -805) 107407) ((-853 . -802) 107386) ((-428 . -317) 107325) ((-478 . -102) T) ((-605 . -989) 107294) 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. -38) 105938) ((-560 . -317) 105742) ((-1191 . -1067) 105625) ((-324 . -1234) T) ((-360 . -239) T) ((-360 . -249) T) ((-321 . -1234) T) ((-297 . -1116) T) ((-1190 . -1067) 105460) ((-1184 . -1067) 105250) ((-1142 . -1067) 105133) ((-1191 . -650) 105030) ((-1190 . -650) 104871) ((-721 . -1238) T) ((-1184 . -650) 104667) ((-1173 . -661) 104651) ((-1142 . -650) 104548) ((-1228 . -566) 104527) ((-829 . -395) 104511) ((-721 . -566) T) ((-605 . -907) 104422) ((-324 . -895) 104406) ((-324 . -897) 104331) ((-137 . -1234) T) ((-321 . -895) 104292) ((-321 . -897) NIL) ((-809 . -317) 104257) ((-327 . -727) 104098) ((-396 . -395) 104082) ((-332 . -331) 104059) ((-495 . -102) T) ((-484 . -25) T) ((-484 . -21) T) ((-428 . -38) 104033) ((-324 . -1054) 103696) ((-227 . -1219) T) ((-227 . -1222) T) ((-3 . -623) 103678) ((-321 . -1054) 103608) ((-882 . -235) 103581) ((-2 . -1116) T) ((-2 . |RecordCategory|) T) ((-1129 . -1074) 103531) ((-843 . -623) 103513) ((-1078 . -238) T) ((-590 . -934) T) ((-574 . -830) T) ((-574 . -934) T) ((-505 . -934) T) ((-137 . -1054) 103497) ((-227 . -95) T) ((-171 . -148) 103476) ((-75 . -451) T) ((0 . -623) 103458) ((-75 . -405) T) ((-171 . -146) 103409) ((-227 . -35) T) ((-49 . -623) 103391) ((-487 . -1074) T) ((-497 . -233) 103373) ((-494 . -984) 103357) ((-219 . -233) 103339) ((-81 . -451) T) ((-81 . -405) T) ((-1162 . -34) T) ((-825 . -174) 103318) ((-741 . -102) T) ((-663 . -656) 103277) ((-1042 . -623) 103244) ((-510 . -294) 103194) ((-324 . -386) 103163) ((-321 . -386) 103124) ((-321 . -347) 103085) ((-1101 . -623) 103067) ((-826 . -963) 103014) ((-672 . -132) T) ((-1257 . -146) 102993) ((-1257 . -148) 102972) ((-1191 . -102) T) ((-1190 . -102) T) ((-1184 . -102) T) ((-1176 . -1116) T) ((-1142 . -102) T) ((-224 . -34) T) ((-297 . -727) 102959) ((-1176 . -620) 102935) ((-603 . -317) NIL) ((-1276 . -1275) 102919) ((-494 . -1116) 102897) ((-1166 . -231) 102847) ((-400 . -623) 102829) ((-520 . -860) T) ((-1136 . -1234) T) ((-1276 . -1262) 102806) 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101830) ((-117 . -111) 101815) ((-1286 . -623) 101797) ((-1257 . -238) T) ((-1242 . -623) 101779) ((-1240 . -860) T) ((-645 . -730) T) ((-617 . -730) T) ((-1228 . -1128) T) ((-1228 . -23) T) ((-1189 . -462) 101710) ((-1184 . -317) 101595) ((-1183 . -1116) T) ((-825 . -524) 101528) ((-1051 . -1234) T) ((-246 . -1067) 101405) ((-1175 . -1116) T) ((-1158 . -658) 101343) ((-957 . -152) 101327) ((-1142 . -317) 101314) ((-1141 . -462) 101265) ((-246 . -650) 101187) ((-1103 . -566) 101118) ((-1103 . -1238) 101097) ((-1096 . -727) 100965) ((-535 . -102) T) ((-530 . -102) 100915) ((-1020 . -1067) 100865) ((-1010 . -1116) T) ((-826 . -907) 100797) ((-792 . -1238) 100776) ((-790 . -1238) 100755) ((-62 . -1234) T) ((-487 . -623) 100707) ((-487 . -624) 100629) ((-792 . -566) 100540) ((-790 . -566) 100471) ((-741 . -317) 100458) ((-711 . -626) 100430) ((-492 . -421) 100399) ((-633 . -934) 100378) ((-464 . -1238) 100357) ((-685 . -524) 100290) ((-674 . -25) T) ((-408 . -623) 100272) ((-674 . -21) T) 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-1072) 99384) ((-219 . -656) 99334) ((-176 . -111) 99245) ((-108 . -727) 99195) ((-281 . -1116) T) ((-280 . -1116) T) ((-279 . -1116) T) ((-278 . -1116) T) ((-277 . -1116) T) ((-276 . -1116) T) ((-275 . -1116) T) ((-214 . -1116) T) ((-213 . -1116) T) ((-171 . -1222) 99173) ((-171 . -1219) 99151) ((-211 . -1116) T) ((-210 . -1116) T) ((-117 . -1065) T) ((-209 . -1116) T) ((-208 . -1116) T) ((-205 . -1116) T) ((-204 . -1116) T) ((-203 . -1116) T) ((-202 . -1116) T) ((-201 . -1116) T) ((-200 . -1116) T) ((-199 . -1116) T) ((-198 . -1116) T) ((-197 . -1116) T) ((-196 . -1116) T) ((-195 . -1116) T) ((-246 . -102) 98941) ((-171 . -35) 98919) ((-171 . -95) 98897) ((-664 . -1054) 98793) ((-492 . -1074) 98743) ((-1129 . -1116) 98533) ((-1158 . -34) T) ((-680 . -499) 98517) ((-73 . -1234) T) ((-105 . -623) 98499) ((-1308 . -623) 98481) ((-390 . -623) 98463) ((-348 . -626) 98415) ((-176 . -626) 98332) ((-1233 . -500) 98313) ((-741 . -38) 98162) ((-581 . -1222) T) ((-581 . -1219) T) ((-541 . -623) 98144) ((-530 . -317) 98082) ((-510 . -623) 98064) ((-510 . -624) 98046) ((-1233 . -623) 98012) ((-1184 . -1168) NIL) ((-1043 . -1087) 97981) ((-1043 . -1116) T) ((-1020 . -102) T) ((-987 . -102) T) ((-928 . -102) T) ((-904 . -1054) 97958) ((-1158 . -736) T) ((-1019 . -658) 97865) ((-486 . -1116) T) ((-473 . -1116) T) ((-596 . -23) T) ((-581 . -35) T) ((-581 . -95) T) ((-437 . -102) T) ((-1079 . -231) 97811) ((-1191 . -38) 97708) ((-876 . -736) T) ((-704 . -934) T) ((-521 . -25) T) ((-517 . -21) T) ((-517 . -25) T) ((-1190 . -38) 97549) ((-348 . -1065) T) ((-1184 . -38) 97345) ((-1096 . -174) T) ((-176 . -1065) T) ((-1142 . -38) 97242) ((-722 . -47) 97219) ((-368 . -174) T) ((-362 . -174) T) ((-529 . -57) 97193) ((-507 . -57) 97143) ((-360 . -1303) 97120) ((-227 . -462) T) ((-327 . -298) 97071) ((-354 . -174) T) ((-176 . -249) T) ((-1247 . -860) 96970) ((-108 . -174) T) ((-882 . -1008) 96954) ((-668 . -1128) T) ((-591 . -372) T) ((-591 . -337) 96941) ((-528 . -337) 96918) ((-528 . -372) T) ((-324 . -315) 96897) ((-321 . -315) T) ((-612 . -860) 96876) ((-1129 . -727) 96818) ((-530 . -290) 96802) ((-668 . -23) T) ((-428 . -233) 96786) ((-321 . -1038) NIL) ((-345 . -23) T) ((-103 . -1026) 96770) ((-45 . -36) 96749) ((-622 . -1116) T) ((-360 . -377) T) ((-534 . -102) T) ((-505 . -27) T) ((-246 . -317) 96687) ((-1103 . -1128) T) ((-1307 . -658) 96661) ((-792 . -1128) T) ((-790 . -1128) T) ((-1195 . -421) 96645) ((-464 . -1128) T) ((-1078 . -462) T) ((-1167 . -1116) T) ((-966 . -462) 96596) ((-1131 . -1099) T) ((-110 . -1116) T) ((-1103 . -23) T) ((-1176 . -524) 96379) ((-827 . -1074) T) ((-792 . -23) T) ((-790 . -23) T) ((-491 . -462) 96330) ((-471 . -23) T) ((-390 . -391) 96309) ((-364 . -235) 96282) ((-361 . -235) 96255) ((-353 . -235) 96228) ((-464 . -23) T) ((-271 . -235) 96201) ((-258 . -907) 96131) ((-257 . -907) 96061) ((-96 . -1116) T) ((-722 . -1234) T) ((-680 . -294) 96038) ((-494 . -524) 95971) ((-1276 . -1067) 95854) ((-1276 . -650) 95751) ((-1269 . -650) 95592) ((-1269 . -1067) 95427) ((-1248 . -650) 95223) ((-297 . -298) T) ((-1248 . -1067) 95013) ((-1098 . -623) 94995) ((-1098 . -624) 94976) ((-417 . -923) 94955) ((-1228 . -132) T) ((-50 . -1128) T) ((-1184 . -410) 94907) ((-1040 . -934) T) ((-1019 . -736) T) ((-853 . -658) 94880) ((-722 . -897) NIL) ((-606 . -1067) 94840) ((-591 . -1128) T) ((-528 . -1128) T) ((-605 . -1067) 94723) ((-1173 . -34) T) ((-1020 . -317) NIL) ((-825 . -499) 94707) ((-606 . -650) 94680) ((-363 . -934) T) ((-605 . -650) 94577) ((-924 . -235) 94564) ((-417 . -658) 94480) ((-50 . -23) T) ((-721 . -132) T) ((-722 . -1054) 94360) ((-591 . -23) T) ((-108 . -524) NIL) ((-528 . -23) T) ((-171 . -419) 94331) ((-1156 . -1116) T) ((-1299 . -1298) 94315) ((-741 . -914) 94292) ((-711 . -805) T) ((-711 . -802) T) ((-1136 . -315) T) ((-388 . -148) T) ((-288 . -623) 94274) ((-287 . -623) 94256) ((-1247 . -1008) 94226) ((-48 . -934) T) ((-685 . -499) 94210) ((-258 . -1291) 94180) ((-257 . -1291) 94150) ((-1193 . -860) T) 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T) ((-463 . -656) 92742) ((-645 . -658) 92726) ((-352 . -1238) T) ((-631 . -111) 92705) ((-617 . -658) 92689) ((-606 . -102) T) ((-319 . -500) 92670) ((-596 . -132) T) ((-605 . -102) T) ((-424 . -1116) T) ((-394 . -1116) T) ((-319 . -623) 92636) ((-229 . -1116) 92614) ((-657 . -524) 92547) ((-642 . -524) 92391) ((-843 . -1065) 92370) ((-654 . -152) 92354) ((-352 . -566) T) ((-722 . -912) 92297) ((-560 . -231) 92247) ((-1276 . -292) 92213) ((-1269 . -292) 92179) ((-1096 . -298) 92130) ((-497 . -858) T) ((-225 . -1128) T) ((-1248 . -292) 92096) ((-1228 . -503) 92062) ((-1020 . -38) 92012) ((-219 . -858) T) ((-428 . -656) 91971) ((-928 . -38) 91923) ((-853 . -804) 91902) ((-853 . -801) 91881) ((-853 . -736) 91860) ((-368 . -298) T) ((-362 . -298) T) ((-354 . -298) T) ((-171 . -462) 91791) ((-437 . -38) 91775) ((-225 . -23) T) ((-108 . -298) T) ((-417 . -804) 91754) ((-417 . -801) 91733) ((-417 . -736) T) ((-510 . -296) 91708) ((-487 . -1072) 91673) ((-668 . -132) T) ((-631 . -626) 91642) 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-1054) 90037) ((-40 . -1238) T) ((-246 . -914) 89969) ((-50 . -132) T) ((-591 . -132) T) ((-528 . -132) T) ((-302 . -658) 89829) ((-352 . -337) 89806) ((-352 . -372) T) ((-330 . -331) 89783) ((-327 . -294) 89741) ((-40 . -566) T) ((-388 . -1219) T) ((-388 . -1222) T) ((-1051 . -1210) 89716) ((-1206 . -241) 89666) ((-1184 . -233) 89618) ((-338 . -1116) T) ((-388 . -95) T) ((-388 . -35) T) ((-1051 . -107) 89564) ((-487 . -1065) T) ((-1308 . -1072) 89548) ((-489 . -241) 89498) ((-1176 . -499) 89432) ((-1299 . -1067) 89416) ((-390 . -1072) 89400) ((-1299 . -650) 89370) ((-487 . -249) T) ((-826 . -102) T) ((-724 . -148) 89349) ((-724 . -146) 89328) ((-494 . -499) 89312) ((-495 . -344) 89281) ((-1308 . -111) 89260) ((-522 . -1116) T) ((-492 . -174) 89239) ((-1015 . -386) 89223) ((-423 . -102) T) ((-390 . -111) 89202) ((-1015 . -347) 89186) ((-286 . -999) 89170) ((-285 . -999) 89154) ((-1020 . -914) NIL) ((-1306 . -623) 89136) ((-1304 . -623) 89118) ((-110 . -524) NIL) ((-1189 . -1260) 89102) 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((-1308 . -1065) T) ((-492 . -524) 87659) ((-1162 . -1234) T) ((-978 . -623) 87641) ((-657 . -499) 87625) ((-642 . -499) 87556) ((-825 . -623) 87287) ((-48 . -27) T) ((-1195 . -727) 87184) ((-966 . -907) 87163) ((-663 . -1116) T) ((-871 . -870) T) ((-446 . -373) 87137) ((-741 . -656) 87047) ((-491 . -907) 87022) ((-1118 . -102) T) ((-986 . -1116) T) ((-874 . -1116) T) ((-826 . -317) 87009) ((-543 . -537) T) ((-543 . -586) T) ((-1304 . -391) 86981) ((-1070 . -524) 86914) ((-1176 . -294) 86890) ((-246 . -233) 86859) ((-258 . -1067) 86736) ((-257 . -1067) 86613) ((-1296 . -727) 86583) ((-1183 . -93) T) ((-1010 . -93) T) ((-827 . -174) 86562) ((-258 . -650) 86484) ((-257 . -650) 86406) ((-1231 . -500) 86383) ((-229 . -524) 86316) ((-631 . -805) 86295) ((-631 . -802) 86274) ((-1231 . -623) 86186) ((-224 . -1234) T) ((-685 . -623) 86118) ((-1191 . -656) 86028) ((-1173 . -1026) 86012) ((-957 . -102) 85962) ((-360 . -736) T) ((-871 . -623) 85944) ((-1190 . -656) 85826) ((-1184 . -656) 85663) 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T) ((-1257 . -963) 84484) ((-251 . -860) 84463) ((-826 . -38) 84312) ((-45 . -524) 84104) ((-1175 . -294) 84054) ((-216 . -1116) T) ((-1166 . -1116) T) ((-882 . -238) 84033) ((-1166 . -620) 84012) ((-596 . -25) T) ((-596 . -21) T) ((-1118 . -317) 83950) ((-977 . -421) 83934) ((-709 . -1238) T) ((-642 . -294) 83887) ((-1103 . -649) 83835) ((-919 . -1116) T) ((-792 . -649) 83783) ((-790 . -649) 83731) ((-352 . -132) T) ((-297 . -623) 83713) ((-880 . -1128) T) ((-709 . -566) T) ((-130 . -626) 83695) ((-464 . -649) 83643) ((-171 . -907) 83600) ((-919 . -917) 83584) ((-388 . -462) T) ((-497 . -1116) T) ((-957 . -317) 83522) ((-711 . -658) 83494) ((-559 . -854) T) ((-219 . -1116) T) ((-324 . -934) 83473) ((-321 . -934) T) ((-321 . -830) NIL) ((-400 . -730) T) ((-880 . -23) T) ((-117 . -658) 83460) ((-484 . -146) 83439) ((-428 . -421) 83423) ((-484 . -148) 83402) ((-110 . -499) 83384) ((-319 . -626) 83365) ((-2 . -623) 83347) ((-188 . -102) T) ((-1175 . -19) 83329) ((-1175 . -614) 83304) 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81840) ((-1247 . -1219) 81806) ((-833 . -1116) T) ((-980 . -983) T) ((-680 . -111) 81785) ((-627 . -1234) T) ((-303 . -524) 81577) ((-1247 . -1222) 81543) ((-1247 . -238) 81448) ((-1242 . -377) T) ((-258 . -317) 81386) ((-257 . -317) 81324) ((-1239 . -854) T) ((-1176 . -624) NIL) ((-1176 . -623) 81306) ((-1158 . -386) 81290) ((-1136 . -830) T) ((-1136 . -934) T) ((-96 . -93) T) ((-1129 . -614) 81267) ((-1096 . -624) 81251) ((-1096 . -623) 81233) ((-1020 . -656) 81183) ((-928 . -656) 81120) ((-825 . -296) 81097) ((-494 . -623) 81029) ((-618 . -152) 80976) ((-497 . -727) 80926) ((-428 . -1074) T) ((-492 . -499) 80910) ((-437 . -656) 80869) ((-335 . -860) 80848) ((-348 . -658) 80822) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -727) 80772) ((-171 . -734) 80743) ((-176 . -658) 80675) ((-591 . -21) T) ((-591 . -25) T) ((-528 . -25) T) ((-528 . -21) T) ((-485 . -152) 80625) ((-1077 . -623) 80607) ((-1009 . -102) T) ((-872 . -102) T) ((-826 . -914) 80543) ((-809 . -421) 80506) ((-40 . -132) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index ffcf7e03..247ad883 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3485733142) -(4461 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3485743638) +(4462 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -332,8 +332,9 @@ |PartialDifferentialDomain&| |PartialDifferentialDomain| |PartialDifferentialEquationsSolverCategory| |PolynomialDecomposition| |AnnaPartialDifferentialEquationPackage| |NumericalPDEProblem| - |PartialDifferentialRing&| |PartialDifferentialRing| |PendantTree| - |Permanent| |PermutationCategory| |PermutationGroup| |Permutation| + |PartialDifferentialRing| |PartialDifferentialSpace&| + |PartialDifferentialSpace| |PendantTree| |Permanent| + |PermutationCategory| |PermutationGroup| |Permutation| |PolynomialFactorizationByRecursion| |PolynomialFactorizationByRecursionUnivariate| |PolynomialFactorizationExplicit&| |PolynomialFactorizationExplicit| @@ -486,665 +487,664 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |delete!| |probablyZeroDim?| |morphism| - |exprToGenUPS| |rightExactQuotient| |bezoutDiscriminant| |e01sbf| - |parents| |quotientByP| |systemCommand| |inv| |ravel| |match?| - |doubleDisc| |prinshINFO| |plus!| |integralRepresents| |red| |gensym| - |HermiteIntegrate| |autoCoerce| |rotatez| |computeBasis| - |fillPascalTriangle| |rk4| |ground?| |reshape| |split!| |randomLC| - |SturmHabichtMultiple| |Is| |UpTriBddDenomInv| |cSin| |nullary?| - |setClosed| |figureUnits| |nextItem| |ground| |commutative?| |irForm| - |numberOfImproperPartitions| |c05nbf| |permutationGroup| |froot| - |increasePrecision| |makeGraphImage| |genericRightTraceForm| - |maxPoints3D| |leadingMonomial| |normal| |linSolve| |restorePrecision| - |indicialEquationAtInfinity| |nextPrimitiveNormalPoly| - |viewWriteAvailable| |univariatePolynomialsGcds| |modularFactor| - |gbasis| |edf2efi| |hue| |leadingCoefficient| |setTex!| |cycleElt| - |adaptive3D?| |normalDeriv| |bivariate?| |constantOpIfCan| - |mkIntegral| |getConstant| |norm| |fixedPointExquo| - |primitiveMonomials| |close| |d02bhf| |s14aaf| |OMconnOutDevice| - |alphanumeric| |listYoungTableaus| F |distdfact| |zeroOf| |powmod| - |divideIfCan!| |integralLastSubResultant| |reductum| |update| - |algDsolve| |middle| |invmultisect| |digit| |inverseIntegralMatrix| - |toScale| |leftMult| |aspFilename| |saturate| |lquo| |display| - |OMReadError?| |elColumn2!| |isEquiv| |createPrimitiveElement| - |revert| |intermediateResultsIF| |vectorise| |universe| - |indiceSubResultantEuclidean| |airyBi| |OMgetError| - |explicitlyFinite?| |quasiComponent| |normalize| |domainTemplate| - |cycleSplit!| |virtualDegree| |backOldPos| |e01bef| |d02bbf| - |OMgetVariable| |univariateSolve| |showIntensityFunctions| - |algebraicVariables| |rewriteIdealWithHeadRemainder| |bumprow| - |FormatArabic| |nlde| |countRealRootsMultiple| |tubeRadius| |palgint0| - |createMultiplicationTable| |gcdcofactprim| |contains?| |moebiusMu| - |reciprocalPolynomial| |fibonacci| |position| |space| |argument| - |intersect| |expr| |singleFactorBound| |fixPredicate| |normFactors| - |rightFactorCandidate| |degreePartition| |iprint| |input| ** - |OMputVariable| |OMunhandledSymbol| |karatsubaDivide| - |ScanFloatIgnoreSpacesIfCan| |operation| |algebraic?| - |brillhartIrreducible?| |callForm?| |e02aef| |tanAn| |library| - |loopPoints| |cycleEntry| |intensity| |f04faf| |midpoints| - |factorAndSplit| |subNodeOf?| |column| |LiePolyIfCan| |remainder| - |prinb| |factorList| |whitePoint| |oneDimensionalArray| - |doubleComplex?| |pseudoRemainder| |sizePascalTriangle| |signAround| - |frobenius| |modifyPoint| |legendre| |size| |variable| - |symmetricSquare| |sdf2lst| |fprindINFO| |pdf2df| |acscIfCan| - |minimumDegree| |mesh?| |useSingleFactorBound| |rowEchelonLocal| - |generalizedInverse| |iterators| |primitivePart| |goodPoint| - |nextIrreduciblePoly| |cCot| |normalise| |swapRows!| - |semiLastSubResultantEuclidean| |set| - |unprotectedRemoveRedundantFactors| |logGamma| |rational?| |lyndon?| - |kroneckerDelta| |binary| |ran| |quoByVar| |errorKind| |setEpilogue!| - |unit?| |expextendedint| |getMatch| |tab| |basisOfRightNucleus| - |previous| |conditionP| |fi2df| |cycleRagits| |wrregime| - |invertibleElseSplit?| |deepestTail| |characteristicPolynomial| - |generalTwoFactor| |binarySearchTree| |push| |getExplanations| - |fTable| |extendedSubResultantGcd| |sqfree| |elements| |headReduced?| - |createNormalElement| |cdr| |pascalTriangle| |notelem| |initTable!| - |commaSeparate| |integralBasis| |bandedHessian| - |removeRedundantFactorsInPols| |c06fqf| |totolex| |trapezoidalo| - |uniform| |iidsum| |sPol| |schema| |primPartElseUnitCanonical| - |purelyAlgebraic?| |say| |basisOfCommutingElements| |changeNameToObjf| - |cAsinh| |true| |printTypes| |arguments| |partialQuotients| |e01daf| - |initiallyReduce| |isPlus| |integrate| |preprocess| |genericPosition| - |s18aef| |colorFunction| |category| |leftAlternative?| |adaptive| - |lazyPseudoQuotient| |autoReduced?| |yCoord| |reset| |lllip| |node| - |ode| |max| |mindegTerm| |fortranLogical| |domain| |subtractIfCan| - |insertBottom!| |iilog| |lSpaceBasis| |clipPointsDefault| - |SturmHabichtCoefficients| |insert| |f02akf| |symbolTableOf| - |PDESolve| |package| |fortranLinkerArgs| |diagonal?| - |generalInfiniteProduct| |write| |radix| |showScalarValues| |inc| - |pair?| |f2df| |selectSumOfSquaresRoutines| |exp| |byteBuffer| - |setImagSteps| |save| |cAcsch| |acoshIfCan| |primextintfrac| |tab1| - |listOfLists| |show| |shellSort| |padecf| |multisect| |distFact| - |leadingCoefficientRicDE| |showAll?| |null?| |clikeUniv| |extractTop!| - |rootPoly| |block| |expPot| |iiatan| |setButtonValue| - |genericRightMinimalPolynomial| |wordInGenerators| - |leftRankPolynomial| |trace| |createIrreduciblePoly| |physicalLength| - |argumentList!| |eof?| |partitions| |algebraicCoefficients?| - |basisOfRightAnnihilator| |fixedPoints| |regime| |eigenvector| - |mergeDifference| |f04qaf| |dihedralGroup| |printCode| |interpolate| - |partialNumerators| |directSum| |rk4f| |varList| |delay| |idealiser| - |e02dff| |rubiksGroup| |mapMatrixIfCan| |RemainderList| - |leftScalarTimes!| |e02bdf| |e04gcf| |positiveRemainder| |clipSurface| - |lazy?| |separateFactors| |cap| |generalizedEigenvector| |minordet| - |OMputObject| |thetaCoord| |readLine!| |open| |removeZero| - |lookupFunction| |fmecg| |dflist| |collectUpper| |dmpToHdmp| - |deepestInitial| |useSingleFactorBound?| |deleteRoutine!| - |OMgetEndBVar| |rowEch| |psolve| |nonSingularModel| |extractProperty| - |splitDenominator| |drawComplex| |cSinh| |addMatchRestricted| - |OMgetString| |obj| |retractIfCan| |finiteBound| |putColorInfo| |bits| - |double| |resultantReduit| |ratPoly| |eyeDistance| |dmp2rfi| |cache| - |constant| |e02dcf| |semiDegreeSubResultantEuclidean| - |numberOfNormalPoly| |addBadValue| |separate| |zeroSetSplit| |dfRange| - |uniform01| |operations| |zeroSquareMatrix| |patternMatchTimes| - |closedCurve?| |outputArgs| |mainValue| |genericLeftDiscriminant| - |cfirst| |df2ef| |showTheRoutinesTable| |imaginary| |iiabs| |euler| - |dmpToP| |discriminant| |root| |iidprod| |safeFloor| |log10| |heap| - |sinIfCan| |toseInvertibleSet| |module| |denomRicDE| |inspect| - |drawToScale| |mainPrimitivePart| |support| |bitand| |f02abf| - |infinity| |internalIntegrate0| |color| |makeSeries| |cosSinInfo| - |reify| |outputFixed| |unrankImproperPartitions1| |coth2trigh| - |bitior| |groebner| |dimensionOfIrreducibleRepresentation| - |explicitlyEmpty?| |minIndex| |constantRight| |s17ajf| - |raisePolynomial| |nsqfree| |keys| |setAdaptive| |partition| - |elliptic| |definingInequation| |singularitiesOf| |antiCommutative?| - |e01bff| |radicalRoots| |setScreenResolution| |prime?| |kernel| - |Lazard| |useEisensteinCriterion?| |map| |taylorRep| |sts2stst| - |isQuotient| |initializeGroupForWordProblem| |tubeRadiusDefault| - |viewport2D| |constantIfCan| |derivative| |numericalOptimization| - |LazardQuotient| |list| |unknownEndian| |perfectNthPower?| - |horizConcat| |OMgetEndAtp| |print| |mainVariable| |lhs| |maxrank| - |setelt!| |imagK| |negative?| |draw| |isTimes| |dihedral| - |checkForZero| |inputOutputBinaryFile| |sinhIfCan| |resolve| - |currentScope| |f04mbf| |rhs| |noLinearFactor?| |repeating| - |csch2sinh| |irVar| |OMgetAttr| |solveRetract| |lexTriangular| - |exponential1| |OMencodingBinary| |ParCondList| |pointColor| - |complexZeros| |cyclicEqual?| |binomial| |resetAttributeButtons| - |distribute| |nullity| |currentEnv| |numberOfVariables| - |lowerPolynomial| |matrixConcat3D| |derivationCoordinates| |moduleSum| - |associates?| |multiEuclideanTree| |SFunction| |convert| |bitTruth| - |height| |rootDirectory| |complexElementary| |pushup| |hasoln| - |argumentListOf| |stirling2| |monomials| |makeObject| |sechIfCan| - |optAttributes| |realZeros| |shallowExpand| |row| |setColumn!| - |palglimint| |continuedFraction| |companionBlocks| |imagJ| |rootPower| - |coef| |listConjugateBases| |primintfldpoly| |child?| |hostPlatform| - |shiftRoots| |parts| |repeatUntilLoop| |solid?| |jacobiIdentity?| - |quasiRegular?| |dom| |inverseLaplace| |prepareDecompose| |iiperm| - |inR?| |complement| |invertible?| |s13acf| |getPickedPoints| - |schwerpunkt| |listexp| |simplify| Y |clipBoolean| - |showFortranOutputStack| |pleskenSplit| |cylindrical| |makeSin| - |subResultantChain| |alternating| |lastSubResultantEuclidean| - |enterInCache| |sqfrFactor| |tryFunctionalDecomposition| - |numberOfIrreduciblePoly| |characteristicSerie| |rightGcd| |stFunc2| - |curveColor| |label| |homogeneous?| |lintgcd| |groebnerFactorize| - |lflimitedint| |primitiveElement| |positive?| |hexDigit| |bothWays| - |jordanAlgebra?| |entry| |divergence| |axesColorDefault| |sncndn| - |completeEchelonBasis| |asecIfCan| |infiniteProduct| |f02wef| |list?| - |critpOrder| |iiacsch| |determinant| |pile| |possiblyInfinite?| - |exprHasWeightCosWXorSinWX| |ffactor| |fortranTypeOf| - |nativeModuleExtension| |leadingIndex| |addmod| |realSolve| |tubePlot| - |coleman| |generators| |remove!| |hex| |LyndonWordsList| |tanNa| - |decomposeFunc| |binaryTree| |meshFun2Var| |basisOfNucleus| - |localIntegralBasis| |minimalPolynomial| |lowerCase!| |readInt16!| - |showAllElements| |newSubProgram| |rationalIfCan| |quatern| - |tanintegrate| |smith| |numberOfHues| |LyndonBasis| |repSq| |e02zaf| - |incr| |dAndcExp| |transcendent?| |cyclic?| - |genericLeftMinimalPolynomial| |permanent| |polyRDE| |swap| - |extensionDegree| |OMputInteger| |constructor| |outputMeasure| |hi| - |real?| |qualifier| |moduloP| |tail| |evaluate| |hdmpToDmp| |d01bbf| - |numberOfChildren| |elRow1!| |palgRDE| |contract| |cSec| - |multiplyCoefficients| |option| |subTriSet?| |stoseInvertibleSet| - |rightUnit| |complexEigenvalues| |bezoutResultant| |showSummary| - |antisymmetric?| |prevPrime| |diagonalMatrix| |constantKernel| - |every?| |ricDsolve| |stosePrepareSubResAlgo| |mappingMode| - |resetVariableOrder| |rules| |units| |multinomial| |HenselLift| - |npcoef| |minset| |top| |compound?| |cycleTail| |LyndonWordsList1| - |monicRightDivide| |showAttributes| |exponent| |matrixDimensions| - |putProperty| |e01bhf| |region| |continue| |cPower| |completeSmith| - |rootRadius| |mathieu11| |composites| |integral| |anticoord| - |solveLinear| |bracket| |bsolve| |tubePointsDefault| |fractRadix| - |status| |removeSuperfluousQuasiComponents| |binomThmExpt| - |rightTraceMatrix| |mappingAst| |name| |gcdcofact| 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- |sh| |setright!| |tubePoints| |midpoint| |indiceSubResultant| - |integralCoordinates| |part?| |critB| |abs| |insertTop!| - |getVariableOrder| |rightLcm| |remove| |integralDerivationMatrix| - |minRowIndex| |radicalEigenvalues| |symFunc| |imagk| |lambert| - |escape| |cyclicParents| |identitySquareMatrix| |groebgen| - |factorSFBRlcUnit| |rationalApproximation| |primitivePart!| |df2st| - |OMgetEndAttr| |complexLimit| |xCoord| |sumSquares| |evaluateInverse| - |fortranLiteralLine| |complexExpand| |center| |last| |xn| - |totalDegree| |OMgetInteger| |isMult| |updatF| |linearDependenceOverZ| - |createNormalPoly| |mapGen| |assoc| |harmonic| |f01bsf| - |outputSpacing| |cos2sec| |voidMode| |mathieu24| |curveColorPalette| - |OMclose| |addPoint2| |viewDefaults| |formula| |element?| |cCosh| - |rootOf| |clearDenominator| |biRank| |rightQuotient| |corrPoly| - |OMreadStr| |range| |linearAssociatedOrder| |euclideanSize| |f02ajf| - |findCycle| |zeroVector| |var2StepsDefault| |reduced?| |acotIfCan| - |wreath| |one?| |f04jgf| |complexEigenvectors| |fortranComplex| - |symmetricGroup| |setMaxPoints3D| |bitCoef| |rightFactorIfCan| - |palgint| |controlPanel| |compactFraction| |returnType!| - |parabolicCylindrical| |mathieu12| |collect| |scale| - |createPrimitiveNormalPoly| |squareFreeFactors| |cosh2sech| |head| - |representationType| |d01amf| |Nul| |screenResolution| |unary?| - |OMsetEncoding| |explogs2trigs| |removeRoughlyRedundantFactorsInPol| - |pack!| |leftCharacteristicPolynomial| |aLinear| |oddlambert| |isExpt| - |crushedSet| |s19acf| |logIfCan| |balancedBinaryTree| |s18acf| |critT| - |heapSort| |palgextint0| |atoms| |rightDiscriminant| |subset?| - |ReduceOrder| |mdeg| |var1Steps| |minPol| |s19adf| |lfextendedint| - |euclideanNormalForm| |cAtanh| |romberg| |linearPolynomials| |c06fpf| - |startTableInvSet!| |mkPrim| |viewSizeDefault| |thenBranch| - |exactQuotient| |cCoth| |mix| |normalElement| |createGenericMatrix| - F2FG |interpretString| |cCsch| |stFuncN| |lifting| - |basisOfLeftAnnihilator| |s17dgf| |removeSquaresIfCan| |divide| - |nextLatticePermutation| |removeRoughlyRedundantFactorsInPols| - |makeViewport2D| |parseString| |LazardQuotient2| |mirror| |setleaves!| - |fortranCompilerName| |realEigenvectors| |string?| |quasiRegular| - |elliptic?| |chebyshevU| |diagonals| |squareFreePrim| |f02awf| - |bfEntry| |reducedQPowers| |increase| |removeSuperfluousCases| - |reducedSystem| |mainContent| |monomialIntPoly| |times!| - |cyclicSubmodule| |sincos| |floor| |lepol| |unmakeSUP| - |exportedOperators| |differentialVariables| |fortranCarriageReturn| - |laplacian| |taylorQuoByVar| |realEigenvalues| |dimension| |leaves| - |henselFact| |ridHack1| |extract!| |e01sff| |mergeFactors| |hspace| - |principal?| |singularAtInfinity?| |commutator| |normInvertible?| - |OMputBVar| |rationalFunction| |nil| |unrankImproperPartitions0| - |resultant| |tanIfCan| |baseRDEsys| |macroExpand| |associative?| - |s18def| |rowEchelon| |headReduce| |hcrf| UP2UTS |iicsc| |innerSolve1| - |bindings| |prime| |rightZero| |c06fuf| |odd?| |polygon?| |computeInt| - |clipParametric| |baseRDE| |birth| |plenaryPower| |lazyGintegrate| - |zero?| |setCondition!| |stronglyReduced?| |denominators| - |approximate| |rowEchLocal| |numFunEvals3D| |ignore?| |iicot| - |zeroDim?| |d01asf| |OMbindTCP| |fixedDivisor| |const| |sum| |complex| - |numerator| |polygon| |df2fi| |readIfCan!| |front| |lazyResidueClass| - |tanh2trigh| |subscript| |limitedint| |approxNthRoot| - |setTopPredicate| |rotatex| |edf2ef| |iibinom| |bottom!| - |factorOfDegree| |patternMatch| |leftExtendedGcd| |alphabetic?| - |branchPoint?| |regularRepresentation| |rank| |mapExponents| - |pushuconst| |factorGroebnerBasis| |iitan| |checkRur| |s17dhf| |point| - |sort!| |OMgetEndObject| |bfKeys| |cn| |OMlistCDs| |updateStatus!| - |is?| |debug| |e01bgf| |failed| |numberOfComposites| |setfirst!| - |multiple?| |gcdPolynomial| |stoseInvertible?| |sinhcosh| - |gcdPrimitive| |factorset| D |degree| |closed?| |complexIntegrate| - |largest| |trace2PowMod| |copy!| |f01mcf| |setPosition| |Gamma| - |cyclic| |mkAnswer| |resetNew| |series| |zerosOf| |pointColorDefault| - |doubleResultant| |factorsOfCyclicGroupSize| |jordanAdmissible?| - |printHeader| |OMUnknownCD?| |f02aaf| |infinite?| |expintegrate| - |rightExtendedGcd| |leadingIdeal| |genericRightTrace| - |numericalIntegration| |attributeData| |c05pbf| - |wordInStrongGenerators| |components| |pToHdmp| |changeMeasure| - |removeIrreducibleRedundantFactors| |separant| |OMencodingUnknown| - |po| |integralAtInfinity?| |s17aef| |direction| |super| |less?| - |lists| |hyperelliptic| |rename| |has?| |reducedForm| |content| |min| - |padicallyExpand| |kovacic| |upperCase| |leftUnits| |janko2| - |stoseIntegralLastSubResultant| |binaryFunction| |cCos| |totalLex| - |printInfo| |viewPosDefault| |traceMatrix| |qroot| |submod| |ideal| - |unitCanonical| |headAst| |meatAxe| |whatInfinity| |cyclicEntries| - |critBonD| |divideIfCan| |conical| |sizeLess?| |rk4qc| |flexibleArray| - |explimitedint| |checkPrecision| |cSech| |ODESolve| |normDeriv2| - |substring?| |rewriteSetWithReduction| |key| |dictionary| - |externalList| |orbit| |stoseInvertibleSetreg| |jacobian| |c06ecf| - |halfExtendedResultant2| |permutations| |crest| |s17def| |atom?| - |ode1| |leader| |leftRegularRepresentation| |s17dlf| |unvectorise| - |untab| |suffix?| |imagE| |filename| |c06ebf| |showTheFTable| |graphs| - |weighted| |elRow2!| |readInt8!| |f01maf| |even?| |tube| |symbolTable| - |loadNativeModule| |stopTableGcd!| |functorData| |e04dgf| |high| - |exprHasLogarithmicWeights| |semiResultantEuclideannaif| - |seriesToOutputForm| |setPrologue!| |prefix?| |makeSUP| |epilogue| - |parse| |OMgetBind| |setMinPoints3D| |gderiv| |numerators| |fortran| - |rootOfIrreduciblePoly| |bandedJacobian| |insertMatch| - |defineProperty| |plus| |omError| |pushFortranOutputStack| - |critMTonD1| |exists?| |primPartElseUnitCanonical!| |associatedSystem| - |makeCos| |elementary| |difference| |generateIrredPoly| |car| - |popFortranOutputStack| |lfextlimint| |e04mbf| |solveLinearlyOverQ| - |deepExpand| |wholeRadix| |unitNormal| |trailingCoefficient| - |summation| |expint| |outputAsFortran| |partialDenominators| |normal?| - |weierstrass| |number?| |fortranDoubleComplex| |tablePow| - |factorSquareFree| |split| |internalAugment| |table| |att2Result| - |cLog| |printingInfo?| |prem| |useEisensteinCriterion| |redPo| - |s17adf| |precision| |subResultantsChain| |times| |normalized?| |new| - |sin?| |permutation| |ratpart| |basisOfCentroid| |getlo| |multiset| - |symmetricRemainder| |stoseInternalLastSubResultant| |addPointLast| - |infix?| |ptree| |unit| |spherical| |branchPointAtInfinity?| - |asinhIfCan| |rootSplit| |flatten| |semicolonSeparate| |sayLength| - |showClipRegion| |mask| |stripCommentsAndBlanks| |terms| - |commutativeEquality| |sylvesterSequence| |shape| |gradient| |init| - |outputFloating| |quadraticForm| |makeCrit| |mathieu23| - |constantToUnaryFunction| |reorder| |upperCase!| |doublyTransitive?| - |optpair| |supRittWu?| |topPredicate| |strongGenerators| - |nextPartition| |monom| |newLine| |exprHasAlgebraicWeight| - |idealiserMatrix| |OMgetAtp| |polarCoordinates| - |monicCompleteDecompose| |aQuartic| |unitsColorDefault| |triangular?| - |rule| |iicosh| |double?| |s15aef| |enumerate| |minimize| - |getZechTable| |external?| |paraboloidal| |extractIndex| - |radicalEigenvector| |cCsc| |roman| |writeUInt8!| |common| |credPol| - |sample| |mainExpression| |createLowComplexityTable| |overset?| - |replaceKthElement| |e02baf| |minrank| |before?| |script| - |BumInSepFFE| |shrinkable| |truncate| |pureLex| |makeResult| |f01qcf| - |normalizeAtInfinity| |leftFactorIfCan| - |removeRedundantFactorsInContents| |selectOrPolynomials| |title| - |makeFloatFunction| |besselI| |endOfFile?| |inGroundField?| - |monomRDEsys| |getMultiplicationTable| |f04adf| |OMputAtp| |unexpand| - |cRationalPower| |myDegree| |fortranDouble| |selectAndPolynomials| - |left| |vector| |rightMinimalPolynomial| |sequence| |limitedIntegrate| - |nodeOf?| |tex| |trigs| |outerProduct| |primitive?| |ratDsolve| - |duplicates| |OMUnknownSymbol?| |right| |differentiate| |safetyMargin| - |innerint| |discreteLog| |rischDE| |e| |logical?| |stronglyReduce| - |rangePascalTriangle| |lazyPseudoDivide| |factor1| - |toseLastSubResultant| |squareTop| |updatD| |removeZeroes| |round| - |close!| |OMgetEndError| |optional?| |stopTable!| |dark| - |viewDeltaYDefault| |tracePowMod| |Ei| |radicalSolve| - |physicalLength!| |stoseInvertibleSetsqfreg| |selectfirst| |setvalue!| - |coefChoose| |rotate!| |bat1| |coerceP| |recip| |realRoots| |tan2cot| - |forLoop| |internal?| |setEmpty!| |outlineRender| |modTree| - |sparsityIF| |minus!| |relationsIdeal| |multMonom| |musserTrials| - |monomRDE| |cartesian| |infix| |iiatanh| |palgLODE0| |trim| - |decompose| |radPoly| |shift| |principalAncestors| |d01ajf| - |supDimElseRittWu?| |subNode?| |any| |pole?| |hash| |makeSketch| - |unaryFunction| |e02ahf| |setClipValue| |d01alf| |latex| |KrullNumber| - |dominantTerm| |count| |degreeSubResultant| - |functionIsContinuousAtEndPoints| |OMsupportsCD?| |next| - |functionIsFracPolynomial?| |squareFree| |primextendedint| |maxdeg| - |mapUnivariate| |child| |fortranLiteral| |pseudoDivide| |triangSolve| - |pushucoef| |irCtor| |cAsin| |d02kef| |setPredicates| - |quasiMonicPolynomials| |OMconnInDevice| |infieldIntegrate| - |maxPoints| |listBranches| |environment| |elem?| |BasicMethod| - |phiCoord| |compiledFunction| |listRepresentation| |symbol| - |nextSublist| |stiffnessAndStabilityFactor| |initials| |readByte!| - |whileLoop| |infieldint| |c06gcf| |chiSquare| |parabolic| - |numericIfCan| |expression| |reducedContinuedFraction| - |stiffnessAndStabilityOfODEIF| |iisinh| |c06frf| |algint| - |leadingExponent| |hdmpToP| |completeHensel| |LowTriBddDenomInv| - |integer| |quartic| |relerror| |s17aff| |open?| |youngGroup| - |possiblyNewVariety?| |startTableGcd!| |linear| - |generalizedContinuumHypothesisAssumed?| |enterPointData| - |rewriteIdealWithRemainder| |returnTypeOf| |points| |makeEq| - |outputAsScript| |e04fdf| |padicFraction| |changeVar| |wholePart| - |characteristic| |exprToXXP| |s21bbf| |substitute| - |ramifiedAtInfinity?| |bringDown| |polynomial| |univariatePolynomial| - |leftGcd| |selectIntegrationRoutines| |isAtom| - |cyclotomicFactorization| |indicialEquation| |compdegd| |btwFact| - |deleteProperty!| |createLowComplexityNormalBasis| |f02aff| - |reduceByQuasiMonic| |selectPDERoutines| |rootKerSimp| |retractable?| - |s14baf| |dualSignature| |erf| |f01rcf| |s14abf| |result| |mat| - |cot2trig| |powerSum| |iisec| |zCoord| |intPatternMatch| |li| - |removeConstantTerm| |squareFreePolynomial| |drawCurves| |OMwrite| - |pquo| |host| |limit| |LagrangeInterpolation| |resultantnaif| |stack| - |tower| |choosemon| |nthExpon| |d01apf| |ParCond| |leaf?| - |nextNormalPoly| |quote| |cyclicCopy| |cAcot| |normalDenom| - |mightHaveRoots| |factorByRecursion| |plotPolar| |complexNumericIfCan| - |cothIfCan| |prepareSubResAlgo| |mapExpon| |create| - |functionIsOscillatory| |polCase| |countable?| |iiacoth| - |nextsousResultant2| |totalGroebner| |orthonormalBasis| |perspective| - |coerceL| |f02adf| |startTable!| |getOrder| |eq| |karatsubaOnce| - |lazyPquo| |diagonal| |denomLODE| |outputGeneral| |lowerCase?| - |getProperty| |clearTheFTable| |iter| |dim| |stFunc1| - |integralMatrixAtInfinity| |length| |linGenPos| |nthr| - |rightCharacteristicPolynomial| |setStatus| |integralMatrix| - |OMputSymbol| |karatsuba| |cAtan| |complexNumeric| |readable?| - |nextSubsetGray| |step| |scripts| |divisors| |printStats!| |shuffle| - |typeLists| |exp1| |addMatch| |newReduc| |diff| |mainMonomial| - |concat| |compBound| |bernoulli| |scanOneDimSubspaces| |alphabetic| - |getMultiplicationMatrix| |test| |kernels| |gethi| - |linearAssociatedExp| |monomialIntegrate| |hypergeometric0F1| - |setUnion| |routines| |extractPoint| |normalizedDivide| |OMserve| - |graphCurves| |factorials| |operator| |pointSizeDefault| - |highCommonTerms| |f04asf| |ListOfTerms| |octon| |listOfMonoms| - |startStats!| |primeFrobenius| |rectangularMatrix| |leadingBasisTerm| - |rootBound| |integral?| |rootsOf| |hconcat| |pToDmp| - |transcendentalDecompose| |Aleph| |cardinality| |s18adf| - |linkToFortran| |univariate| |semiSubResultantGcdEuclidean2| |imagi| - |parametric?| |brillhartTrials| |plot| |leftLcm| |subHeight| - |prindINFO| |areEquivalent?| |mapdiv| |component| |s17agf| |s18aff| - |float?| |monic?| |seriesSolve| |rational| - |rightRegularRepresentation| |zeroDimPrimary?| |makeVariable| - |leviCivitaSymbol| |nextsubResultant2| |halfExtendedSubResultantGcd2| - |weakBiRank| |prefix| |failed?| |eq?| |lfunc| |factor| |OMputFloat| - |OMencodingSGML| |writeByte!| |f04maf| - |zeroSetSplitIntoTriangularSystems| |singRicDE| |belong?| |iisqrt2| - |complete| |shallowCopy| |sqrt| |isAbsolutelyIrreducible?| |asimpson| - |scan| |setLegalFortranSourceExtensions| |chiSquare1| |monicDivide| - |maxint| |coerceS| |OMmakeConn| |setValue!| |real| |closeComponent| - |cup| |reseed| |concat!| |iipow| |constantLeft| |f04axf| - |setMaxPoints| |absolutelyIrreducible?| |complexNormalize| |imag| - |complexSolve| |declare| |lprop| |cross| |noValueMode| |stop| - |flagFactor| |roughUnitIdeal?| |alphanumeric?| |laguerre| - |numberOfCycles| |showRegion| |directProduct| |prolateSpheroidal| - |inHallBasis?| |debug3D| |symbol?| |e04naf| |mr| |edf2fi| - |endSubProgram| |simpleBounds?| |firstDenom| |cycles| - |lastSubResultantElseSplit| |pushNewContour| |measure| |axes| |iiexp| - |variable?| SEGMENT |bubbleSort!| |fracPart| |firstUncouplingMatrix| - |brace| |kind| |resize| |e02bcf| |product| |pdct| |viewpoint| - |getButtonValue| |fill!| |freeOf?| |readLineIfCan!| |factors| - |categories| |destruct| |e02daf| |viewDeltaXDefault| |op| |sequences| - |iiacsc| |OMgetFloat| |rightRank| |extendedint| |mantissa| |eulerE| - |depth| |iomode| |c06gbf| |tanQ| |linearPart| |merge| - |expenseOfEvaluationIF| |rischDEsys| |typeForm| |power| |weights| - |pdf2ef| |f02bbf| |showTheIFTable| |mainCoefficients| |coerceImages| - |powern| |currentCategoryFrame| |tanh2coth| |minPoly| |level| - |parametersOf| |viewThetaDefault| |explicitEntries?| |magnitude| - |integer?| |readBytes!| |symmetric?| |laurentRep| |internalInfRittWu?| - |swapColumns!| |setProperty| |degreeSubResultantEuclidean| - |sylvesterMatrix| |An| |monomial| |e02ajf| |internalIntegrate| - |collectQuasiMonic| |sorted?| |solveid| |inverse| |completeEval| - |alternatingGroup| |readUInt8!| |OMopenString| |multivariate| - |goodnessOfFit| |fglmIfCan| |green| |rightDivide| |OMputEndAttr| - |noKaratsuba| |OMputBind| |coordinates| |validExponential| - |testModulus| |variables| |linearlyDependent?| - |selectOptimizationRoutines| |union| |hitherPlane| |trueEqual| - |geometric| |presuper| |e04jaf| |aromberg| |lazyIntegrate| |sech2cosh| - |rootSimp| |setLabelValue| |roughBasicSet| |hessian| |f01qef| - |charClass| |mainKernel| |rquo| |iCompose| |f02bjf| |s17acf| - |genericRightNorm| |besselJ| |shanksDiscLogAlgorithm| |primeFactor| - |eigenvectors| |upperCase?| |minColIndex| |clipWithRanges| |f02xef| - |leftFactor| |ip4Address| |numFunEvals| |simplifyLog| |quasiMonic?| - |binding| |perfectSqrt| |moreAlgebraic?| |pomopo!| |nthExponent| - |SturmHabichtSequence| |aCubic| |mpsode| |returns| |aQuadratic| - |getDatabase| |realElementary| |variationOfParameters| |cAcoth| - |chainSubResultants| |taylor| |yCoordinates| |isOr| |comp| |imagj| - |setIntersection| |setVariableOrder| |copies| |cAsech| |getMeasure| - |exprToUPS| |f01rdf| |laurent| |children| |quotient| |d02raf| - |polynomialZeros| |distance| |identification| |bivariatePolynomials| - |putGraph| |makeMulti| |OMencodingXML| |reverse| |puiseux| - |linearAssociatedLog| |someBasis| |factorPolynomial| |splitConstant| - |pointData| |basisOfRightNucloid| |dequeue!| |point?| |e02bbf| - |adaptive?| |wordsForStrongGenerators| |overlabel| |sinh2csch| |nil| + |Record| |Union| |genericLeftDiscriminant| |nullary| |parents| + |leftTraceMatrix| |OMgetBVar| |laplace| |resultantnaif| |solveLinear| + |setEmpty!| |systemCommand| |inv| |ravel| |match?| + |irreducibleFactors| |cartesian| |complexEigenvectors| |d02gaf| + |s19acf| |safeCeiling| |autoCoerce| |coth2trigh| |zeroSquareMatrix| + |getPickedPoints| |dequeue| |f02bbf| |ground?| |reshape| |c02agf| + |fractionFreeGauss!| |transcendent?| |normalize| |OMputEndApp| + |transform| |leadingExponent| |cubic| |multiEuclideanTree| + |subResultantGcdEuclidean| |ground| |digit?| |powerAssociative?| + |complexExpand| |besselK| |iFTable| |ran| |padicFraction| + |stripCommentsAndBlanks| |cSec| |OMgetInteger| |leadingMonomial| + |normal| |realEigenvalues| |combineFeatureCompatibility| |move| + |cyclotomic| |selectAndPolynomials| |sec2cos| |prod| |exactQuotient!| + |OMgetError| |decompose| |leadingCoefficient| |structuralConstants| + |isobaric?| |nullSpace| |supRittWu?| |OMencodingXML| + |numberOfChildren| |coordinates| |determinant| |bezoutDiscriminant| + |quadraticNorm| |primitiveMonomials| |close| |paren| |nilFactor| + |indices| |iipow| |listBranches| F |c06eaf| |credPol| |unitVector| + |numberOfFractionalTerms| |monicCompleteDecompose| |reductum| |update| + |incrementKthElement| |brillhartTrials| |reduceBasisAtInfinity| + |basisOfLeftNucloid| |split| |parametric?| |s14abf| |s18aff| |tRange| + |realSolve| |display| |removeRedundantFactorsInContents| |infieldint| + |halfExtendedSubResultantGcd1| |mightHaveRoots| |toroidal| + |linearPart| |makeop| |e01bhf| |collectUpper| |subResultantsChain| + |column| |fixedPointExquo| |hconcat| |divideIfCan| + |certainlySubVariety?| |rowEchelon| |zero?| |prepareDecompose| + |e02akf| |exteriorDifferential| |d01apf| + |rewriteSetByReducingWithParticularGenerators| |trivialIdeal?| + |monicRightDivide| |tryFunctionalDecomposition| |qPot| + |branchPointAtInfinity?| |lazyPremWithDefault| |divideIfCan!| + |representationType| |polygamma| |stoseInvertibleSet| |midpoint| + |groebner?| |lllp| |iiatan| |internalInfRittWu?| |position| + |character?| |d01ajf| |expr| |lagrange| |loopPoints| + |createPrimitiveNormalPoly| |sinhIfCan| |airyAi| |polyRDE| + |extractClosed| |input| ** |lowerCase?| |showFortranOutputStack| + |OMgetEndError| |unexpand| |operation| |stoseInternalLastSubResultant| + |yCoordinates| |inHallBasis?| |makeSin| |pushNewContour| |library| + |viewpoint| |charpol| |prevPrime| |identification| |OMgetBind| + |GospersMethod| |nodes| |unprotectedRemoveRedundantFactors| |deepCopy| + |inverseIntegralMatrix| |cCos| |OMputEndObject| |meatAxe| |latex| + |headAst| |OMputObject| |flexibleArray| |normalForm| |morphism| + |sqfree| |size| |listLoops| |variable| |sPol| |accuracyIF| + |insertionSort!| |scripted?| |pointData| |triangSolve| |chvar| + |index?| |f02aff| |iterators| |besselJ| |modulus| + |initializeGroupForWordProblem| |modifyPointData| |tracePowMod| + |factorsOfCyclicGroupSize| |set| |dihedral| |e02zaf| |stopTable!| + |rightTraceMatrix| |leftRank| |sequences| |cAtanh| |d01anf| |revert| + |completeHermite| |removeSinhSq| |yellow| |normalizedAssociate| + |acscIfCan| |arbitrary| |unravel| |checkForZero| |previous| + |csch2sinh| |aQuadratic| |graphCurves| |readInt16!| |composites| + |simplify| |weight| |bezoutMatrix| |changeName| |realEigenvectors| + |addMatch| |conjugates| |toseLastSubResultant| |makeEq| + |mergeDifference| |addPointLast| |OMgetAttr| |numberOfFactors| + |getCurve| |c06gsf| |showAll?| |monomial?| |green| + |lastSubResultantEuclidean| |associatedSystem| |chiSquare| |reify| + |callForm?| |genericRightDiscriminant| |normFactors| |toseInvertible?| + |subresultantVector| |say| |attributeData| |ramified?| + |cyclePartition| |true| |readLineIfCan!| |arguments| |writable?| + |expintegrate| |e01saf| |f04atf| |rarrow| |radix| |skewSFunction| + |leaf?| |genericPosition| |category| |lfinfieldint| |explicitEntries?| + |linears| |optpair| |splitNodeOf!| |reset| |components| |node| + |physicalLength!| |sumOfDivisors| |normalise| |curry| |domain| + |mapUp!| |expenseOfEvaluation| |safeFloor| |ranges| |s17ajf| + |extractProperty| |insert| |genericRightTrace| |gradient| |expandLog| + |package| |makeCrit| |listConjugateBases| |f02bjf| |squareFree| + |mainValue| |write| |inc| |taylorQuoByVar| |rightGcd| |cyclicGroup| + |exp| |seriesToOutputForm| |extendedEuclidean| |save| |rombergo| + |makeResult| |finite?| |overbar| |permutationRepresentation| |show| + |c05nbf| |realZeros| |s17dlf| |iiabs| |normalDenom| |over| |d01fcf| + |coefficients| |leftFactorIfCan| |useSingleFactorBound| |sechIfCan| + |relativeApprox| |ellipticCylindrical| |clip| |heapSort| + |algebraicVariables| |bsolve| |trace| |rangePascalTriangle| + |setTopPredicate| |purelyTranscendental?| |pr2dmp| |operators| + |OMParseError?| |expextendedint| |split!| |less?| |changeBase| + |createLowComplexityTable| |meshFun2Var| |rightRecip| |sqfrFactor| + |f01rcf| |option?| |trigs2explogs| |setMaxPoints3D| |varList| + |mainCharacterization| |iiacsc| |d01aqf| |e01sff| |infinite?| + |digamma| |iisech| |collectUnder| |selectFiniteRoutines| + |lazyEvaluate| |selectSumOfSquaresRoutines| + |functionIsFracPolynomial?| |fortranCompilerName| |traverse| + |outputForm| |maxPoints| |rightScalarTimes!| |norm| |lighting| + |basisOfLeftAnnihilator| |open| |algint| |chainSubResultants| + |extendedint| |cyclicCopy| |nextPartition| |pdct| |OMputApp| |equiv| + |rightLcm| |normal01| |maxColIndex| |rootKerSimp| |shiftRoots| + |maxIndex| |mappingMode| |powers| |monomRDE| |basisOfCentroid| |obj| + |retractIfCan| |pushdown| |minordet| |cCoth| |double| + |zeroDimensional?| |variable?| |triangularSystems| |moduloP| |cache| + |constant| |inputBinaryFile| |supersub| |setRealSteps| |complexRoots| + |nthFactor| |isTimes| |clipBoolean| |commutativeEquality| |operations| + |RittWuCompare| |safetyMargin| |OMgetSymbol| |inverseLaplace| + |ScanRoman| |crushedSet| |c02aff| |close!| |ParCond| |makingStats?| + |generalizedEigenvectors| |chineseRemainder| |localAbs| + |semiLastSubResultantEuclidean| |quartic| |log10| + |semiResultantEuclidean2| |primPartElseUnitCanonical!| + |algebraicDecompose| |exp1| |solveLinearPolynomialEquationByRecursion| + |invertIfCan| |cycleLength| |edf2fi| |pushdterm| |lowerCase!| |bitand| + |shiftRight| |infinity| |internalLastSubResultant| |att2Result| + |fullPartialFraction| |showIntensityFunctions| |subspace| + |lazyResidueClass| |monic?| UP2UTS |diagonalMatrix| |bitior| |tanAn| + |exprHasLogarithmicWeights| |changeThreshhold| |returns| + |getMultiplicationMatrix| |fortranDouble| |outputGeneral| |repSq| + |keys| |typeList| |OMputAtp| |hexDigit| |uniform01| |fglmIfCan| + |factor1| |ffactor| |generalInfiniteProduct| |binaryTree| |tanNa| + |kernel| |nextColeman| |iidprod| |map| |zoom| |isQuotient| + |symmetricGroup| |semiIndiceSubResultantEuclidean| |approxNthRoot| + |makeMulti| |makeTerm| |listexp| |mathieu11| |list| |printStats!| + |prolateSpheroidal| |cyclic| |updatD| |primlimitedint| |hspace| + |airyBi| |print| |lhs| |torsion?| |paraboloidal| |characteristicSerie| + |iidsum| |draw| |doublyTransitive?| |doubleResultant| |resolve| + |ptFunc| |rhs| |quote| |cyclicEntries| |csubst| |d01asf| + |specialTrigs| |call| |preprocess| |fill!| |odd?| |hasPredicate?| + |polygon| |chiSquare1| |chebyshevU| |s17adf| |prinpolINFO| + |numericalIntegration| |reducedSystem| |solid| |currentEnv| |plus!| + |splitConstant| |opeval| |exprToXXP| |stopTableInvSet!| |symbolIfCan| + |fracPart| |makeGraphImage| |OMputEndAttr| |rk4qc| |convert| + |selectfirst| |conjunction| |height| |asecIfCan| |pomopo!| + |numberOfVariables| |points| |testModulus| |graphImage| |makeObject| + |rewriteIdealWithRemainder| |pureLex| |reduced?| |fortranReal| + |iCompose| |Aleph| |hdmpToDmp| |indiceSubResultantEuclidean| + |optAttributes| |s15adf| |ipow| |coef| |matrixGcd| |f04axf| |froot| + |viewDeltaYDefault| |parts| |untab| |cosIfCan| |lex| |mainExpression| + |irVar| |dom| |torsionIfCan| |definingEquations| |remainder| + |laurentRep| |dioSolve| |iteratedInitials| |polar| |rotatez| + |complex?| |saturate| |splitSquarefree| Y |rk4| |clipSurface| + |setClipValue| |readInt32!| |powmod| |duplicates?| |cSech| |times!| + |fixPredicate| |iicsch| |lastSubResultantElseSplit| |blankSeparate| + |extendedSubResultantGcd| |mainSquareFreePart| |inverseColeman| + |ef2edf| |label| |boundOfCauchy| |pair?| |rightRank| |permanent| + |e02daf| |rdHack1| |basisOfLeftNucleus| |shufflein| |OMgetObject| + |entry| |subset?| |constant?| |lintgcd| |rightExactQuotient| + |property| |SturmHabichtMultiple| |select!| |stFunc2| |iiacoth| + |rootPower| |linearAssociatedExp| |tableForDiscreteLogarithm| + |wordInStrongGenerators| |initTable!| |just| |iroot| |deleteProperty!| + |cap| |HenselLift| |oddInfiniteProduct| |constantRight| + |quadraticForm| |cycleTail| |OMputVariable| |crest| + |computeCycleEntry| |clipPointsDefault| |linear?| |maxrank| |smith| + |OMgetString| |symmetricTensors| |gcdcofact| |exponential1| + |evenInfiniteProduct| |f02akf| |imagj| |symmetricProduct| + |setAttributeButtonStep| |cAcot| |initials| |imaginary| |row| + |vertConcat| |incr| |addPoint2| |monomials| |shape| + |halfExtendedResultant1| |setRow!| |primeFactor| |sup| |edf2df| + |selectPDERoutines| |viewThetaDefault| |constructor| |lfextlimint| + |hi| |overset?| |invertibleSet| |lifting| |tail| + |primPartElseUnitCanonical| |real?| |unit?| |e02bef| |rroot| + |twoFactor| |eigenvector| |viewport2D| |surface| |option| |goto| + |idealSimplify| |brillhartIrreducible?| + |semiDegreeSubResultantEuclidean| |showSummary| |predicates| + |primeFrobenius| |gensym| |e01baf| |upperBound| |polynomialZeros| + |e02def| |numericIfCan| |nodeOf?| |semiSubResultantGcdEuclidean2| + |rules| |units| |mainCoefficients| |inrootof| |redPo| + |getVariableOrder| |top| |ocf2ocdf| |randnum| + |rewriteIdealWithQuasiMonicGenerators| |listOfLists| |setImagSteps| + |showAttributes| |separate| |f07adf| |externalList| |any?| |continue| + |trace2PowMod| |indicialEquation| |flagFactor| |rationalFunction| + |rightCharacteristicPolynomial| |extensionDegree| |leadingIdeal| + |lprop| |rootDirectory| |deepExpand| |hasoln| |lazyIrreducibleFactors| + |subCase?| |setright!| |members| |changeMeasure| |prem| |name| |cCsc| + |unknown| |numFunEvals3D| |cycleSplit!| |getMeasure| |closeComponent| + |summation| |getProperties| |comment| |f01bsf| |body| + |setVariableOrder| |tanh2trigh| |conjug| |clearTable!| + |reducedQPowers| |viewPosDefault| |code| |slex| + |constantToUnaryFunction| |makeCos| |expIfCan| |sparsityIF| |s15aef| + |subSet| |stopMusserTrials| |ricDsolve| |kroneckerDelta| |e04jaf| + |gcdPolynomial| |sinIfCan| |localReal?| |null| |newSubProgram| + |userOrdered?| |critT| |gcdPrimitive| |makeSUP| |box| |radicalSolve| + |derivative| |readLine!| |iomode| |delta| |not| EQ |colorFunction| + |complexLimit| |removeDuplicates!| |lowerCase| |elliptic| + |gcdcofactprim| |clipParametric| |sizeMultiplication| |UP2ifCan| |and| + |cCosh| |curryLeft| |euclideanSize| + |removeRoughlyRedundantFactorsInPols| |f04adf| |functorData| + |generate| |expenseOfEvaluationIF| |stronglyReduce| |coHeight| |or| + |makeSeries| |besselI| |UnVectorise| |prologue| |goodPoint| + |bitLength| |getZechTable| |internalSubPolSet?| |bfKeys| |totolex| + |xor| |se2rfi| |poisson| |even?| |assert| |leftMinimalPolynomial| + |genericRightMinimalPolynomial| |incrementBy| |port| |minColIndex| + |stoseInvertibleSetreg| |atoms| |pattern| |case| |orthonormalBasis| + |leastMonomial| |has?| |lineColorDefault| |c06gqf| |expand| |laguerre| + |printTypes| |complexNormalize| |postfix| |Zero| |complexEigenvalues| + |viewZoomDefault| |groebgen| |interpretString| |intChoose| |module| + |irCtor| |filterWhile| |withPredicates| |t| |cardinality| |One| |is?| + |removeSuperfluousQuasiComponents| |drawToScale| FG2F + |stoseLastSubResultant| |s13adf| |filterUntil| |OMencodingSGML| + |fractionPart| |host| |lambda| |nand| |printStatement| + |collectQuasiMonic| |topFortranOutputStack| |e02bcf| |commutative?| + |search| |select| |continuedFraction| |var1Steps| |cos2sec| + |triangular?| |message| |meshPar2Var| |laurentIfCan| |ode1| |adjoint| + |ode2| |find| |deepestInitial| |selectOptimizationRoutines| + |setfirst!| |multisect| |balancedFactorisation| |more?| + |OMlistSymbols| |univariatePolynomials| |completeEval| |modifyPoint| + |selectPolynomials| |recoverAfterFail| |roughEqualIdeals?| |nrows| + |setFormula!| |evenlambert| |readable?| |minrank| |integerIfCan| + |probablyZeroDim?| |eyeDistance| |FormatRoman| |ncols| |elt| + |writeBytes!| |removeSquaresIfCan| |deref| |cyclicEqual?| + |OMputEndBind| |symmetricSquare| |retract| |fixedPoints| |head| + |setClosed| |isAbsolutelyIrreducible?| |minRowIndex| |critB| |bumptab| + |dilog| |s13aaf| |e04gcf| |zero| |power| |clikeUniv| |inGroundField?| + |key?| |sech2cosh| |push!| |localIntegralBasis| |primlimintfrac| + |cons| |sin| |graphs| |makeRecord| |escape| |changeNameToObjf| + |toseSquareFreePart| |computeCycleLength| |nothing| |Vectorise| |And| + |rightQuotient| |firstDenom| |cos| |f02xef| |lazyPseudoQuotient| + |useEisensteinCriterion?| |monomialIntPoly| |setOrder| + |functionIsOscillatory| |initiallyReduce| |coerceP| |minimumExponent| + |Or| |tan| |nor| |floor| |rowEchelonLocal| |aspFilename| |imagJ| + |constantOpIfCan| |fortranCarriageReturn| |hessian| |Not| |OMclose| + |cot| |lookupFunction| |maxdeg| |zeroVector| |pushup| + |selectNonFiniteRoutines| |fortranLinkerArgs| |univariatePolynomial| + |condition| |multiset| |cSinh| |sec| |physicalLength| |principal?| + |setProperties| |mainVariable| |generateIrredPoly| + |setScreenResolution| |collect| |jokerMode| |csc| |logical?| |sincos| + |basisOfMiddleNucleus| |critBonD| |integralDerivationMatrix| + |palgextint| |factorOfDegree| |interpret| + |zeroSetSplitIntoTriangularSystems| |source| |RemainderList| |asin| + |startStats!| |pascalTriangle| |findBinding| |complement| |prinshINFO| + |atom?| |vedf2vef| |reducedDiscriminant| |randomLC| |dec| |acos| + |unitNormal| |numberOfComposites| |entries| |double?| |scalarMatrix| + |balancedBinaryTree| |computeInt| |atan| |plusInfinity| + |subresultantSequence| |f04mbf| |singleFactorBound| |bit?| |capacity| + |s21baf| |external?| |readBytes!| |acot| |minusInfinity| |red| + |isAtom| |char| |rst| |s17dgf| |leftDivide| |setref| + |ScanFloatIgnoreSpacesIfCan| |asec| |wreath| |orbit| + |degreeSubResultantEuclidean| |singular?| |ksec| + |linearAssociatedOrder| |selectMultiDimensionalRoutines| + |primaryDecomp| |acsc| |target| |minimize| |OMputError| |perfectSqrt| + |d02raf| |e01daf| |OMputBVar| |sub| |sinh| |basisOfCommutingElements| + |setIntersection| |rationalApproximation| |pquo| |splitLinear| + |totalGroebner| F2FG |diagonalProduct| |frobenius| |cosh| + |SturmHabichtCoefficients| |printingInfo?| |decimal| |content| + |extendedResultant| |solveLinearlyOverQ| |inspect| |c06fqf| |type| + |OMmakeConn| |tanh| |setLabelValue| |jordanAlgebra?| |bitTruth| + |padicallyExpand| |outputList| |rowEchLocal| |cycleEntry| |PDESolve| + |nonQsign| |inconsistent?| |coth| |basis| |newTypeLists| |palgextint0| + |discriminant| |bringDown| |fixedPoint| |OMUnknownSymbol?| |status| + |float| |qelt| |sh| |digit| |addBadValue| |sech| |btwFact| + |HermiteIntegrate| |radicalEigenvector| |second| |qsetelt| |eof?| + |internalIntegrate| |reverse!| |sinhcosh| |nextItem| |insertRoot!| + |rightNorm| |csch| |nthRootIfCan| |monicRightFactorIfCan| |belong?| + |third| |mapCoef| |integralLastSubResultant| |remove!| |e02baf| + |xRange| |constantOperator| |unitNormalize| |asinh| + |hypergeometric0F1| |standardBasisOfCyclicSubmodule| |f02aef| |extend| + |complexZeros| |compile| |s21bdf| |OMgetEndAttr| + |nextLatticePermutation| |yRange| |lyndon?| |void| |OMputAttr| |acosh| + |constDsolve| |setAdaptive| |duplicates| |showTheSymbolTable| + |leftNorm| |d02kef| |getGraph| |cAtan| |zRange| |leftMult| |hexDigit?| + |modTree| |atanh| |outputSpacing| |e02agf| |sn| |nextSublist| + |insertBottom!| |map!| |color| |f01maf| |restorePrecision| |direction| + |pushucoef| |acoth| |factorSquareFreeByRecursion| |toseInvertibleSet| + |baseRDEsys| |sign| |qsetelt!| |acothIfCan| |lazyIntegrate| + |identitySquareMatrix| |exponential| |exponents| |linSolve| |asech| + |upperCase?| |abelianGroup| |patternVariable| |mesh| |omError| + |largest| |ip4Address| |squareFreePolynomial| |generalSqFr| + |createGenericMatrix| |getConstant| |regime| |iiacot| |quasiMonic?| + |differentialVariables| |f04asf| |updateStatus!| |create| GE |qqq| + |multiple| |hue| |getStream| |rischDEsys| |binding| |cAcosh| + |intcompBasis| |mathieu24| |simplifyExp| |nextPrime| GT + |nonSingularModel| |applyQuote| |parseString| |coerceL| |s17aef| + |Lazard| |mainContent| |pack!| |f04maf| |hasTopPredicate?| LE + |setlast!| |e02gaf| |zag| |eq?| |createPrimitivePoly| + |leftExtendedGcd| |expandTrigProducts| |predicate| |equality| + |degreeSubResultant| |difference| |powern| LT |acsch| |outputArgs| + |tubePoints| |f02wef| |tensorProduct| |graphStates| |isPower| + |findCycle| |ceiling| |curve?| |rootsOf| |LazardQuotient| + |mapMatrixIfCan| |mathieu23| |ruleset| |backOldPos| |minPol| + |numberOfPrimitivePoly| |unitsColorDefault| |hclf| |d02bhf| |bottom!| + |makeVariable| |subst| |badValues| |algSplitSimple| |bits| |qinterval| + |OMputFloat| |LyndonWordsList1| |shuffle| |relationsIdeal| |cycle| + |rightTrace| |c06ecf| |expandPower| |ratPoly| |removeConstantTerm| + |whileLoop| |nthExponent| |fortranLogical| |nthFractionalTerm| + |createNormalPoly| |deleteRoutine!| |represents| |leftExactQuotient| + |directory| |repeating| |rootSplit| |removeRedundantFactorsInPols| + |suchThat| |extractTop!| |sinh2csch| |makeUnit| |tree| |index| + |diophantineSystem| |shallowCopy| |LyndonCoordinates| |maxPoints3D| + |writeLine!| |primes| |adaptive| |cosh2sech| |subtractIfCan| + |OMgetEndObject| |An| |nlde| |implies| |ode| |initial| |simpson| + |radicalSimplify| |isEquiv| |atanhIfCan| |selectIntegrationRoutines| + |fintegrate| |sin?| |SturmHabicht| |applyRules| |packageCall| + |strongGenerators| |lepol| |internalZeroSetSplit| |mapUnivariateIfCan| + |prime| |node?| |lastSubResultant| |pair| |leftRankPolynomial| + |entry?| |numerators| |dimensions| |objects| + |solveLinearPolynomialEquation| |leftZero| |rightTrim| |mapUnivariate| + |monicLeftDivide| |bright| |getOperator| |areEquivalent?| + |complexElementary| |parameters| |regularRepresentation| |delay| + |push| |possiblyNewVariety?| |base| |bat1| |leftTrim| |f01rdf| + |characteristicPolynomial| |antisymmetric?| + |createNormalPrimitivePoly| |BumInSepFFE| |arg1| |normDeriv2| + |subNode?| |trueEqual| |Frobenius| |cyclotomicDecomposition| + |hermiteH| |invertibleElseSplit?| |removeZero| |eval| |doubleDisc| + |dequeue!| |arg2| |iiacsch| |adaptive?| |lexico| |OMputEndBVar| + |iicos| |integralCoordinates| |checkRur| |midpoints| |cPower| |light| + |doubleComplex?| |LagrangeInterpolation| |BasicMethod| |anticoord| + |mathieu12| |atrapezoidal| |reindex| |f04jgf| |inR?| |generators| + |conditions| |curve| |henselFact| |pdf2ef| |OMreceive| |e04naf| + |basisOfRightAnnihilator| |algebraicOf| |error| |hasHi| |alternating| + |meshPar1Var| |binary| |match| |generic| |startTableInvSet!| + |putProperty| |dihedralGroup| |front| |halfExtendedSubResultantGcd2| + |setchildren!| |coefficient| |equation| |setProperty| |updatF| + |d01bbf| |square?| |headReduced?| |Ci| |part?| |myDegree| + |partialNumerators| |associatorDependence| |nthExpon| + |sortConstraints| |zeroMatrix| |fi2df| |function| |numberOfComponents| + |radicalEigenvectors| |makeYoungTableau| |exprHasWeightCosWXorSinWX| + |optimize| |stiffnessAndStabilityOfODEIF| |startTable!| |symFunc| + |nextsousResultant2| |imagI| |finiteBasis| |OMputBind| |contract| + |diag| |mainVariables| |dominantTerm| |measure2Result| |OMReadError?| + |problemPoints| |OMlistCDs| |e04fdf| |writeUInt8!| |bivariate?| + |lazyPquo| |exactQuotient| BY |support| |internalDecompose| + |repeating?| |createIrreduciblePoly| |defineProperty| |empty?| + |transcendenceDegree| |dflist| |radicalRoots| |hostPlatform| |qroot| + |cExp| |blue| |horizConcat| |listRepresentation| |tanQ| + |clearTheFTable| |rightAlternative?| |leftLcm| |elliptic?| + |elaboration| |compBound| |quotedOperators| |eigenMatrix| + |listYoungTableaus| |s18def| |quadratic| |addmod| |lazyGintegrate| + |isExpt| |genericLeftTrace| |in?| |replace| |ODESolve| + |changeWeightLevel| |doubleRank| |setleft!| |sort| |iterationVar| + |medialSet| |refine| |matrixDimensions| |normalDeriv| |modularFactor| + |realElementary| |extractIfCan| |s13acf| |sin2csc| |Nul| + |doubleFloatFormat| |iprint| |rem| |generic?| |littleEndian| + |binaryFunction| |removeDuplicates| |subTriSet?| |properties| + |var2Steps| |denominator| |expPot| |semiResultantEuclidean1| + |stoseSquareFreePart| |inRadical?| |quo| |multiEuclidean| |diff| + |removeRoughlyRedundantFactorsInContents| |tab| |id| |spherical| NOT + |cSin| |showClipRegion| |translate| |totalDegree| |trunc| + |OMsetEncoding| |extension| |univariatePolynomialsGcds| |bag| + |quasiComponent| |lo| |groebnerIdeal| OR |s18dcf| |random| + |associates?| |trim| |infinityNorm| |e01bff| |div| |quoted?| + |rational| |simplifyPower| |linearDependenceOverZ| + |subscriptedVariables| AND |clearTheIFTable| |controlPanel| |lcm| + |bivariateSLPEBR| |putGraph| |dAndcExp| |exquo| |iExquo| |delete| + |cycleElt| |coerceListOfPairs| |OMencodingUnknown| |sts2stst| |iicsc| + |pseudoDivide| |powerSum| |ScanArabic| ~= |c06gcf| |janko2| |redPol| + |noKaratsuba| |lift| |sumOfSquares| |createZechTable| |s17agf| + |euclideanNormalForm| |append| |arity| |prepareSubResAlgo| |#| + |f02agf| |f07aef| |f01ref| |printHeader| |reduce| |polarCoordinates| + |unitCanonical| |leadingCoefficientRicDE| |laguerreL| |gcd| + |plotPolar| |substitute| ~ |infix| |createThreeSpace| |nullity| + |factorSquareFree| |OMserve| |false| |buildSyntax| |characteristic| + |integer?| |polyRicDE| |complexForm| |iicosh| |dmpToP| + |rationalPoint?| |limit| |number?| |irDef| |LowTriBddDenomInv| + |KrullNumber| |factorGroebnerBasis| |axesColorDefault| |apply| + |exptMod| |wronskianMatrix| |minus!| |complete| |lyndonIfCan| + |internal?| |groebSolve| |eigenvalues| |normalizeAtInfinity| |/\\| + |optional?| |matrix| |first| |sylvesterMatrix| |insertMatch| + |oneDimensionalArray| |sayLength| |f01qdf| |getOperands| + |transcendentalDecompose| |intPatternMatch| |\\/| |rest| |vark| |axes| + |generalizedEigenvector| |low| |lp| |cylindrical| |elRow2!| + |lexTriangular| |indicialEquationAtInfinity| |algebraicCoefficients?| + |returnType!| |OMsupportsCD?| |tanIfCan| |palgint| + |componentUpperBound| |coerce| * |drawComplexVectorField| |asechIfCan| + |stirling1| |OMputSymbol| |musserTrials| |elColumn2!| + |cyclotomicFactorization| |coleman| |LiePoly| + |removeRoughlyRedundantFactorsInPol| |construct| |bernoulliB| |queue| + |unrankImproperPartitions1| |numerator| |pile| |divide| + |genericRightNorm| |numer| |stronglyReduced?| |ref| |pointSizeDefault| + |generator| |setScreenResolution3D| |indiceSubResultant| |iiexp| + |addiag| |complementaryBasis| |denom| |concat!| |branchPoint?| |ideal| + |swap!| = |isOpen?| |Gamma| |iitanh| |shade| |squareFreePart| + |readUInt32!| |algintegrate| |distFact| |dimension| |palgRDE| |fmecg| + |iisqrt3| |elRow1!| |exists?| |viewSizeDefault| |univcase| |c06gbf| + |pi| |byte| |convergents| |normalizedDivide| |e02bbf| < |youngGroup| + |leadingTerm| |quoByVar| |elaborate| |wrregime| |rangeIsFinite| + |width| |c06fpf| |secIfCan| |categoryMode| > |wholeRagits| + |subResultantGcd| |numberOfMonomials| |stoseInvertible?sqfreg| + |tablePow| |coordinate| |setLength!| |genericRightTraceForm| + |invertible?| <= |integral| UTS2UP |integral?| + |inverseIntegralMatrixAtInfinity| |nil?| |asinhIfCan| |mindegTerm| + |radicalOfLeftTraceForm| |linearMatrix| |nextNormalPoly| |jacobi| >= + |plot| |mesh?| |scalarTypeOf| |LyndonWordsList| |hdmpToP| + |swapColumns!| |presuper| |pdf2df| |fortranComplex| |bytes| + |leadingIndex| |cAcsch| |fullDisplay| |solveInField| |llprop| + |contours| |generalLambert| |forLoop| |rightDiscriminant| + |outputAsScript| |vconcat| |calcRanges| |symbol?| |rightPower| |iitan| + |choosemon| |stoseInvertible?reg| |explicitlyFinite?| + |supDimElseRittWu?| |tan2trig| |expint| + |currentScope| |hermite| + |pToDmp| |distribute| |value| |setMinPoints| |clearCache| |mat| + |var1StepsDefault| |primitive?| |numeric| |getProperty| |int| + |encodingDirectory| |conditionP| - |contractSolve| |disjunction| + |basisOfRightNucloid| |selectODEIVPRoutines| |lSpaceBasis| + |coefChoose| |bipolar| |radical| |moduleSum| |optional| |cAsec| + |bumprow| / |legendreP| |whatInfinity| |invmod| |deriv| |terms| + |showTheIFTable| |setTex!| |arrayStack| |component| |log| + |lfextendedint| |gderiv| |bivariatePolynomials| |setMinPoints3D| + |iiGamma| |changeVar| |jordanAdmissible?| |isMult| |s19abf| |elements| + |indicialEquations| |redmat| |setPosition| |antiCommutative?| + |rationalPower| RF2UTS |subResultantChain| |makeViewport3D| + |signature| |numberOfDivisors| |argumentList!| |setelt| |localUnquote| + |univariateSolve| |cot2trig| |exponent| |moebius| |debug3D| + |functionIsContinuousAtEndPoints| |getDatabase| |leftRecip| + |normalized?| |size?| |OMgetAtp| |getlo| |declare!| |f01brf| + |divergence| |float?| |dn| |bandedJacobian| |c06frf| |f02aaf| |copy| + |pleskenSplit| |rotate| |fortranInteger| |mainVariable?| |dictionary| + |adaptive3D?| |droot| |getMatch| |lfintegrate| |csc2sin| |exprex| + |f04qaf| |tanintegrate| |nativeModuleExtension| |primintfldpoly| + |headReduce| |style| |measure| |datalist| |cAcoth| |enterInCache| + |getBadValues| |mapSolve| |degreePartition| |negative?| |schwerpunkt| + |d02gbf| |pointLists| |setCondition!| |oblateSpheroidal| + |getButtonValue| |kovacic| |zeroDimPrime?| |cot2tan| |minimumDegree| + |makeViewport2D| |gbasis| |OMreadFile| |alphabetic?| |tubePlot| + |options| |commaSeparate| |getIdentifier| |OMcloseConn| |trapezoidal| + |completeEchelonBasis| |outputFixed| |setOfMinN| |increasePrecision| + |twist| |setButtonValue| |semiSubResultantGcdEuclidean1| + |dualSignature| |univariate?| |bumptab1| |tanSum| |solveRetract| + |open?| |iiasec| |harmonic| |swap| |makeFR| |distdfact| |B1solve| + |approximants| |dark| |divideExponents| |segment| |validExponential| + |hcrf| |exponentialOrder| |s17acf| |reverseLex| |output| |string| + |associative?| |rename!| |swapRows!| |bat| |s19aaf| |bigEndian| + |maximumExponent| |rightFactorCandidate| |euler| |pToHdmp| + |UpTriBddDenomInv| |var2StepsDefault| |sizeLess?| |LiePolyIfCan| + |isOp| |conical| |monicModulo| |sample| |elaborateFile| |neglist| + |irForm| |outputMeasure| |selectsecond| |fillPascalTriangle| + |pointPlot| |mappingAst| |cond| |zeroDim?| |discreteLog| + |hostByteOrder| |showArrayValues| |signatureAst| |build| + |complexNumericIfCan| |d01gaf| |internalAugment| |parabolic| + |weierstrass| |s17ahf| |normal?| |newReduc| |Si| |Ei| |e02aef| + |palgintegrate| |separant| |euclideanGroebner| |d01amf| + |quasiRegular?| |evaluate| |tan2cot| |setPoly| |insert!| |rootBound| + |dmpToHdmp| |exQuo| |slash| |homogeneous?| |mpsode| |e02ahf| + |nextsubResultant2| |basisOfCenter| |seriesSolve| |factorials| + |removeCosSq| |root| |showScalarValues| |c05pbf| |goodnessOfFit| + |factorFraction| |derivationCoordinates| |numberOfIrreduciblePoly| + |f01qcf| |iiasinh| |explimitedint| |multinomial| |e02adf| |squareTop| + |remove| |graeffe| |weighted| |factors| |enqueue!| |solveid| + |fibonacci| |bitCoef| |resultant| |monicDivide| |minPoints3D| + |stoseInvertibleSetsqfreg| |outputFloating| |exprToGenUPS| + |limitedint| |screenResolution3D| |setDifference| |quatern| |reseed| + |stopTableGcd!| |gethi| |truncate| |center| |last| |factorPolynomial| + |empty| |mergeFactors| |jacobiIdentity?| |sumSquares| |isOr| + |polyPart| |integrate| |assoc| |setnext!| |rectangularMatrix| + |besselY| |reduceByQuasiMonic| |setLegalFortranSourceExtensions| + |idealiserMatrix| |thetaCoord| |stoseIntegralLastSubResultant| + |maxRowIndex| |addPoint| |formula| |setleaves!| + |stiffnessAndStabilityFactor| |lieAdmissible?| |OMgetEndApp| + |compound?| |imports| |round| |coth2tanh| |setprevious!| |anfactor| + |hasSolution?| |e01sef| |sturmSequence| |lazyPseudoDivide| |rquo| + |setrest!| |dimensionsOf| |f01mcf| |tubeRadiusDefault| |pol| + |rightDivide| |alphabetic| |shanksDiscLogAlgorithm| + |internalSubQuasiComponent?| |imagi| |permutationGroup| + |palginfieldint| |lowerBound| |lookup| |minset| |palglimint| + |totalfract| |rightMult| |constantLeft| |positiveRemainder| + |getGoodPrime| |assign| |setsubMatrix!| |createMultiplicationMatrix| + |imagK| |sdf2lst| |romberg| |element?| |mulmod| |symmetric?| + |create3Space| |cotIfCan| |moebiusMu| |rootRadius| |merge| + |eisensteinIrreducible?| |rewriteIdealWithHeadRemainder| |expt| + |positive?| |cycles| |limitPlus| |Hausdorff| |OMopenString| + |perfectNthRoot| |leftQuotient| |divisors| |mapdiv| |varselect| |Beta| + |OMopenFile| |squareMatrix| |viewport3D| |taylorIfCan| + |rightExtendedGcd| |charthRoot| |alphanumeric?| |s01eaf| |dual| + |colorDef| |minIndex| |totalLex| |biRank| |universe| |stirling2| + |sylvesterSequence| |leastPower| |PollardSmallFactor| |ratDenom| + |invmultisect| |shallowExpand| |OMgetFloat| |currentSubProgram| + |zerosOf| |nextNormalPrimitivePoly| |bubbleSort!| |d02ejf| |uniform| + |domainTemplate| |legendre| |every?| |addMatchRestricted| |notelem| + |mainKernel| |flexible?| |heap| |semicolonSeparate| + |removeSuperfluousCases| |socf2socdf| |dfRange| |badNum| + |pointColorDefault| |setStatus| |trailingCoefficient| + |createMultiplicationTable| |fprindINFO| |scan| |divisor| |f02fjf| + |basisOfNucleus| |s18aef| |high| |showTheRoutinesTable| + |viewDeltaXDefault| |resultantEuclidean| |bracket| |iicot| |mdeg| + |separateFactors| |reduceLODE| |power!| |branchIfCan| + |showAllElements| |e02dcf| |leaves| |unvectorise| |decrease| + |resultantReduitEuclidean| |factorList| |removeSinSq| |typeLists| + |showRegion| |genericLeftMinimalPolynomial| |setEpilogue!| + |setPrologue!| |s17dcf| |nil| |f07fef| |algebraicSort| |critM| + |e01sbf| |macroExpand| |inputOutputBinaryFile| |schema| |noValueMode| + |algebraic?| |comparison| |vspace| |LyndonBasis| |decomposeFunc| + |eulerE| |allRootsOf| |rightUnit| |upperCase!| |putProperties| + |removeRedundantFactors| |partition| |singularitiesOf| |unaryFunction| + |null?| |OMsend| |point?| |limitedIntegrate| |rename| |linkToFortran| + |alphanumeric| |approximate| |absolutelyIrreducible?| |nthRoot| + |principalAncestors| |insertTop!| |printInfo!| |ldf2lst| |cAsech| + |byteBuffer| |cCot| |sum| |complex| |uncouplingMatrices| |reopen!| + |lflimitedint| |stFuncN| |clearFortranOutputStack| |tab1| |resize| + |nthr| |partialDenominators| |primextendedint| |order| |countable?| + |variationOfParameters| |shrinkable| |closed| |setValue!| + |normalizeIfCan| |exprHasAlgebraicWeight| |leftTrace| + |primitiveElement| |Is| |rank| |bfEntry| |e02ddf| |acosIfCan| + |realRoots| |messagePrint| |roughBase?| |point| |retractable?| + |enterPointData| |cn| |OMputInteger| |innerSolve| |linearDependence| + |debug| |moreAlgebraic?| |palgint0| |failed| |innerint| + |rationalIfCan| |associatedEquations| |imagE| |degree| |headRemainder| + |leadingBasisTerm| |s18acf| D |parametersOf| |SturmHabichtSequence| + |makeSketch| |numberOfHues| |resetAttributeButtons| |scaleRoots| + |discriminantEuclidean| |quickSort| |inverse| |startPolynomial| + |freeOf?| |acotIfCan| |series| |cAcos| |rightRemainder| |palgLODE| + |curveColor| |bounds| |createPrimitiveElement| |readUInt8!| + |extractBottom!| |modularGcd| |reduction| |padecf| |f07fdf| + |someBasis| |chebyshevT| |getMultiplicationTable| |vectorise| + |setMaxPoints| |distance| |ddFact| |conjugate| |htrigs| |iiacosh| + |useEisensteinCriterion| |primitivePart| |charClass| |iflist2Result| + |fixedDivisor| |super| |resetVariableOrder| |lists| + |innerEigenvectors| |connectTo| |infieldIntegrate| |solid?| |iiasin| + |npcoef| |min| |cup| |pastel| |OMgetEndAtp| |firstUncouplingMatrix| + |aCubic| GF2FG |squareFreeLexTriangular| |setelt!| |cyclicSubmodule| + |printInfo| |categoryFrame| |infiniteProduct| |OMbindTCP| + |constantKernel| |linearlyDependent?| |roughBasicSet| + |factorSquareFreePolynomial| |binomThmExpt| |ReduceOrder| |setColumn!| + |increase| |zeroSetSplit| |multiple?| |replaceKthElement| + |leftRegularRepresentation| |checkPrecision| |acoshIfCan| |prinb| + |removeZeroes| |lazy?| |substring?| |s17def| |key| |constantIfCan| + |computeBasis| |getCode| |listOfMonoms| |polygon?| |qualifier| + |numberOfNormalPoly| |superHeight| |orbits| |presub| |graphState| + |subscript| |leader| |reducedContinuedFraction| + |numberOfImproperPartitions| |nextPrimitivePoly| |symmetricPower| + |suffix?| |parent| |filename| |removeIrreducibleRedundantFactors| + |primextintfrac| |scanOneDimSubspaces| |decreasePrecision| |e02bdf| + |f2df| |genericLeftNorm| |iisin| |tube| |symbolTable| + |loadNativeModule| |nthCoef| |iiasech| |explicitlyEmpty?| |e04ucf| + |reducedForm| |s17aff| |rk4a| |check| |prefix?| |selectOrPolynomials| + |viewDefaults| |parse| |complexSolve| |cross| |separateDegrees| + |mkIntegral| |fortran| |simpleBounds?| |shellSort| |d01alf| + |cosSinInfo| |plus| |roughUnitIdeal?| |pushFortranOutputStack| + |e04mbf| |elementary| |const| |elseBranch| |mapDown!| |cLog| |copy!| + |nonLinearPart| |unrankImproperPartitions0| |popFortranOutputStack| + |firstNumer| |copies| |d03edf| |modularGcdPrimitive| |partialFraction| + |bothWays| |wholeRadix| |exprToUPS| |cCsch| |outputAsFortran| + |denominators| |df2ef| |symbolTableOf| |minPoly| |linearAssociatedLog| + |ignore?| |initiallyReduced?| |pmintegrate| |trapezoidalo| |table| + |contains?| |createLowComplexityNormalBasis| |stoseInvertible?| + |s17akf| |totalDifferential| |leadingSupport| |OMreadStr| |precision| + |maxrow| |times| |getSyntaxFormsFromFile| |new| |removeCoshSq| + |cscIfCan| |viewWriteDefault| |mathieu22| + |generalizedContinuumHypothesisAssumed?| |drawComplex| |polyred| + |argumentListOf| |f02axf| |infix?| |ptree| |e04dgf| + |solveLinearPolynomialEquationByFractions| |pseudoQuotient| |roman| + |edf2efi| |virtualDegree| |flatten| |appendPoint| + |semiResultantEuclideannaif| |mask| |OMgetType| |upDateBranches| + |sequence| |jacobian| |s18adf| |init| |cfirst| |integralRepresents| + |xCoord| |interpolate| |extractIndex| |numberOfCycles| |range| + |OMputEndError| |linGenPos| |extract!| |matrixConcat3D| |systemSizeIF| + |trigs| |shiftLeft| |monom| |reorder| |partialQuotients| |increment| + |clearDenominator| |groebnerFactorize| |OMsupportsSymbol?| |readByte!| + |rootOf| |nextSubsetGray| |rule| |cAsin| |clipWithRanges| |leftFactor| + |figureUnits| |karatsubaDivide| |eigenvectors| |asimpson| |f02ajf| + |isPlus| |simpsono| |reciprocalPolynomial| |position!| |rubiksGroup| + |rightOne| |rightMinimalPolynomial| |purelyAlgebraic?| + |linearlyDependentOverZ?| |common| |traceMatrix| |companionBlocks| + |cAsinh| |voidMode| |rational?| |script| |normalElement| + |antisymmetricTensors| |createRandomElement| |coord| + |mainPrimitivePart| |rur| |expintfldpoly| |writeByte!| |monomRDEsys| + |dimensionOfIrreducibleRepresentation| |title| |ratpart| |perspective| + |polCase| |factorset| |mirror| |denomRicDE| |baseRDE| |taylorRep| + |resultantEuclideannaif| |sorted?| |compdegd| |rspace| |acschIfCan| + |left| |vector| |OMputString| |pow| |numericalOptimization| + |generalizedInverse| |tex| |signAround| |outerProduct| |e01bgf| + |tanh2coth| |superscript| |infRittWu?| |right| |differentiate| + |coerceImages| |testDim| |integers| |f2st| |e| |iisec| |resetNew| + |monomialIntegrate| |minPoints| |unary?| |connect| |intersect| + |normInvertible?| |dmp2rfi| |factorsOfDegree| |squareFreePrim| + |augment| |curryRight| |sturmVariationsOf| |df2mf| |binomial| + |quotient| |fractRagits| |usingTable?| |psolve| |showTheFTable| + |coercePreimagesImages| |compose| |d01gbf| |factorSFBRlcUnit| + |infLex?| |cyclic?| |autoReduced?| |roughSubIdeal?| |logIfCan| + |rootSimp| |enumerate| |basicSet| |dot| |complexIntegrate| |f02awf| + |lllip| |closedCurve?| |leftUnit| |ord| |rationalPoints| |mkcomm| + |OMwrite| |aromberg| |ramifiedAtInfinity?| |tableau| + |parabolicCylindrical| |rischNormalize| |shift| |tubeRadius| |scopes| + |abs| |product| |any| |highCommonTerms| |hash| |exportedOperators| + |errorKind| |d03faf| |environment| |logGamma| |leftUnits| |singRicDE| + |interReduce| |count| |failed?| |computePowers| |d02bbf| + |noLinearFactor?| |next| |commutator| |makeFloatFunction| |e02dff| + |SFunction| |stosePrepareSubResAlgo| |rk4f| |binarySearchTree| + |pointColor| |integralBasisAtInfinity| |coerceS| |integralAtInfinity?| + |multiplyExponents| |leftGcd| |isImplies| |wordInGenerators| |elem?| + |hitherPlane| |leastAffineMultiple| |bezoutResultant| |resetBadValues| + |bipolarCylindrical| |cTanh| |getRef| |prime?| |symbol| |df2st| + |genus| |karatsuba| |conditionsForIdempotents| + |integralMatrixAtInfinity| |perfectSquare?| |extractSplittingLeaf| + |solve| |setFieldInfo| |minimalPolynomial| |expression| |read!| + |fortranLiteralLine| |zeroDimPrimary?| |OMconnInDevice| |Lazard2| + |iifact| |rowEch| |interval| |approxSqrt| |integer| |critpOrder| + |weights| |lambert| |rightUnits| |putColorInfo| |d02cjf| |cdr| + |linear| |findConstructor| |associator| |useSingleFactorBound?| + |readInt8!| |mapExpon| |thenBranch| |OMputEndAtp| |zeroOf| |octon| + |rootProduct| |makeprod| |lyndon| |xn| |logpart| |subPolSet?| + |alternative?| |overlabel| |rischDE| |polynomial| |binaryTournament| + |rCoord| |FormatArabic| |irreducibleRepresentation| |cyclicParents| + |transpose| |randomR| |leftAlternative?| |copyInto!| |laplacian| + |outputAsTex| |fractRadix| |log2| |routines| |oddlambert| |erf| + |clearTheSymbolTable| |result| |radicalEigenvalues| |oddintegers| + |write!| |diagonal?| |useNagFunctions| |iibinom| |leftDiscriminant| + |li| |triangulate| |bandedHessian| |nsqfree| |redpps| |fTable| + |algDsolve| |firstSubsetGray| |integerBound| |central?| |c06fuf| + |stack| |bindings| |minGbasis| |lquo| |tower| |before?| + |primintegrate| |toScale| |characteristicSet| |pop!| |digits| + |quasiMonicPolynomials| |positiveSolve| |quotientByP| |patternMatch| + |internalIntegrate0| |extendedIntegrate| |plenaryPower| |topPredicate| + |lowerPolynomial| |identity| |f04arf| |recolor| |compiledFunction| + |subQuasiComponent?| |block| |setAdaptive3D| |particularSolution| + |sumOfKthPowerDivisors| |d01akf| |eq| |expressIdealMember| + |permutations| |aQuartic| |unit| |antiCommutator| |rotate!| + |outputBinaryFile| |radPoly| |sizePascalTriangle| |iter| |f04faf| + |dim| |region| |setErrorBound| |length| |divisorCascade| |palgLODE0| + |mindeg| |endSubProgram| |pushuconst| |complexNumeric| + |resultantReduit| |simplifyLog| |outlineRender| |fortranCharacter| + |LazardQuotient2| |step| |scripts| |leftRemainder| |prefixRagits| + |quasiRegular| |purelyAlgebraicLeadingMonomial?| |irreducible?| + |aLinear| |knownInfBasis| |frst| |irreducibleFactor| |concat| + |coshIfCan| |member?| |subNodeOf?| |numberOfOperations| |groebner| + |test| |kernels| |sort!| |numberOfComputedEntries| |argument| |solve1| + |palglimint0| |endOfFile?| |wholePart| |OMconnOutDevice| |ListOfTerms| + |upperCase| |operator| |denomLODE| |multiplyCoefficients| |rdregime| + |leftOne| |fortranLiteral| |epilogue| |readIfCan!| |mkAnswer| + |permutation| |asinIfCan| |lazyPseudoRemainder| |car| |children| + |nextPrimitiveNormalPoly| |definingInequation| |karatsubaOnce| + |cRationalPower| |mix| |leftCharacteristicPolynomial| |viewPhiDefault| + |prindINFO| |perfectNthPower?| |univariate| |bombieriNorm| + |nextIrreduciblePoly| |gramschmidt| |diagonals| |currentCategoryFrame| + |intensity| |rootNormalize| |ratDsolve| |pade| |lfunc| |c06ekf| |kmax| + |possiblyInfinite?| |generalizedContinuumHypothesisAssumed| + |finiteBound| |pole?| |tValues| |argscript| |recur| |writeInt8!| + |isList| |closedCurve| |rotatey| |prefix| |c06ebf| |hex| + |setPredicates| |iiperm| |factor| |returnTypeOf| |weakBiRank| + |setUnion| |birth| |eulerPhi| |child?| |OMunhandledSymbol| + |wordsForStrongGenerators| |ridHack1| |sqrt| |quadratic?| |s17dhf| + |ParCondList| |lexGroebner| |factorByRecursion| |rotatex| + |createNormalElement| |multMonom| |leviCivitaSymbol| |qfactor| |real| + |rightFactorIfCan| |rootPoly| |one?| |symmetricRemainder| + |completeHensel| |interactiveEnv| |OMgetEndBVar| |commonDenominator| + |printCode| |extendIfCan| |imag| |declare| |semiDiscriminantEuclidean| + |bernoulli| |squareFreeFactors| |alternatingGroup| |stop| |mvar| + |singularAtInfinity?| |iilog| |countRealRootsMultiple| + |halfExtendedResultant2| |drawCurves| |directProduct| |f02abf| + |lifting1| |yCoord| |scale| |maxint| |mr| |errorInfo| |countRealRoots| + |consnewpol| |OMconnectTCP| |list?| |evaluateInverse| + |mainDefiningPolynomial| |intermediateResultsIF| |top!| |critMTonD1| + |e04ycf| |idealiser| SEGMENT |rootOfIrreduciblePoly| |numFunEvals| + |brace| |kind| |linearPolynomials| |mapBivariate| |s19adf| |nary?| + |satisfy?| |curveColorPalette| |cothIfCan| |e02ajf| |compactFraction| + |antiAssociative?| |categories| |destruct| |f02adf| |closed?| |op| + |child| |newLine| |pointColorPalette| |raisePolynomial| |mantissa| + |s21bbf| |processTemplate| |depth| |innerSolve1| |atanIfCan| + |whitePoint| |hMonic| |unmakeSUP| |critMonD1| |corrPoly| |typeForm| + |symmetricDifference| |mapExponents| |s14aaf| |readUInt16!| + |getExplanations| |quasiAlgebraicSet| |leftPower| |generalTwoFactor| + |f01qef| |patternMatchTimes| |s20acf| |level| |nthFlag| |stFunc1| + |beauzamyBound| |mainMonomials| |semiResultantReduitEuclidean| + |e01bef| |extractPoint| |basisOfRightNucleus| |recip| + |OMencodingBinary| |lieAlgebra?| |isNot| |unknownEndian| |phiCoord| + |monomial| |iisinh| |iicoth| |edf2ef| |space| |df2fi| |mainForm| + |s21bcf| |partitions| |fortranDoubleComplex| |unparse| |multivariate| + |directSum| |root?| |drawStyle| |d03eef| |middle| |fortranTypeOf| + |cTan| |pseudoRemainder| |screenResolution| |merge!| |variables| + |iiatanh| |primitivePart!| |union| |monicDecomposeIfCan| |rightZero| + |relerror| |zCoord| |nullary?| |mapGen| |tanhIfCan| |youngDiagram| + |iisqrt2| |isConnected?| |imagk| |leftScalarTimes!| |mapmult| + |integralBasis| |tryFunctionalDecomposition?| |setStatus!| |ldf2vmf| + |gcdprim| |overlap| |generalPosition| |composite| |hyperelliptic| + |identityMatrix| |palgRDE0| |inf| |definingPolynomial| |max| + |startTableGcd!| |submod| |sncndn| |deepestTail| |delete!| |cschIfCan| + |constantCoefficientRicDE| |po| |cycleRagits| |subMatrix| LODO2FUN + |f04mcf| |getOrder| |viewWriteAvailable| |pmComplexintegrate| + |OMUnknownCD?| |magnitude| |mkPrim| |seed| |subHeight| |diagonal| + |taylor| |factorAndSplit| |genericLeftTraceForm| |cAcsc| |comp| + |completeSmith| |OMgetApp| |lazyPrem| |c05adf| |OMgetEndBind| + |factorial| |principalIdeal| |laurent| |s14baf| |lazyVariations| + |isAnd| |repeatUntilLoop| |string?| |s20adf| |ScanFloatIgnoreSpaces| + |OMread| |back| |geometric| |reverse| |puiseux| |tubePointsDefault| + |noncommutativeJordanAlgebra?| |OMgetVariable| |reflect| + |splitDenominator| |integralMatrix| |setvalue!| + |rewriteSetWithReduction| |iiacos| |rightRankPolynomial| + |explogs2trigs| |rightRegularRepresentation| |mainMonomial| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index f78a1329..20c9d342 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5419 +1,5424 @@ -(3235829 . 3485733166) -((-4331 (((-112) (-1 (-112) |#2| |#2|) $) 86) (((-112) $) NIL)) (-3565 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3134 ((|#2| $ (-574) |#2|) NIL) ((|#2| $ (-1250 (-574)) |#2|) 44)) (-2163 (($ $) 80)) (-2881 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-417 (-574))) |has| |#1| (-38 (-417 (-574)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2833 (|has| |#1| (-923)) (|has| |#1| (-566)) (|has| |#1| (-462))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-417 (-574)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2833 (|has| |#1| (-923)) (|has| |#1| (-566)) (|has| |#1| (-462)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-626 #0#) -2833 (|has| |#1| (-1054 (-417 (-574)))) (|has| |#1| (-38 (-417 (-574))))) ((-626 (-574)) . T) ((-626 |#1|) . T) ((-626 |#2|) . T) ((-626 |#3|) . T) ((-626 $) -2833 (|has| |#1| (-923)) (|has| |#1| (-566)) (|has| |#1| (-462))) ((-623 (-872)) . 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T) ((-1054 |#2|) . T) ((-1054 |#3|) . T) ((-1067 #0#) |has| |#1| (-38 (-417 (-574)))) ((-1067 |#1|) . T) ((-1067 $) -2833 (|has| |#1| (-923)) (|has| |#1| (-566)) (|has| |#1| (-462)) (|has| |#1| (-174))) ((-1072 #0#) |has| |#1| (-38 (-417 (-574)))) ((-1072 |#1|) . T) ((-1072 $) -2833 (|has| |#1| (-923)) (|has| |#1| (-566)) (|has| |#1| (-462)) (|has| |#1| (-174))) ((-1065) . T) ((-1074) . T) ((-1128) . T) ((-1116) . T) ((-1234) . 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T) ((-294 |#2| $) -12 (|has| |#1| (-372)) (|has| |#2| (-294 |#2| |#2|))) ((-294 $ $) |has| (-574) (-1127)) ((-298) -2832 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-315) |has| |#1| (-372)) ((-317 |#2|) -12 (|has| |#1| (-372)) (|has| |#2| (-317 |#2|))) ((-372) |has| |#1| (-372)) ((-347 |#2|) |has| |#1| (-372)) ((-386 |#2|) |has| |#1| (-372)) ((-410 |#2|) |has| |#1| (-372)) ((-462) |has| |#1| (-372)) ((-503) |has| |#1| (-38 (-417 (-574)))) ((-524 (-1192) |#2|) -12 (|has| |#1| (-372)) (|has| |#2| (-524 (-1192) |#2|))) ((-524 |#2| |#2|) -12 (|has| |#1| (-372)) (|has| |#2| (-317 |#2|))) ((-566) -2832 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-656 #1#) -2832 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-656 (-574)) . T) ((-656 |#1|) . T) ((-656 |#2|) |has| |#1| (-372)) ((-656 $) . T) ((-658 #1#) -2832 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-658 #3=(-574)) -12 (|has| |#1| (-372)) (|has| |#2| (-649 (-574)))) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-372)) ((-658 $) . T) ((-650 #1#) -2832 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-650 |#1|) |has| |#1| (-174)) ((-650 |#2|) |has| |#1| (-372)) ((-650 $) -2832 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-649 #3#) -12 (|has| |#1| (-372)) (|has| |#2| (-649 (-574)))) ((-649 |#2|) |has| |#1| (-372)) ((-727 #1#) -2832 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-727 |#1|) |has| |#1| (-174)) ((-727 |#2|) |has| |#1| (-372)) ((-727 $) -2832 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-736) . T) ((-801) -12 (|has| |#1| (-372)) (|has| |#2| (-830))) ((-802) -12 (|has| |#1| (-372)) (|has| |#2| (-830))) ((-804) -12 (|has| |#1| (-372)) (|has| |#2| (-830))) ((-805) -12 (|has| |#1| (-372)) (|has| |#2| (-830))) ((-830) -12 (|has| |#1| (-372)) (|has| |#2| (-830))) ((-858) -12 (|has| |#1| (-372)) (|has| |#2| (-830))) ((-860) -2832 (-12 (|has| |#1| (-372)) (|has| |#2| (-860))) (-12 (|has| |#1| (-372)) (|has| |#2| (-830)))) ((-913 (-1192)) -2832 (-12 (|has| |#1| (-372)) (|has| |#2| (-913 (-1192)))) (-12 (|has| |#1| (-15 * (|#1| (-574) |#1|))) (|has| |#1| (-913 (-1192))))) ((-897 (-388)) -12 (|has| |#1| (-372)) (|has| |#2| (-897 (-388)))) ((-897 (-574)) -12 (|has| |#1| (-372)) (|has| |#2| (-897 (-574)))) ((-895 |#2|) |has| |#1| (-372)) ((-922) -12 (|has| |#1| (-372)) (|has| |#2| (-922))) ((-988 |#1| #0# (-1097)) . 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NIL) (-1244 2973294 2973539 2973927 "ULSCCAT-" 2973932 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1243 2962534 2969016 2969059 "ULSCAT" 2969922 NIL ULSCAT (NIL T) -9 NIL 2970653 NIL) (-1242 2961964 2962043 2962222 "ULS2" 2962449 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1241 2961083 2961593 2961700 "UINT8" 2961811 T UINT8 (NIL) -8 NIL NIL 2961896) (-1240 2960201 2960711 2960818 "UINT64" 2960929 T UINT64 (NIL) -8 NIL NIL 2961014) (-1239 2959319 2959829 2959936 "UINT32" 2960047 T UINT32 (NIL) -8 NIL NIL 2960132) (-1238 2958437 2958947 2959054 "UINT16" 2959165 T UINT16 (NIL) -8 NIL NIL 2959250) (-1237 2956740 2957697 2957727 "UFD" 2957939 T UFD (NIL) -9 NIL 2958053 NIL) (-1236 2956534 2956580 2956675 "UFD-" 2956680 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1235 2955616 2955799 2956015 "UDVO" 2956340 T UDVO (NIL) -7 NIL NIL NIL) (-1234 2953432 2953841 2954312 "UDPO" 2955180 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1233 2953365 2953370 2953400 "TYPE" 2953405 T TYPE (NIL) -9 NIL NIL NIL) (-1232 2953125 2953320 2953351 "TYPEAST" 2953356 T TYPEAST (NIL) -8 NIL NIL NIL) (-1231 2952096 2952298 2952538 "TWOFACT" 2952919 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1230 2951119 2951505 2951740 "TUPLE" 2951896 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1229 2948810 2949329 2949868 "TUBETOOL" 2950602 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1228 2947659 2947864 2948105 "TUBE" 2948603 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1227 2942388 2946631 2946914 "TS" 2947411 NIL TS (NIL T) -8 NIL NIL NIL) (-1226 2931028 2935147 2935244 "TSETCAT" 2940513 NIL TSETCAT (NIL T T T T) -9 NIL 2942044 NIL) (-1225 2925760 2927360 2929251 "TSETCAT-" 2929256 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1224 2920399 2921246 2922175 "TRMANIP" 2924896 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1223 2919840 2919903 2920066 "TRIMAT" 2920331 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1222 2917706 2917943 2918300 "TRIGMNIP" 2919589 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1221 2917226 2917339 2917369 "TRIGCAT" 2917582 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1220 2916895 2916974 2917115 "TRIGCAT-" 2917120 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1219 2913740 2915753 2916034 "TREE" 2916649 NIL TREE (NIL T) -8 NIL NIL NIL) (-1218 2913014 2913542 2913572 "TRANFUN" 2913607 T TRANFUN (NIL) -9 NIL 2913673 NIL) (-1217 2912293 2912484 2912764 "TRANFUN-" 2912769 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1216 2912097 2912129 2912190 "TOPSP" 2912254 T TOPSP (NIL) -7 NIL NIL NIL) (-1215 2911445 2911560 2911714 "TOOLSIGN" 2911978 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1214 2910079 2910622 2910861 "TEXTFILE" 2911228 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1213 2907991 2908532 2908961 "TEX" 2909672 T TEX (NIL) -8 NIL NIL NIL) (-1212 2907772 2907803 2907875 "TEX1" 2907954 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1211 2907420 2907483 2907573 "TEMUTL" 2907704 T TEMUTL (NIL) -7 NIL NIL NIL) (-1210 2905574 2905854 2906179 "TBCMPPK" 2907143 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1209 2897351 2903734 2903790 "TBAGG" 2904190 NIL TBAGG (NIL T T) -9 NIL 2904401 NIL) (-1208 2892421 2893909 2895663 "TBAGG-" 2895668 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1207 2891805 2891912 2892057 "TANEXP" 2892310 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1206 2891316 2891580 2891670 "TALGOP" 2891750 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1205 2884706 2891173 2891266 "TABLE" 2891271 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1204 2884118 2884217 2884355 "TABLEAU" 2884603 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1203 2878726 2879946 2881194 "TABLBUMP" 2882904 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1202 2877948 2878095 2878276 "SYSTEM" 2878567 T SYSTEM (NIL) -8 NIL NIL NIL) (-1201 2874407 2875106 2875889 "SYSSOLP" 2877199 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1200 2874205 2874362 2874393 "SYSPTR" 2874398 T SYSPTR (NIL) -8 NIL NIL NIL) (-1199 2873241 2873746 2873865 "SYSNNI" 2874051 NIL SYSNNI (NIL NIL) -8 NIL NIL 2874136) (-1198 2872540 2872999 2873078 "SYSINT" 2873138 NIL SYSINT (NIL NIL) -8 NIL NIL 2873183) (-1197 2868872 2869818 2870528 "SYNTAX" 2871852 T SYNTAX (NIL) -8 NIL NIL NIL) (-1196 2866030 2866632 2867264 "SYMTAB" 2868262 T SYMTAB (NIL) -8 NIL NIL NIL) (-1195 2861279 2862181 2863164 "SYMS" 2865069 T SYMS (NIL) -8 NIL NIL NIL) (-1194 2858514 2860737 2860967 "SYMPOLY" 2861084 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1193 2858031 2858106 2858229 "SYMFUNC" 2858426 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1192 2854051 2855343 2856156 "SYMBOL" 2857240 T SYMBOL (NIL) -8 NIL NIL NIL) (-1191 2847590 2849279 2850999 "SWITCH" 2852353 T SWITCH (NIL) -8 NIL NIL NIL) (-1190 2840824 2846411 2846714 "SUTS" 2847345 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1189 2832890 2840071 2840344 "SUPXS" 2840609 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1188 2824560 2832508 2832634 "SUP" 2832799 NIL SUP (NIL T) -8 NIL NIL NIL) (-1187 2823719 2823846 2824063 "SUPFRACF" 2824428 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1186 2823340 2823399 2823512 "SUP2" 2823654 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1185 2821788 2822062 2822418 "SUMRF" 2823039 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1184 2821123 2821189 2821381 "SUMFS" 2821709 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1183 2804919 2820300 2820551 "SULS" 2820930 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2804521 2804741 2804811 "SUCHTAST" 2804871 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1181 2803816 2804046 2804186 "SUCH" 2804429 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1180 2797683 2798722 2799681 "SUBSPACE" 2802904 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1179 2797113 2797203 2797367 "SUBRESP" 2797571 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1178 2790481 2791778 2793089 "STTF" 2795849 NIL STTF (NIL T) -7 NIL NIL NIL) (-1177 2784654 2785774 2786921 "STTFNC" 2789381 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1176 2775967 2777836 2779630 "STTAYLOR" 2782895 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1175 2769097 2775831 2775914 "STRTBL" 2775919 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1174 2764461 2769052 2769083 "STRING" 2769088 T STRING (NIL) -8 NIL NIL NIL) (-1173 2759290 2763804 2763834 "STRICAT" 2763893 T STRICAT (NIL) -9 NIL 2763955 NIL) (-1172 2752043 2756909 2757520 "STREAM" 2758714 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1171 2751553 2751630 2751774 "STREAM3" 2751960 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1170 2750535 2750718 2750953 "STREAM2" 2751366 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1169 2750223 2750275 2750368 "STREAM1" 2750477 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1168 2749239 2749420 2749651 "STINPROD" 2750039 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1167 2748791 2749001 2749031 "STEP" 2749111 T STEP (NIL) -9 NIL 2749189 NIL) (-1166 2747978 2748280 2748428 "STEPAST" 2748665 T STEPAST (NIL) -8 NIL NIL NIL) (-1165 2741410 2747877 2747954 "STBL" 2747959 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1164 2736505 2740601 2740644 "STAGG" 2740797 NIL STAGG (NIL T) -9 NIL 2740886 NIL) (-1163 2734207 2734809 2735681 "STAGG-" 2735686 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1162 2732354 2733977 2734069 "STACK" 2734150 NIL STACK (NIL T) -8 NIL NIL NIL) (-1161 2725049 2730495 2730951 "SREGSET" 2731984 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1160 2717474 2718843 2720356 "SRDCMPK" 2723655 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1159 2710359 2714884 2714914 "SRAGG" 2716217 T SRAGG (NIL) -9 NIL 2716825 NIL) (-1158 2709376 2709631 2710010 "SRAGG-" 2710015 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1157 2703747 2708323 2708744 "SQMATRIX" 2709002 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1156 2697432 2700465 2701192 "SPLTREE" 2703092 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1155 2693395 2694088 2694734 "SPLNODE" 2696858 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1154 2692442 2692675 2692705 "SPFCAT" 2693149 T SPFCAT (NIL) -9 NIL NIL NIL) (-1153 2691179 2691389 2691653 "SPECOUT" 2692200 T SPECOUT (NIL) -7 NIL NIL NIL) (-1152 2682289 2684161 2684191 "SPADXPT" 2688867 T SPADXPT (NIL) -9 NIL 2691031 NIL) (-1151 2682050 2682090 2682159 "SPADPRSR" 2682242 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1150 2680099 2682005 2682036 "SPADAST" 2682041 T SPADAST (NIL) -8 NIL NIL NIL) (-1149 2672044 2673817 2673860 "SPACEC" 2678233 NIL SPACEC (NIL T) -9 NIL 2680049 NIL) (-1148 2670174 2671976 2672025 "SPACE3" 2672030 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1147 2668926 2669097 2669388 "SORTPAK" 2669979 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1146 2667018 2667321 2667733 "SOLVETRA" 2668590 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1145 2666068 2666290 2666551 "SOLVESER" 2666791 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1144 2661372 2662260 2663255 "SOLVERAD" 2665120 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1143 2657187 2657796 2658525 "SOLVEFOR" 2660739 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1142 2651457 2656536 2656633 "SNTSCAT" 2656638 NIL SNTSCAT (NIL T T T T) -9 NIL 2656708 NIL) (-1141 2645563 2649780 2650171 "SMTS" 2651147 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1140 2640159 2645451 2645528 "SMP" 2645533 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1139 2638318 2638619 2639017 "SMITH" 2639856 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1138 2630844 2635130 2635233 "SMATCAT" 2636584 NIL SMATCAT (NIL NIL T T T) -9 NIL 2637134 NIL) (-1137 2627562 2628447 2629705 "SMATCAT-" 2629710 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1136 2625228 2626798 2626841 "SKAGG" 2627102 NIL SKAGG (NIL T) -9 NIL 2627237 NIL) (-1135 2621504 2624701 2624885 "SINT" 2625037 T SINT (NIL) -8 NIL NIL 2625199) (-1134 2621276 2621314 2621380 "SIMPAN" 2621460 T SIMPAN (NIL) -7 NIL NIL NIL) (-1133 2620555 2620811 2620951 "SIG" 2621158 T SIG (NIL) -8 NIL NIL NIL) (-1132 2619393 2619614 2619889 "SIGNRF" 2620314 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1131 2618226 2618377 2618661 "SIGNEF" 2619222 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1130 2617532 2617809 2617933 "SIGAST" 2618124 T SIGAST (NIL) -8 NIL NIL NIL) (-1129 2615222 2615676 2616182 "SHP" 2617073 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1128 2609218 2615123 2615199 "SHDP" 2615204 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1127 2608791 2608983 2609013 "SGROUP" 2609106 T SGROUP (NIL) -9 NIL 2609168 NIL) (-1126 2608649 2608675 2608748 "SGROUP-" 2608753 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1125 2605440 2606138 2606861 "SGCF" 2607948 T SGCF (NIL) -7 NIL NIL NIL) (-1124 2599808 2604887 2604984 "SFRTCAT" 2604989 NIL SFRTCAT (NIL T T T T) -9 NIL 2605028 NIL) (-1123 2593229 2594247 2595383 "SFRGCD" 2598791 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1122 2586355 2587428 2588614 "SFQCMPK" 2592162 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1121 2585975 2586064 2586175 "SFORT" 2586296 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1120 2585093 2585815 2585936 "SEXOF" 2585941 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1119 2584200 2584974 2585042 "SEX" 2585047 T SEX (NIL) -8 NIL NIL NIL) (-1118 2579981 2580696 2580791 "SEXCAT" 2583413 NIL SEXCAT (NIL T T T T T) -9 NIL 2583973 NIL) (-1117 2577134 2579915 2579963 "SET" 2579968 NIL SET (NIL T) -8 NIL NIL NIL) (-1116 2575358 2575847 2576152 "SETMN" 2576875 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1115 2574854 2575006 2575036 "SETCAT" 2575212 T SETCAT (NIL) -9 NIL 2575322 NIL) (-1114 2574546 2574624 2574754 "SETCAT-" 2574759 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1113 2570907 2573007 2573050 "SETAGG" 2573920 NIL SETAGG (NIL T) -9 NIL 2574260 NIL) (-1112 2570365 2570481 2570718 "SETAGG-" 2570723 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1111 2569808 2570061 2570162 "SEQAST" 2570286 T SEQAST (NIL) -8 NIL NIL NIL) (-1110 2569007 2569301 2569362 "SEGXCAT" 2569648 NIL SEGXCAT (NIL T T) -9 NIL 2569768 NIL) (-1109 2568013 2568673 2568855 "SEG" 2568860 NIL SEG (NIL T) -8 NIL NIL NIL) (-1108 2566992 2567206 2567249 "SEGCAT" 2567771 NIL SEGCAT (NIL T) -9 NIL 2567992 NIL) (-1107 2565924 2566355 2566563 "SEGBIND" 2566819 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1106 2565545 2565604 2565717 "SEGBIND2" 2565859 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1105 2565118 2565346 2565423 "SEGAST" 2565490 T SEGAST (NIL) -8 NIL NIL NIL) (-1104 2564337 2564463 2564667 "SEG2" 2564962 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1103 2563708 2564272 2564319 "SDVAR" 2564324 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1102 2556146 2563478 2563608 "SDPOL" 2563613 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1101 2554739 2555005 2555324 "SCPKG" 2555861 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1100 2553903 2554075 2554267 "SCOPE" 2554569 T SCOPE (NIL) -8 NIL NIL NIL) (-1099 2553123 2553257 2553436 "SCACHE" 2553758 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1098 2552769 2552955 2552985 "SASTCAT" 2552990 T SASTCAT (NIL) -9 NIL 2553003 NIL) (-1097 2552256 2552604 2552680 "SAOS" 2552715 T SAOS (NIL) -8 NIL NIL NIL) (-1096 2551821 2551856 2552029 "SAERFFC" 2552215 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1095 2545671 2551718 2551798 "SAE" 2551803 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1094 2545264 2545299 2545458 "SAEFACT" 2545630 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1093 2543585 2543899 2544300 "RURPK" 2544930 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1092 2542222 2542528 2542833 "RULESET" 2543419 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1091 2539445 2539975 2540433 "RULE" 2541903 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1090 2539057 2539239 2539322 "RULECOLD" 2539397 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1089 2538847 2538875 2538946 "RTVALUE" 2539008 T RTVALUE (NIL) -8 NIL NIL NIL) (-1088 2538318 2538564 2538658 "RSTRCAST" 2538775 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1087 2533166 2533961 2534881 "RSETGCD" 2537517 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1086 2522396 2527475 2527572 "RSETCAT" 2531691 NIL RSETCAT (NIL T T T T) -9 NIL 2532788 NIL) (-1085 2520323 2520862 2521686 "RSETCAT-" 2521691 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1084 2512709 2514085 2515605 "RSDCMPK" 2518922 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1083 2510688 2511155 2511229 "RRCC" 2512315 NIL RRCC (NIL T T) -9 NIL 2512659 NIL) (-1082 2510039 2510213 2510492 "RRCC-" 2510497 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1081 2509482 2509735 2509836 "RPTAST" 2509960 T RPTAST (NIL) -8 NIL NIL NIL) (-1080 2483198 2492646 2492713 "RPOLCAT" 2503379 NIL RPOLCAT (NIL T T T) -9 NIL 2506539 NIL) (-1079 2474696 2477036 2480158 "RPOLCAT-" 2480163 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1078 2465627 2472907 2473389 "ROUTINE" 2474236 T ROUTINE (NIL) -8 NIL NIL NIL) (-1077 2462374 2465253 2465393 "ROMAN" 2465509 T ROMAN (NIL) -8 NIL NIL NIL) (-1076 2460618 2461234 2461494 "ROIRC" 2462179 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1075 2456850 2459134 2459164 "RNS" 2459468 T RNS (NIL) -9 NIL 2459742 NIL) (-1074 2455359 2455742 2456276 "RNS-" 2456351 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1073 2454762 2455170 2455200 "RNG" 2455205 T RNG (NIL) -9 NIL 2455226 NIL) (-1072 2453765 2454127 2454329 "RNGBIND" 2454613 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1071 2453164 2453552 2453595 "RMODULE" 2453600 NIL RMODULE (NIL T) -9 NIL 2453627 NIL) (-1070 2452000 2452094 2452430 "RMCAT2" 2453065 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1069 2448850 2451346 2451643 "RMATRIX" 2451762 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1068 2441677 2443937 2444052 "RMATCAT" 2447411 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2448393 NIL) (-1067 2441052 2441199 2441506 "RMATCAT-" 2441511 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1066 2440453 2440674 2440717 "RLINSET" 2440911 NIL RLINSET (NIL T) -9 NIL 2441002 NIL) (-1065 2440020 2440095 2440223 "RINTERP" 2440372 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1064 2439078 2439632 2439662 "RING" 2439718 T RING (NIL) -9 NIL 2439810 NIL) (-1063 2438870 2438914 2439011 "RING-" 2439016 NIL RING- (NIL T) -8 NIL NIL NIL) (-1062 2437711 2437948 2438206 "RIDIST" 2438634 T RIDIST (NIL) -7 NIL NIL NIL) (-1061 2429000 2437179 2437385 "RGCHAIN" 2437559 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1060 2428350 2428756 2428797 "RGBCSPC" 2428855 NIL RGBCSPC (NIL T) -9 NIL 2428907 NIL) (-1059 2427508 2427889 2427930 "RGBCMDL" 2428162 NIL RGBCMDL (NIL T) -9 NIL 2428276 NIL) (-1058 2424502 2425116 2425786 "RF" 2426872 NIL RF (NIL T) -7 NIL NIL NIL) (-1057 2424148 2424211 2424314 "RFFACTOR" 2424433 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1056 2423873 2423908 2424005 "RFFACT" 2424107 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1055 2421990 2422354 2422736 "RFDIST" 2423513 T RFDIST (NIL) -7 NIL NIL NIL) (-1054 2421443 2421535 2421698 "RETSOL" 2421892 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1053 2421079 2421159 2421202 "RETRACT" 2421335 NIL RETRACT (NIL T) -9 NIL 2421422 NIL) (-1052 2420928 2420953 2421040 "RETRACT-" 2421045 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1051 2420530 2420750 2420820 "RETAST" 2420880 T RETAST (NIL) -8 NIL NIL NIL) (-1050 2413268 2420183 2420310 "RESULT" 2420425 T RESULT (NIL) -8 NIL NIL NIL) (-1049 2411859 2412537 2412736 "RESRING" 2413171 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1048 2411495 2411544 2411642 "RESLATC" 2411796 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1047 2411200 2411235 2411342 "REPSQ" 2411454 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1046 2408622 2409202 2409804 "REP" 2410620 T REP (NIL) -7 NIL NIL NIL) (-1045 2408319 2408354 2408465 "REPDB" 2408581 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1044 2402219 2403608 2404831 "REP2" 2407131 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1043 2398596 2399277 2400085 "REP1" 2401446 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1042 2391292 2396737 2397193 "REGSET" 2398226 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1041 2390057 2390440 2390690 "REF" 2391077 NIL REF (NIL T) -8 NIL NIL NIL) (-1040 2389434 2389537 2389704 "REDORDER" 2389941 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1039 2385402 2388647 2388874 "RECLOS" 2389262 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1038 2384454 2384635 2384850 "REALSOLV" 2385209 T REALSOLV (NIL) -7 NIL NIL NIL) (-1037 2384300 2384341 2384371 "REAL" 2384376 T REAL (NIL) -9 NIL 2384411 NIL) (-1036 2380783 2381585 2382469 "REAL0Q" 2383465 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1035 2376384 2377372 2378433 "REAL0" 2379764 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1034 2375855 2376101 2376195 "RDUCEAST" 2376312 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1033 2375260 2375332 2375539 "RDIV" 2375777 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1032 2374328 2374502 2374715 "RDIST" 2375082 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1031 2372925 2373212 2373584 "RDETRS" 2374036 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1030 2370737 2371191 2371729 "RDETR" 2372467 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1029 2369362 2369640 2370037 "RDEEFS" 2370453 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1028 2367871 2368177 2368602 "RDEEF" 2369050 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1027 2361932 2364852 2364882 "RCFIELD" 2366177 T RCFIELD (NIL) -9 NIL 2366908 NIL) (-1026 2359996 2360500 2361196 "RCFIELD-" 2361271 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1025 2356265 2358097 2358140 "RCAGG" 2359224 NIL RCAGG (NIL T) -9 NIL 2359689 NIL) (-1024 2355893 2355987 2356150 "RCAGG-" 2356155 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1023 2355228 2355340 2355505 "RATRET" 2355777 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1022 2354781 2354848 2354969 "RATFACT" 2355156 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1021 2354089 2354209 2354361 "RANDSRC" 2354651 T RANDSRC (NIL) -7 NIL NIL NIL) (-1020 2353823 2353867 2353940 "RADUTIL" 2354038 T RADUTIL (NIL) -7 NIL NIL NIL) (-1019 2346844 2352654 2352965 "RADIX" 2353546 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1018 2338360 2346686 2346816 "RADFF" 2346821 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1017 2338007 2338082 2338112 "RADCAT" 2338272 T RADCAT (NIL) -9 NIL NIL NIL) (-1016 2337789 2337837 2337937 "RADCAT-" 2337942 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1015 2335887 2337559 2337651 "QUEUE" 2337732 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1014 2332335 2335820 2335868 "QUAT" 2335873 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1013 2331966 2332009 2332140 "QUATCT2" 2332286 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1012 2325162 2328597 2328639 "QUATCAT" 2329430 NIL QUATCAT (NIL T) -9 NIL 2330196 NIL) (-1011 2321301 2322338 2323728 "QUATCAT-" 2323824 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1010 2318766 2320377 2320420 "QUAGG" 2320801 NIL QUAGG (NIL T) -9 NIL 2320976 NIL) (-1009 2318368 2318588 2318658 "QQUTAST" 2318718 T QQUTAST (NIL) -8 NIL NIL NIL) (-1008 2317381 2317881 2318046 "QFORM" 2318249 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1007 2308188 2313516 2313558 "QFCAT" 2314226 NIL QFCAT (NIL T) -9 NIL 2315227 NIL) (-1006 2303533 2304796 2306470 "QFCAT-" 2306566 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1005 2303164 2303207 2303338 "QFCAT2" 2303484 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1004 2302619 2302729 2302861 "QEQUAT" 2303054 T QEQUAT (NIL) -8 NIL NIL NIL) (-1003 2295745 2296818 2298004 "QCMPACK" 2301552 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1002 2293283 2293731 2294161 "QALGSET" 2295400 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1001 2292518 2292694 2292930 "QALGSET2" 2293101 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1000 2291203 2291427 2291746 "PWFFINTB" 2292291 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-999 2289385 2289553 2289907 "PUSHVAR" 2291017 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-998 2285303 2286357 2286398 "PTRANFN" 2288282 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-997 2283705 2283996 2284318 "PTPACK" 2285014 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-996 2283337 2283394 2283503 "PTFUNC2" 2283642 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-995 2277782 2282179 2282220 "PTCAT" 2282516 NIL PTCAT (NIL T) -9 NIL 2282669 NIL) (-994 2277440 2277475 2277599 "PSQFR" 2277741 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-993 2276035 2276333 2276667 "PSEUDLIN" 2277138 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-992 2262798 2265169 2267493 "PSETPK" 2273795 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-991 2255816 2258556 2258652 "PSETCAT" 2261673 NIL PSETCAT (NIL T T T T) -9 NIL 2262487 NIL) (-990 2253652 2254286 2255107 "PSETCAT-" 2255112 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-989 2253001 2253166 2253194 "PSCURVE" 2253462 T PSCURVE (NIL) -9 NIL 2253629 NIL) (-988 2248999 2250515 2250580 "PSCAT" 2251424 NIL PSCAT (NIL T T T) -9 NIL 2251664 NIL) (-987 2248062 2248278 2248678 "PSCAT-" 2248683 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-986 2246421 2247131 2247394 "PRTITION" 2247819 T PRTITION (NIL) -8 NIL NIL NIL) (-985 2245896 2246142 2246234 "PRTDAST" 2246349 T PRTDAST (NIL) -8 NIL NIL NIL) (-984 2234986 2237200 2239388 "PRS" 2243758 NIL PRS (NIL T T) -7 NIL NIL NIL) (-983 2232797 2234336 2234376 "PRQAGG" 2234559 NIL PRQAGG (NIL T) -9 NIL 2234661 NIL) (-982 2232133 2232438 2232466 "PROPLOG" 2232605 T PROPLOG (NIL) -9 NIL 2232720 NIL) (-981 2231737 2231794 2231917 "PROPFUN2" 2232056 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-980 2231052 2231173 2231345 "PROPFUN1" 2231598 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-979 2229233 2229799 2230096 "PROPFRML" 2230788 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-978 2228702 2228809 2228937 "PROPERTY" 2229125 T PROPERTY (NIL) -8 NIL NIL NIL) (-977 2222760 2226868 2227688 "PRODUCT" 2227928 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-976 2220038 2222218 2222452 "PR" 2222571 NIL PR (NIL T T) -8 NIL NIL NIL) (-975 2219834 2219866 2219925 "PRINT" 2219999 T PRINT (NIL) -7 NIL NIL NIL) (-974 2219174 2219291 2219443 "PRIMES" 2219714 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-973 2217239 2217640 2218106 "PRIMELT" 2218753 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-972 2216968 2217017 2217045 "PRIMCAT" 2217169 T PRIMCAT (NIL) -9 NIL NIL NIL) (-971 2213083 2216906 2216951 "PRIMARR" 2216956 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-970 2212090 2212268 2212496 "PRIMARR2" 2212901 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-969 2211733 2211789 2211900 "PREASSOC" 2212028 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-968 2211208 2211341 2211369 "PPCURVE" 2211574 T PPCURVE (NIL) -9 NIL 2211710 NIL) (-967 2210803 2211003 2211086 "PORTNUM" 2211145 T PORTNUM (NIL) -8 NIL NIL NIL) (-966 2208162 2208561 2209153 "POLYROOT" 2210384 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-965 2202255 2207766 2207926 "POLY" 2208035 NIL POLY (NIL T) -8 NIL NIL NIL) (-964 2201638 2201696 2201930 "POLYLIFT" 2202191 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-963 2197913 2198362 2198991 "POLYCATQ" 2201183 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-962 2184495 2189712 2189777 "POLYCAT" 2193291 NIL POLYCAT (NIL T T T) -9 NIL 2195169 NIL) (-961 2177722 2179646 2182110 "POLYCAT-" 2182115 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-960 2177309 2177377 2177497 "POLY2UP" 2177648 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-959 2176941 2176998 2177107 "POLY2" 2177246 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-958 2175626 2175865 2176141 "POLUTIL" 2176715 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-957 2173981 2174258 2174589 "POLTOPOL" 2175348 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-956 2169446 2173917 2173963 "POINT" 2173968 NIL POINT (NIL T) -8 NIL NIL NIL) (-955 2167633 2167990 2168365 "PNTHEORY" 2169091 T PNTHEORY (NIL) -7 NIL NIL NIL) (-954 2166091 2166388 2166787 "PMTOOLS" 2167331 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-953 2165684 2165762 2165879 "PMSYM" 2166007 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-952 2165192 2165261 2165436 "PMQFCAT" 2165609 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-951 2164547 2164657 2164813 "PMPRED" 2165069 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-950 2163940 2164026 2164188 "PMPREDFS" 2164448 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-949 2162604 2162812 2163190 "PMPLCAT" 2163702 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-948 2162136 2162215 2162367 "PMLSAGG" 2162519 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-947 2161609 2161685 2161867 "PMKERNEL" 2162054 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-946 2161226 2161301 2161414 "PMINS" 2161528 NIL PMINS (NIL T) -7 NIL NIL NIL) (-945 2160668 2160737 2160946 "PMFS" 2161151 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-944 2159896 2160014 2160219 "PMDOWN" 2160545 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-943 2159063 2159221 2159402 "PMASS" 2159735 T PMASS (NIL) -7 NIL NIL NIL) (-942 2158336 2158446 2158609 "PMASSFS" 2158950 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-941 2157991 2158059 2158153 "PLOTTOOL" 2158262 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-940 2152598 2153802 2154950 "PLOT" 2156863 T PLOT (NIL) -8 NIL NIL NIL) (-939 2148402 2149446 2150367 "PLOT3D" 2151697 T PLOT3D (NIL) -8 NIL NIL NIL) (-938 2147314 2147491 2147726 "PLOT1" 2148206 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-937 2122705 2127380 2132231 "PLEQN" 2142580 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-936 2122023 2122145 2122325 "PINTERP" 2122570 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-935 2121716 2121763 2121866 "PINTERPA" 2121970 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-934 2120932 2121480 2121567 "PI" 2121607 T PI (NIL) -8 NIL NIL 2121674) (-933 2119229 2120204 2120232 "PID" 2120414 T PID (NIL) -9 NIL 2120548 NIL) (-932 2118980 2119017 2119092 "PICOERCE" 2119186 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-931 2118300 2118439 2118615 "PGROEB" 2118836 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-930 2113887 2114701 2115606 "PGE" 2117415 T PGE (NIL) -7 NIL NIL NIL) (-929 2112010 2112257 2112623 "PGCD" 2113604 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-928 2111348 2111451 2111612 "PFRPAC" 2111894 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-927 2107988 2109896 2110249 "PFR" 2111027 NIL PFR (NIL T) -8 NIL NIL NIL) (-926 2106377 2106621 2106946 "PFOTOOLS" 2107735 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-925 2104910 2105149 2105500 "PFOQ" 2106134 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-924 2103411 2103623 2103979 "PFO" 2104694 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-923 2099964 2103300 2103369 "PF" 2103374 NIL PF (NIL NIL) -8 NIL NIL NIL) (-922 2097298 2098569 2098597 "PFECAT" 2099182 T PFECAT (NIL) -9 NIL 2099566 NIL) (-921 2096743 2096897 2097111 "PFECAT-" 2097116 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-920 2095346 2095598 2095899 "PFBRU" 2096492 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-919 2093212 2093564 2093996 "PFBR" 2094997 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-918 2089258 2090724 2091371 "PERM" 2092598 NIL PERM (NIL T) -8 NIL NIL NIL) (-917 2084492 2085465 2086335 "PERMGRP" 2088421 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-916 2082611 2083571 2083612 "PERMCAT" 2084012 NIL PERMCAT (NIL T) -9 NIL 2084310 NIL) (-915 2082264 2082305 2082429 "PERMAN" 2082564 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-914 2079752 2081929 2082051 "PENDTREE" 2082175 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-913 2077776 2078544 2078585 "PDRING" 2079242 NIL PDRING (NIL T) -9 NIL 2079528 NIL) (-912 2076879 2077097 2077459 "PDRING-" 2077464 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-911 2074094 2074872 2075540 "PDEPROB" 2076231 T PDEPROB (NIL) -8 NIL NIL NIL) (-910 2071639 2072143 2072698 "PDEPACK" 2073559 T PDEPACK (NIL) -7 NIL NIL NIL) (-909 2070551 2070741 2070992 "PDECOMP" 2071438 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-908 2068130 2068973 2069001 "PDECAT" 2069788 T PDECAT (NIL) -9 NIL 2070501 NIL) (-907 2067759 2067814 2067868 "PDDOM" 2068033 NIL PDDOM (NIL T T) -9 NIL 2068113 NIL) (-906 2067578 2067608 2067715 "PDDOM-" 2067720 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-905 2067329 2067362 2067452 "PCOMP" 2067539 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-904 2065507 2066130 2066427 "PBWLB" 2067058 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-903 2057980 2059580 2060918 "PATTERN" 2064190 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-902 2057612 2057669 2057778 "PATTERN2" 2057917 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-901 2055369 2055757 2056214 "PATTERN1" 2057201 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-900 2052737 2053318 2053799 "PATRES" 2054934 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-899 2052301 2052368 2052500 "PATRES2" 2052664 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-898 2050184 2050589 2050996 "PATMATCH" 2051968 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-897 2049694 2049903 2049944 "PATMAB" 2050051 NIL PATMAB (NIL T) -9 NIL 2050134 NIL) (-896 2048212 2048548 2048806 "PATLRES" 2049499 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-895 2047758 2047881 2047922 "PATAB" 2047927 NIL PATAB (NIL T) -9 NIL 2048099 NIL) (-894 2045940 2046335 2046758 "PARTPERM" 2047355 T PARTPERM (NIL) -7 NIL NIL NIL) (-893 2045561 2045624 2045726 "PARSURF" 2045871 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-892 2045193 2045250 2045359 "PARSU2" 2045498 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-891 2044957 2044997 2045064 "PARSER" 2045146 T PARSER (NIL) -7 NIL NIL NIL) (-890 2044578 2044641 2044743 "PARSCURV" 2044888 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-889 2044210 2044267 2044376 "PARSC2" 2044515 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-888 2043849 2043907 2044004 "PARPCURV" 2044146 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-887 2043481 2043538 2043647 "PARPC2" 2043786 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-886 2042542 2042854 2043036 "PARAMAST" 2043319 T PARAMAST (NIL) -8 NIL NIL NIL) (-885 2042062 2042148 2042267 "PAN2EXPR" 2042443 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-884 2040839 2041183 2041411 "PALETTE" 2041854 T PALETTE (NIL) -8 NIL NIL NIL) (-883 2039232 2039844 2040204 "PAIR" 2040525 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-882 2033011 2038489 2038684 "PADICRC" 2039086 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-881 2026135 2032355 2032540 "PADICRAT" 2032858 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-880 2024450 2026072 2026117 "PADIC" 2026122 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-879 2021560 2023124 2023164 "PADICCT" 2023745 NIL PADICCT (NIL NIL) -9 NIL 2024027 NIL) (-878 2020517 2020717 2020985 "PADEPAC" 2021347 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-877 2019729 2019862 2020068 "PADE" 2020379 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-876 2018116 2018937 2019217 "OWP" 2019533 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-875 2017609 2017822 2017919 "OVERSET" 2018039 T OVERSET (NIL) -8 NIL NIL NIL) (-874 2016655 2017214 2017386 "OVAR" 2017477 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-873 2015919 2016040 2016201 "OUT" 2016514 T OUT (NIL) -7 NIL NIL NIL) (-872 2004791 2007028 2009228 "OUTFORM" 2013739 T OUTFORM (NIL) -8 NIL NIL NIL) (-871 2004127 2004388 2004515 "OUTBFILE" 2004684 T OUTBFILE (NIL) -8 NIL NIL NIL) (-870 2003434 2003599 2003627 "OUTBCON" 2003945 T OUTBCON (NIL) -9 NIL 2004111 NIL) (-869 2003035 2003147 2003304 "OUTBCON-" 2003309 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-868 2002415 2002764 2002853 "OSI" 2002966 T OSI (NIL) -8 NIL NIL NIL) (-867 2001945 2002283 2002311 "OSGROUP" 2002316 T OSGROUP (NIL) -9 NIL 2002338 NIL) (-866 2000690 2000917 2001202 "ORTHPOL" 2001692 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-865 1998241 2000525 2000646 "OREUP" 2000651 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-864 1995644 1997932 1998059 "ORESUP" 1998183 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-863 1993172 1993672 1994233 "OREPCTO" 1995133 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-862 1986858 1989059 1989100 "OREPCAT" 1991448 NIL OREPCAT (NIL T) -9 NIL 1992552 NIL) (-861 1984005 1984787 1985845 "OREPCAT-" 1985850 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-860 1983156 1983454 1983482 "ORDSET" 1983791 T ORDSET (NIL) -9 NIL 1983955 NIL) (-859 1982587 1982735 1982959 "ORDSET-" 1982964 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-858 1981152 1981943 1981971 "ORDRING" 1982173 T ORDRING (NIL) -9 NIL 1982298 NIL) (-857 1980797 1980891 1981035 "ORDRING-" 1981040 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-856 1980177 1980640 1980668 "ORDMON" 1980673 T ORDMON (NIL) -9 NIL 1980694 NIL) (-855 1979339 1979486 1979681 "ORDFUNS" 1980026 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-854 1978677 1979096 1979124 "ORDFIN" 1979189 T ORDFIN (NIL) -9 NIL 1979263 NIL) (-853 1975236 1977263 1977672 "ORDCOMP" 1978301 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-852 1974502 1974629 1974815 "ORDCOMP2" 1975096 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-851 1971083 1971993 1972807 "OPTPROB" 1973708 T OPTPROB (NIL) -8 NIL NIL NIL) (-850 1967885 1968524 1969228 "OPTPACK" 1970399 T OPTPACK (NIL) -7 NIL NIL NIL) (-849 1965572 1966338 1966366 "OPTCAT" 1967185 T OPTCAT (NIL) -9 NIL 1967835 NIL) (-848 1964956 1965249 1965354 "OPSIG" 1965487 T OPSIG (NIL) -8 NIL NIL NIL) (-847 1964724 1964763 1964829 "OPQUERY" 1964910 T OPQUERY (NIL) -7 NIL NIL NIL) (-846 1961855 1963035 1963539 "OP" 1964253 NIL OP (NIL T) -8 NIL NIL NIL) (-845 1961229 1961455 1961496 "OPERCAT" 1961708 NIL OPERCAT (NIL T) -9 NIL 1961805 NIL) (-844 1960984 1961040 1961157 "OPERCAT-" 1961162 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-843 1957797 1959781 1960150 "ONECOMP" 1960648 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-842 1957102 1957217 1957391 "ONECOMP2" 1957669 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1956521 1956627 1956757 "OMSERVER" 1956992 T OMSERVER (NIL) -7 NIL NIL NIL) (-840 1953383 1955961 1956001 "OMSAGG" 1956062 NIL OMSAGG (NIL T) -9 NIL 1956126 NIL) (-839 1952006 1952269 1952551 "OMPKG" 1953121 T OMPKG (NIL) -7 NIL NIL NIL) (-838 1951436 1951539 1951567 "OM" 1951866 T OM (NIL) -9 NIL NIL NIL) (-837 1949983 1950985 1951154 "OMLO" 1951317 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-836 1948943 1949090 1949310 "OMEXPR" 1949809 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-835 1948234 1948489 1948625 "OMERR" 1948827 T OMERR (NIL) -8 NIL NIL NIL) (-834 1947385 1947655 1947815 "OMERRK" 1948094 T OMERRK (NIL) -8 NIL NIL NIL) (-833 1946836 1947062 1947170 "OMENC" 1947297 T OMENC (NIL) -8 NIL NIL NIL) (-832 1940731 1941916 1943087 "OMDEV" 1945685 T OMDEV (NIL) -8 NIL NIL NIL) (-831 1939800 1939971 1940165 "OMCONN" 1940557 T OMCONN (NIL) -8 NIL NIL NIL) (-830 1938321 1939297 1939325 "OINTDOM" 1939330 T OINTDOM (NIL) -9 NIL 1939351 NIL) (-829 1935659 1937009 1937346 "OFMONOID" 1938016 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-828 1935031 1935596 1935641 "ODVAR" 1935646 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-827 1932454 1934776 1934931 "ODR" 1934936 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-826 1924946 1932230 1932356 "ODPOL" 1932361 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-825 1918912 1924818 1924923 "ODP" 1924928 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-824 1917678 1917893 1918168 "ODETOOLS" 1918686 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-823 1914645 1915303 1916019 "ODESYS" 1917011 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-822 1909527 1910435 1911460 "ODERTRIC" 1913720 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-821 1908953 1909035 1909229 "ODERED" 1909439 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-820 1905841 1906389 1907066 "ODERAT" 1908376 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-819 1902800 1903265 1903862 "ODEPRRIC" 1905370 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-818 1900743 1901339 1901825 "ODEPROB" 1902334 T ODEPROB (NIL) -8 NIL NIL NIL) (-817 1897263 1897748 1898395 "ODEPRIM" 1900222 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-816 1896512 1896614 1896874 "ODEPAL" 1897155 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-815 1892674 1893465 1894329 "ODEPACK" 1895668 T ODEPACK (NIL) -7 NIL NIL NIL) (-814 1891735 1891842 1892064 "ODEINT" 1892563 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-813 1885836 1887261 1888708 "ODEIFTBL" 1890308 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-812 1881234 1882020 1882972 "ODEEF" 1884995 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-811 1880583 1880672 1880895 "ODECONST" 1881139 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-810 1878708 1879369 1879397 "ODECAT" 1880002 T ODECAT (NIL) -9 NIL 1880533 NIL) (-809 1875563 1878413 1878535 "OCT" 1878618 NIL OCT (NIL T) -8 NIL NIL NIL) (-808 1875201 1875244 1875371 "OCTCT2" 1875514 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-807 1869812 1872247 1872287 "OC" 1873384 NIL OC (NIL T) -9 NIL 1874242 NIL) (-806 1867039 1867787 1868777 "OC-" 1868871 NIL OC- (NIL T T) -8 NIL NIL NIL) (-805 1866391 1866859 1866887 "OCAMON" 1866892 T OCAMON (NIL) -9 NIL 1866913 NIL) (-804 1865922 1866263 1866291 "OASGP" 1866296 T OASGP (NIL) -9 NIL 1866316 NIL) (-803 1865183 1865672 1865700 "OAMONS" 1865740 T OAMONS (NIL) -9 NIL 1865783 NIL) (-802 1864597 1865030 1865058 "OAMON" 1865063 T OAMON (NIL) -9 NIL 1865083 NIL) (-801 1863855 1864373 1864401 "OAGROUP" 1864406 T OAGROUP (NIL) -9 NIL 1864426 NIL) (-800 1863545 1863595 1863683 "NUMTUBE" 1863799 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-799 1857118 1858636 1860172 "NUMQUAD" 1862029 T NUMQUAD (NIL) -7 NIL NIL NIL) (-798 1852874 1853862 1854887 "NUMODE" 1856113 T NUMODE (NIL) -7 NIL NIL NIL) (-797 1850229 1851109 1851137 "NUMINT" 1852060 T NUMINT (NIL) -9 NIL 1852824 NIL) (-796 1849177 1849374 1849592 "NUMFMT" 1850031 T NUMFMT (NIL) -7 NIL NIL NIL) (-795 1835536 1838481 1841013 "NUMERIC" 1846684 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-794 1829906 1834985 1835080 "NTSCAT" 1835085 NIL NTSCAT (NIL T T T T) -9 NIL 1835124 NIL) (-793 1829100 1829265 1829458 "NTPOLFN" 1829745 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-792 1817088 1825925 1826737 "NSUP" 1828321 NIL NSUP (NIL T) -8 NIL NIL NIL) (-791 1816720 1816777 1816886 "NSUP2" 1817025 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-790 1806857 1816494 1816627 "NSMP" 1816632 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-789 1805289 1805590 1805947 "NREP" 1806545 NIL NREP (NIL T) -7 NIL NIL NIL) (-788 1803880 1804132 1804490 "NPCOEF" 1805032 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-787 1802946 1803061 1803277 "NORMRETR" 1803761 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-786 1800987 1801277 1801686 "NORMPK" 1802654 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-785 1800672 1800700 1800824 "NORMMA" 1800953 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-784 1800472 1800629 1800658 "NONE" 1800663 T NONE (NIL) -8 NIL NIL NIL) (-783 1800261 1800290 1800359 "NONE1" 1800436 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-782 1799758 1799820 1799999 "NODE1" 1800193 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-781 1798039 1798890 1799145 "NNI" 1799492 T NNI (NIL) -8 NIL NIL 1799727) (-780 1796459 1796772 1797136 "NLINSOL" 1797707 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-779 1792700 1793695 1794594 "NIPROB" 1795580 T NIPROB (NIL) -8 NIL NIL NIL) (-778 1791457 1791691 1791993 "NFINTBAS" 1792462 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-777 1790631 1791107 1791148 "NETCLT" 1791320 NIL NETCLT (NIL T) -9 NIL 1791402 NIL) (-776 1789339 1789570 1789851 "NCODIV" 1790399 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-775 1789101 1789138 1789213 "NCNTFRAC" 1789296 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-774 1787281 1787645 1788065 "NCEP" 1788726 NIL NCEP (NIL T) -7 NIL NIL NIL) (-773 1786132 1786905 1786933 "NASRING" 1787043 T NASRING (NIL) -9 NIL 1787123 NIL) (-772 1785927 1785971 1786065 "NASRING-" 1786070 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-771 1785034 1785559 1785587 "NARNG" 1785704 T NARNG (NIL) -9 NIL 1785795 NIL) (-770 1784726 1784793 1784927 "NARNG-" 1784932 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-769 1783605 1783812 1784047 "NAGSP" 1784511 T NAGSP (NIL) -7 NIL NIL NIL) (-768 1774877 1776561 1778234 "NAGS" 1781952 T NAGS (NIL) -7 NIL NIL NIL) (-767 1773425 1773733 1774064 "NAGF07" 1774566 T NAGF07 (NIL) -7 NIL NIL NIL) (-766 1767963 1769254 1770561 "NAGF04" 1772138 T NAGF04 (NIL) -7 NIL NIL NIL) (-765 1760931 1762545 1764178 "NAGF02" 1766350 T NAGF02 (NIL) -7 NIL NIL NIL) (-764 1756155 1757255 1758372 "NAGF01" 1759834 T NAGF01 (NIL) -7 NIL NIL NIL) (-763 1749783 1751349 1752934 "NAGE04" 1754590 T NAGE04 (NIL) -7 NIL NIL NIL) (-762 1740952 1743073 1745203 "NAGE02" 1747673 T NAGE02 (NIL) -7 NIL NIL NIL) (-761 1736905 1737852 1738816 "NAGE01" 1740008 T NAGE01 (NIL) -7 NIL NIL NIL) (-760 1734700 1735234 1735792 "NAGD03" 1736367 T NAGD03 (NIL) -7 NIL NIL NIL) (-759 1726450 1728378 1730332 "NAGD02" 1732766 T NAGD02 (NIL) -7 NIL NIL NIL) (-758 1720261 1721686 1723126 "NAGD01" 1725030 T NAGD01 (NIL) -7 NIL NIL NIL) (-757 1716470 1717292 1718129 "NAGC06" 1719444 T NAGC06 (NIL) -7 NIL NIL NIL) (-756 1714935 1715267 1715623 "NAGC05" 1716134 T NAGC05 (NIL) -7 NIL NIL NIL) (-755 1714311 1714430 1714574 "NAGC02" 1714811 T NAGC02 (NIL) -7 NIL NIL NIL) (-754 1713270 1713853 1713893 "NAALG" 1713972 NIL NAALG (NIL T) -9 NIL 1714033 NIL) (-753 1713105 1713134 1713224 "NAALG-" 1713229 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-752 1707055 1708163 1709350 "MULTSQFR" 1712001 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-751 1706374 1706449 1706633 "MULTFACT" 1706967 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-750 1699098 1703011 1703064 "MTSCAT" 1704134 NIL MTSCAT (NIL T T) -9 NIL 1704649 NIL) (-749 1698810 1698864 1698956 "MTHING" 1699038 NIL MTHING (NIL T) -7 NIL NIL NIL) (-748 1698602 1698635 1698695 "MSYSCMD" 1698770 T MSYSCMD (NIL) -7 NIL NIL NIL) (-747 1694684 1697357 1697677 "MSET" 1698315 NIL MSET (NIL T) -8 NIL NIL NIL) (-746 1691753 1694245 1694286 "MSETAGG" 1694291 NIL MSETAGG (NIL T) -9 NIL 1694325 NIL) (-745 1687595 1689132 1689877 "MRING" 1691053 NIL MRING (NIL T T) -8 NIL NIL NIL) (-744 1687161 1687228 1687359 "MRF2" 1687522 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-743 1686779 1686814 1686958 "MRATFAC" 1687120 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-742 1684391 1684686 1685117 "MPRFF" 1686484 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-741 1678599 1684245 1684342 "MPOLY" 1684347 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-740 1678089 1678124 1678332 "MPCPF" 1678558 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-739 1677603 1677646 1677830 "MPC3" 1678040 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-738 1676798 1676879 1677100 "MPC2" 1677518 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-737 1675099 1675436 1675826 "MONOTOOL" 1676458 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-736 1674324 1674641 1674669 "MONOID" 1674888 T MONOID (NIL) -9 NIL 1675035 NIL) (-735 1673870 1673989 1674170 "MONOID-" 1674175 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-734 1663968 1670009 1670068 "MONOGEN" 1670742 NIL MONOGEN (NIL T T) -9 NIL 1671198 NIL) (-733 1661186 1661921 1662921 "MONOGEN-" 1663040 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-732 1660019 1660465 1660493 "MONADWU" 1660885 T MONADWU (NIL) -9 NIL 1661123 NIL) (-731 1659391 1659550 1659798 "MONADWU-" 1659803 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-730 1658750 1658994 1659022 "MONAD" 1659229 T MONAD (NIL) -9 NIL 1659341 NIL) (-729 1658435 1658513 1658645 "MONAD-" 1658650 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-728 1656724 1657348 1657627 "MOEBIUS" 1658188 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-727 1656002 1656406 1656446 "MODULE" 1656451 NIL MODULE (NIL T) -9 NIL 1656490 NIL) (-726 1655570 1655666 1655856 "MODULE-" 1655861 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-725 1653250 1653934 1654261 "MODRING" 1655394 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-724 1650194 1651355 1651876 "MODOP" 1652779 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-723 1648782 1649261 1649538 "MODMONOM" 1650057 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-722 1638737 1647073 1647487 "MODMON" 1648419 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-721 1635893 1637581 1637857 "MODFIELD" 1638612 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1634870 1635174 1635364 "MMLFORM" 1635723 T MMLFORM (NIL) -8 NIL NIL NIL) (-719 1634396 1634439 1634618 "MMAP" 1634821 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-718 1632475 1633242 1633283 "MLO" 1633706 NIL MLO (NIL T) -9 NIL 1633948 NIL) (-717 1629841 1630357 1630959 "MLIFT" 1631956 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-716 1629232 1629316 1629470 "MKUCFUNC" 1629752 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-715 1628831 1628901 1629024 "MKRECORD" 1629155 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-714 1627878 1628040 1628268 "MKFUNC" 1628642 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-713 1627266 1627370 1627526 "MKFLCFN" 1627761 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-712 1626543 1626645 1626830 "MKBCFUNC" 1627159 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-711 1623218 1626097 1626233 "MINT" 1626427 T MINT (NIL) -8 NIL NIL NIL) (-710 1622030 1622273 1622550 "MHROWRED" 1622973 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-709 1617410 1620565 1620970 "MFLOAT" 1621645 T MFLOAT (NIL) -8 NIL NIL NIL) (-708 1616767 1616843 1617014 "MFINFACT" 1617322 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-707 1613082 1613930 1614814 "MESH" 1615903 T MESH (NIL) -7 NIL NIL NIL) (-706 1611472 1611784 1612137 "MDDFACT" 1612769 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-705 1608267 1610631 1610672 "MDAGG" 1610927 NIL MDAGG (NIL T) -9 NIL 1611070 NIL) (-704 1597914 1607560 1607767 "MCMPLX" 1608080 T MCMPLX (NIL) -8 NIL NIL NIL) (-703 1597051 1597197 1597398 "MCDEN" 1597763 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-702 1594941 1595211 1595591 "MCALCFN" 1596781 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-701 1593866 1594106 1594339 "MAYBE" 1594747 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-700 1591478 1592001 1592563 "MATSTOR" 1593337 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-699 1587435 1590850 1591098 "MATRIX" 1591263 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-698 1583201 1583908 1584644 "MATLIN" 1586792 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-697 1573307 1576493 1576570 "MATCAT" 1581450 NIL MATCAT (NIL T T T) -9 NIL 1582867 NIL) (-696 1569663 1570684 1572040 "MATCAT-" 1572045 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-695 1568257 1568410 1568743 "MATCAT2" 1569498 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-694 1566369 1566693 1567077 "MAPPKG3" 1567932 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-693 1565350 1565523 1565745 "MAPPKG2" 1566193 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-692 1563849 1564133 1564460 "MAPPKG1" 1565056 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-691 1562928 1563255 1563432 "MAPPAST" 1563692 T MAPPAST (NIL) -8 NIL NIL NIL) (-690 1562539 1562597 1562720 "MAPHACK3" 1562864 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-689 1562131 1562192 1562306 "MAPHACK2" 1562471 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-688 1561569 1561672 1561814 "MAPHACK1" 1562022 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-687 1559648 1560269 1560573 "MAGMA" 1561297 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-686 1559127 1559372 1559463 "MACROAST" 1559577 T MACROAST (NIL) -8 NIL NIL NIL) (-685 1555545 1557366 1557827 "M3D" 1558699 NIL M3D (NIL T) -8 NIL NIL NIL) (-684 1549620 1553884 1553925 "LZSTAGG" 1554707 NIL LZSTAGG (NIL T) -9 NIL 1555002 NIL) (-683 1545578 1546751 1548208 "LZSTAGG-" 1548213 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-682 1542665 1543469 1543956 "LWORD" 1545123 NIL LWORD (NIL T) -8 NIL NIL NIL) (-681 1542241 1542469 1542544 "LSTAST" 1542610 T LSTAST (NIL) -8 NIL NIL NIL) (-680 1535318 1542012 1542146 "LSQM" 1542151 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-679 1534542 1534681 1534909 "LSPP" 1535173 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-678 1532354 1532655 1533111 "LSMP" 1534231 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-677 1529133 1529807 1530537 "LSMP1" 1531656 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-676 1522979 1528270 1528311 "LSAGG" 1528373 NIL LSAGG (NIL T) -9 NIL 1528451 NIL) (-675 1519674 1520598 1521811 "LSAGG-" 1521816 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-674 1517273 1518818 1519067 "LPOLY" 1519469 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-673 1516855 1516940 1517063 "LPEFRAC" 1517182 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-672 1515176 1515949 1516202 "LO" 1516687 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1514828 1514940 1514968 "LOGIC" 1515079 T LOGIC (NIL) -9 NIL 1515160 NIL) (-670 1514690 1514713 1514784 "LOGIC-" 1514789 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-669 1513883 1514023 1514216 "LODOOPS" 1514546 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-668 1511306 1513799 1513865 "LODO" 1513870 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-667 1509844 1510079 1510432 "LODOF" 1511053 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-666 1506048 1508479 1508520 "LODOCAT" 1508958 NIL LODOCAT (NIL T) -9 NIL 1509169 NIL) (-665 1505781 1505839 1505966 "LODOCAT-" 1505971 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-664 1503101 1505622 1505740 "LODO2" 1505745 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-663 1500536 1503038 1503083 "LODO1" 1503088 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-662 1499417 1499582 1499887 "LODEEF" 1500359 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-661 1494720 1497611 1497652 "LNAGG" 1498514 NIL LNAGG (NIL T) -9 NIL 1498949 NIL) (-660 1493867 1494081 1494423 "LNAGG-" 1494428 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-659 1490003 1490792 1491431 "LMOPS" 1493282 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-658 1489406 1489794 1489835 "LMODULE" 1489840 NIL LMODULE (NIL T) -9 NIL 1489866 NIL) (-657 1486604 1489051 1489174 "LMDICT" 1489316 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-656 1486010 1486231 1486272 "LLINSET" 1486463 NIL LLINSET (NIL T) -9 NIL 1486554 NIL) (-655 1485709 1485918 1485978 "LITERAL" 1485983 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-654 1478872 1484643 1484947 "LIST" 1485438 NIL LIST (NIL T) -8 NIL NIL NIL) (-653 1478397 1478471 1478610 "LIST3" 1478792 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-652 1477404 1477582 1477810 "LIST2" 1478215 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-651 1475538 1475850 1476249 "LIST2MAP" 1477051 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-650 1475134 1475371 1475412 "LINSET" 1475417 NIL LINSET (NIL T) -9 NIL 1475451 NIL) (-649 1473863 1474396 1474437 "LINEXP" 1474788 NIL LINEXP (NIL T) -9 NIL 1474979 NIL) (-648 1472440 1472700 1473011 "LINDEP" 1473615 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-647 1469207 1469926 1470703 "LIMITRF" 1471695 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-646 1467510 1467806 1468215 "LIMITPS" 1468902 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-645 1461938 1467021 1467249 "LIE" 1467331 NIL LIE (NIL T T) -8 NIL NIL NIL) (-644 1460886 1461355 1461395 "LIECAT" 1461535 NIL LIECAT (NIL T) -9 NIL 1461686 NIL) (-643 1460727 1460754 1460842 "LIECAT-" 1460847 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-642 1453314 1460267 1460423 "LIB" 1460591 T LIB (NIL) -8 NIL NIL NIL) (-641 1448949 1449832 1450767 "LGROBP" 1452431 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-640 1446947 1447221 1447571 "LF" 1448670 NIL LF (NIL T T) -7 NIL NIL NIL) (-639 1445787 1446479 1446507 "LFCAT" 1446714 T LFCAT (NIL) -9 NIL 1446853 NIL) (-638 1442689 1443319 1444007 "LEXTRIPK" 1445151 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-637 1439433 1440259 1440762 "LEXP" 1442269 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-636 1438909 1439154 1439246 "LETAST" 1439361 T LETAST (NIL) -8 NIL NIL NIL) (-635 1437307 1437620 1438021 "LEADCDET" 1438591 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-634 1436497 1436571 1436800 "LAZM3PK" 1437228 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-633 1431414 1434574 1435112 "LAUPOL" 1436009 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-632 1430993 1431037 1431198 "LAPLACE" 1431364 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-631 1428932 1430094 1430345 "LA" 1430826 NIL LA (NIL T T T) -8 NIL NIL NIL) (-630 1427926 1428510 1428551 "LALG" 1428613 NIL LALG (NIL T) -9 NIL 1428672 NIL) (-629 1427640 1427699 1427835 "LALG-" 1427840 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-628 1427475 1427499 1427540 "KVTFROM" 1427602 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-627 1426398 1426842 1427027 "KTVLOGIC" 1427310 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-626 1426233 1426257 1426298 "KRCFROM" 1426360 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-625 1425137 1425324 1425623 "KOVACIC" 1426033 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-624 1424972 1424996 1425037 "KONVERT" 1425099 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-623 1424807 1424831 1424872 "KOERCE" 1424934 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-622 1422638 1423400 1423777 "KERNEL" 1424463 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-621 1422134 1422215 1422347 "KERNEL2" 1422552 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-620 1415904 1420673 1420727 "KDAGG" 1421104 NIL KDAGG (NIL T T) -9 NIL 1421310 NIL) (-619 1415433 1415557 1415762 "KDAGG-" 1415767 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-618 1408581 1415094 1415249 "KAFILE" 1415311 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-617 1403009 1408092 1408320 "JORDAN" 1408402 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-616 1402388 1402658 1402779 "JOINAST" 1402908 T JOINAST (NIL) -8 NIL NIL NIL) (-615 1402234 1402293 1402348 "JAVACODE" 1402353 T JAVACODE (NIL) -8 NIL NIL NIL) (-614 1398486 1400439 1400493 "IXAGG" 1401422 NIL IXAGG (NIL T T) -9 NIL 1401881 NIL) (-613 1397405 1397711 1398130 "IXAGG-" 1398135 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-612 1392935 1397327 1397386 "IVECTOR" 1397391 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-611 1391701 1391938 1392204 "ITUPLE" 1392702 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-610 1390203 1390380 1390675 "ITRIGMNP" 1391523 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-609 1388948 1389152 1389435 "ITFUN3" 1389979 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-608 1388580 1388637 1388746 "ITFUN2" 1388885 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-607 1387739 1388060 1388234 "ITFORM" 1388426 T ITFORM (NIL) -8 NIL NIL NIL) (-606 1385700 1386759 1387037 "ITAYLOR" 1387494 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-605 1374645 1379837 1381000 "ISUPS" 1384570 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-604 1373749 1373889 1374125 "ISUMP" 1374492 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-603 1369124 1373694 1373735 "ISTRING" 1373740 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-602 1368600 1368845 1368937 "ISAST" 1369052 T ISAST (NIL) -8 NIL NIL NIL) (-601 1367809 1367891 1368107 "IRURPK" 1368514 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-600 1366745 1366946 1367186 "IRSN" 1367589 T IRSN (NIL) -7 NIL NIL NIL) (-599 1364816 1365171 1365600 "IRRF2F" 1366383 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-598 1364563 1364601 1364677 "IRREDFFX" 1364772 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-597 1363178 1363437 1363736 "IROOT" 1364296 NIL IROOT (NIL T) -7 NIL NIL NIL) (-596 1359782 1360862 1361554 "IR" 1362518 NIL IR (NIL T) -8 NIL NIL NIL) (-595 1358987 1359275 1359426 "IRFORM" 1359651 T IRFORM (NIL) -8 NIL NIL NIL) (-594 1356600 1357095 1357661 "IR2" 1358465 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-593 1355700 1355813 1356027 "IR2F" 1356483 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-592 1355491 1355525 1355585 "IPRNTPK" 1355660 T IPRNTPK (NIL) -7 NIL NIL NIL) (-591 1352072 1355380 1355449 "IPF" 1355454 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-590 1350399 1351997 1352054 "IPADIC" 1352059 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-589 1349711 1349959 1350089 "IP4ADDR" 1350289 T IP4ADDR (NIL) -8 NIL NIL NIL) (-588 1349085 1349340 1349472 "IOMODE" 1349599 T IOMODE (NIL) -8 NIL NIL NIL) (-587 1348158 1348682 1348809 "IOBFILE" 1348978 T IOBFILE (NIL) -8 NIL NIL NIL) (-586 1347646 1348062 1348090 "IOBCON" 1348095 T IOBCON (NIL) -9 NIL 1348116 NIL) (-585 1347157 1347215 1347398 "INVLAPLA" 1347582 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-584 1336805 1339159 1341545 "INTTR" 1344821 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-583 1333140 1333882 1334747 "INTTOOLS" 1335990 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-582 1332726 1332817 1332934 "INTSLPE" 1333043 T INTSLPE (NIL) -7 NIL NIL NIL) (-581 1330679 1332649 1332708 "INTRVL" 1332713 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-580 1328281 1328793 1329368 "INTRF" 1330164 NIL INTRF (NIL T) -7 NIL NIL NIL) (-579 1327692 1327789 1327931 "INTRET" 1328179 NIL INTRET (NIL T) -7 NIL NIL NIL) (-578 1325689 1326078 1326548 "INTRAT" 1327300 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-577 1322952 1323535 1324154 "INTPM" 1325174 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-576 1319697 1320296 1321034 "INTPAF" 1322338 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-575 1314876 1315838 1316889 "INTPACK" 1318666 T INTPACK (NIL) -7 NIL NIL NIL) (-574 1311774 1314673 1314782 "INT" 1314787 T INT (NIL) -8 NIL NIL NIL) (-573 1311026 1311178 1311386 "INTHERTR" 1311616 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-572 1310465 1310545 1310733 "INTHERAL" 1310940 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-571 1308311 1308754 1309211 "INTHEORY" 1310028 T INTHEORY (NIL) -7 NIL NIL NIL) (-570 1299717 1301338 1303110 "INTG0" 1306663 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-569 1280290 1285080 1289890 "INTFTBL" 1294927 T INTFTBL (NIL) -8 NIL NIL NIL) (-568 1279539 1279677 1279850 "INTFACT" 1280149 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-567 1276966 1277412 1277969 "INTEF" 1279093 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-566 1275333 1276072 1276100 "INTDOM" 1276401 T INTDOM (NIL) -9 NIL 1276608 NIL) (-565 1274702 1274876 1275118 "INTDOM-" 1275123 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-564 1271090 1273018 1273072 "INTCAT" 1273871 NIL INTCAT (NIL T) -9 NIL 1274192 NIL) (-563 1270562 1270665 1270793 "INTBIT" 1270982 T INTBIT (NIL) -7 NIL NIL NIL) (-562 1269261 1269415 1269722 "INTALG" 1270407 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-561 1268744 1268834 1268991 "INTAF" 1269165 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-560 1262087 1268554 1268694 "INTABL" 1268699 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-559 1261420 1261886 1261951 "INT8" 1261985 T INT8 (NIL) -8 NIL NIL 1262030) (-558 1260752 1261218 1261283 "INT64" 1261317 T INT64 (NIL) -8 NIL NIL 1261362) (-557 1260084 1260550 1260615 "INT32" 1260649 T INT32 (NIL) -8 NIL NIL 1260694) (-556 1259416 1259882 1259947 "INT16" 1259981 T INT16 (NIL) -8 NIL NIL 1260026) (-555 1254211 1256977 1257005 "INS" 1257939 T INS (NIL) -9 NIL 1258604 NIL) (-554 1251451 1252222 1253196 "INS-" 1253269 NIL INS- (NIL T) -8 NIL NIL NIL) (-553 1250226 1250453 1250751 "INPSIGN" 1251204 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-552 1249344 1249461 1249658 "INPRODPF" 1250106 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-551 1248238 1248355 1248592 "INPRODFF" 1249224 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-550 1247238 1247390 1247650 "INNMFACT" 1248074 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-549 1246435 1246532 1246720 "INMODGCD" 1247137 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-548 1244943 1245188 1245512 "INFSP" 1246180 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-547 1244127 1244244 1244427 "INFPROD0" 1244823 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-546 1240982 1242192 1242707 "INFORM" 1243620 T INFORM (NIL) -8 NIL NIL NIL) (-545 1240592 1240652 1240750 "INFORM1" 1240917 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-544 1240115 1240204 1240318 "INFINITY" 1240498 T INFINITY (NIL) -7 NIL NIL NIL) (-543 1239291 1239835 1239936 "INETCLTS" 1240034 T INETCLTS (NIL) -8 NIL NIL NIL) (-542 1237907 1238157 1238478 "INEP" 1239039 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-541 1237156 1237804 1237869 "INDE" 1237874 NIL INDE (NIL T) -8 NIL NIL NIL) (-540 1236720 1236788 1236905 "INCRMAPS" 1237083 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-539 1235538 1235989 1236195 "INBFILE" 1236534 T INBFILE (NIL) -8 NIL NIL NIL) (-538 1230837 1231774 1232718 "INBFF" 1234626 NIL INBFF (NIL T) -7 NIL NIL NIL) (-537 1229745 1230014 1230042 "INBCON" 1230555 T INBCON (NIL) -9 NIL 1230821 NIL) (-536 1228997 1229220 1229496 "INBCON-" 1229501 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-535 1228476 1228721 1228812 "INAST" 1228926 T INAST (NIL) -8 NIL NIL NIL) (-534 1227903 1228155 1228261 "IMPTAST" 1228390 T IMPTAST (NIL) -8 NIL NIL NIL) (-533 1224349 1227747 1227851 "IMATRIX" 1227856 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-532 1223057 1223180 1223496 "IMATQF" 1224205 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-531 1221277 1221504 1221841 "IMATLIN" 1222813 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-530 1215855 1221201 1221259 "ILIST" 1221264 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-529 1213760 1215715 1215828 "IIARRAY2" 1215833 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-528 1209158 1213671 1213735 "IFF" 1213740 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-527 1208505 1208775 1208891 "IFAST" 1209062 T IFAST (NIL) -8 NIL NIL NIL) (-526 1203500 1207797 1207985 "IFARRAY" 1208362 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-525 1202680 1203404 1203477 "IFAMON" 1203482 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-524 1202264 1202329 1202383 "IEVALAB" 1202590 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-523 1201939 1202007 1202167 "IEVALAB-" 1202172 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-522 1201570 1201853 1201916 "IDPO" 1201921 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1200820 1201459 1201534 "IDPOAMS" 1201539 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-520 1200127 1200709 1200784 "IDPOAM" 1200789 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-519 1199186 1199462 1199515 "IDPC" 1199928 NIL IDPC (NIL T T) -9 NIL 1200077 NIL) (-518 1198655 1199078 1199151 "IDPAM" 1199156 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-517 1198031 1198547 1198620 "IDPAG" 1198625 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-516 1197676 1197867 1197942 "IDENT" 1197976 T IDENT (NIL) -8 NIL NIL NIL) (-515 1193931 1194779 1195674 "IDECOMP" 1196833 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-514 1186768 1187854 1188901 "IDEAL" 1192967 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-513 1185928 1186040 1186240 "ICDEN" 1186652 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-512 1184999 1185408 1185555 "ICARD" 1185801 T ICARD (NIL) -8 NIL NIL NIL) (-511 1183059 1183372 1183777 "IBPTOOLS" 1184676 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-510 1178666 1182679 1182792 "IBITS" 1182978 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-509 1175389 1175965 1176660 "IBATOOL" 1178083 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-508 1173168 1173630 1174163 "IBACHIN" 1174924 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-507 1170997 1173014 1173117 "IARRAY2" 1173122 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-506 1167103 1170923 1170980 "IARRAY1" 1170985 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-505 1161141 1165515 1165996 "IAN" 1166642 T IAN (NIL) -8 NIL NIL NIL) (-504 1160652 1160709 1160882 "IALGFACT" 1161078 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-503 1160180 1160293 1160321 "HYPCAT" 1160528 T HYPCAT (NIL) -9 NIL NIL NIL) (-502 1159718 1159835 1160021 "HYPCAT-" 1160026 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-501 1159313 1159513 1159596 "HOSTNAME" 1159655 T HOSTNAME (NIL) -8 NIL NIL NIL) (-500 1159158 1159195 1159236 "HOMOTOP" 1159241 NIL HOMOTOP (NIL T) -9 NIL 1159274 NIL) (-499 1155790 1157168 1157209 "HOAGG" 1158190 NIL HOAGG (NIL T) -9 NIL 1158869 NIL) (-498 1154384 1154783 1155309 "HOAGG-" 1155314 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-497 1148293 1153977 1154127 "HEXADEC" 1154254 T HEXADEC (NIL) -8 NIL NIL NIL) (-496 1147041 1147263 1147526 "HEUGCD" 1148070 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-495 1146117 1146878 1147008 "HELLFDIV" 1147013 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-494 1144296 1145894 1145982 "HEAP" 1146061 NIL HEAP (NIL T) -8 NIL NIL NIL) (-493 1143559 1143848 1143982 "HEADAST" 1144182 T HEADAST (NIL) -8 NIL NIL NIL) (-492 1137569 1143474 1143536 "HDP" 1143541 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-491 1131468 1137204 1137356 "HDMP" 1137470 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-490 1130792 1130932 1131096 "HB" 1131324 T HB (NIL) -7 NIL NIL NIL) (-489 1124178 1130638 1130742 "HASHTBL" 1130747 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-488 1123654 1123899 1123991 "HASAST" 1124106 T HASAST (NIL) -8 NIL NIL NIL) (-487 1121432 1123276 1123458 "HACKPI" 1123492 T HACKPI (NIL) -8 NIL NIL NIL) (-486 1117100 1121285 1121398 "GTSET" 1121403 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-485 1110515 1116978 1117076 "GSTBL" 1117081 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-484 1102793 1109546 1109811 "GSERIES" 1110306 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-483 1101934 1102351 1102379 "GROUP" 1102582 T GROUP (NIL) -9 NIL 1102716 NIL) (-482 1101300 1101459 1101710 "GROUP-" 1101715 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-481 1099667 1099988 1100375 "GROEBSOL" 1100977 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-480 1098581 1098869 1098920 "GRMOD" 1099449 NIL GRMOD (NIL T T) -9 NIL 1099617 NIL) (-479 1098349 1098385 1098513 "GRMOD-" 1098518 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-478 1093639 1094703 1095703 "GRIMAGE" 1097369 T GRIMAGE (NIL) -8 NIL NIL NIL) (-477 1092105 1092366 1092690 "GRDEF" 1093335 T GRDEF (NIL) -7 NIL NIL NIL) (-476 1091549 1091665 1091806 "GRAY" 1091984 T GRAY (NIL) -7 NIL NIL NIL) (-475 1090736 1091142 1091193 "GRALG" 1091346 NIL GRALG (NIL T T) -9 NIL 1091439 NIL) (-474 1090397 1090470 1090633 "GRALG-" 1090638 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-473 1087174 1089982 1090160 "GPOLSET" 1090304 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-472 1086528 1086585 1086843 "GOSPER" 1087111 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-471 1082260 1082966 1083492 "GMODPOL" 1086227 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-470 1081265 1081449 1081687 "GHENSEL" 1082072 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-469 1075421 1076264 1077284 "GENUPS" 1080349 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-468 1075118 1075169 1075258 "GENUFACT" 1075364 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-467 1074530 1074607 1074772 "GENPGCD" 1075036 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-466 1074004 1074039 1074252 "GENMFACT" 1074489 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-465 1072570 1072827 1073134 "GENEEZ" 1073747 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-464 1066629 1072181 1072343 "GDMP" 1072493 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-463 1055972 1060400 1061506 "GCNAALG" 1065612 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-462 1054299 1055161 1055189 "GCDDOM" 1055444 T GCDDOM (NIL) -9 NIL 1055601 NIL) (-461 1053769 1053896 1054111 "GCDDOM-" 1054116 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-460 1052441 1052626 1052930 "GB" 1053548 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-459 1041057 1043387 1045779 "GBINTERN" 1050132 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-458 1038894 1039186 1039607 "GBF" 1040732 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-457 1037675 1037840 1038107 "GBEUCLID" 1038710 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-456 1037024 1037149 1037298 "GAUSSFAC" 1037546 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-455 1035391 1035693 1036007 "GALUTIL" 1036743 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-454 1033699 1033973 1034297 "GALPOLYU" 1035118 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-453 1031064 1031354 1031761 "GALFACTU" 1033396 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-452 1022870 1024369 1025977 "GALFACT" 1029496 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-451 1020258 1020916 1020944 "FVFUN" 1022100 T FVFUN (NIL) -9 NIL 1022820 NIL) (-450 1019524 1019706 1019734 "FVC" 1020025 T FVC (NIL) -9 NIL 1020208 NIL) (-449 1019167 1019349 1019417 "FUNDESC" 1019476 T FUNDESC (NIL) -8 NIL NIL NIL) (-448 1018782 1018964 1019045 "FUNCTION" 1019119 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-447 1016526 1017104 1017570 "FT" 1018336 T FT (NIL) -8 NIL NIL NIL) (-446 1015317 1015827 1016030 "FTEM" 1016343 T FTEM (NIL) -8 NIL NIL NIL) (-445 1013608 1013897 1014294 "FSUPFACT" 1015008 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-444 1012005 1012294 1012626 "FST" 1013296 T FST (NIL) -8 NIL NIL NIL) (-443 1011204 1011310 1011498 "FSRED" 1011887 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-442 1009903 1010159 1010506 "FSPRMELT" 1010919 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-441 1007209 1007647 1008133 "FSPECF" 1009466 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-440 988581 997052 997093 "FS" 1000977 NIL FS (NIL T) -9 NIL 1003266 NIL) (-439 977224 980217 984274 "FS-" 984574 NIL FS- (NIL T T) -8 NIL NIL NIL) (-438 976752 976806 976976 "FSINT" 977165 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-437 975044 975745 976048 "FSERIES" 976531 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-436 974086 974202 974426 "FSCINT" 974924 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-435 970294 973030 973071 "FSAGG" 973441 NIL FSAGG (NIL T) -9 NIL 973700 NIL) (-434 968056 968657 969453 "FSAGG-" 969548 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-433 967098 967241 967468 "FSAGG2" 967909 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-432 964780 965060 965607 "FS2UPS" 966816 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-431 964414 964457 964586 "FS2" 964731 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-430 963292 963463 963765 "FS2EXPXP" 964239 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-429 962718 962833 962985 "FRUTIL" 963172 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-428 954131 958213 959571 "FR" 961392 NIL FR (NIL T) -8 NIL NIL NIL) (-427 949145 951820 951860 "FRNAALG" 953180 NIL FRNAALG (NIL T) -9 NIL 953778 NIL) (-426 944818 945894 947169 "FRNAALG-" 947919 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-425 944456 944499 944626 "FRNAAF2" 944769 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-424 942831 943305 943601 "FRMOD" 944268 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-423 940574 941206 941524 "FRIDEAL" 942622 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-422 939765 939852 940143 "FRIDEAL2" 940481 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-421 938898 939312 939353 "FRETRCT" 939358 NIL FRETRCT (NIL T) -9 NIL 939534 NIL) (-420 938010 938241 938592 "FRETRCT-" 938597 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-419 935098 936308 936367 "FRAMALG" 937249 NIL FRAMALG (NIL T T) -9 NIL 937541 NIL) (-418 933232 933687 934317 "FRAMALG-" 934540 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-417 927062 932705 932982 "FRAC" 932987 NIL FRAC (NIL T) -8 NIL NIL NIL) (-416 926698 926755 926862 "FRAC2" 926999 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-415 926334 926391 926498 "FR2" 926635 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-414 920847 923740 923768 "FPS" 924887 T FPS (NIL) -9 NIL 925444 NIL) (-413 920296 920405 920569 "FPS-" 920715 NIL FPS- (NIL T) -8 NIL NIL NIL) (-412 917598 919267 919295 "FPC" 919520 T FPC (NIL) -9 NIL 919662 NIL) (-411 917391 917431 917528 "FPC-" 917533 NIL FPC- (NIL T) -8 NIL NIL NIL) (-410 916181 916879 916920 "FPATMAB" 916925 NIL FPATMAB (NIL T) -9 NIL 917077 NIL) (-409 913854 914357 914783 "FPARFRAC" 915818 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-408 909248 909746 910428 "FORTRAN" 913286 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-407 906964 907464 908003 "FORT" 908729 T FORT (NIL) -7 NIL NIL NIL) (-406 904640 905202 905230 "FORTFN" 906290 T FORTFN (NIL) -9 NIL 906914 NIL) (-405 904404 904454 904482 "FORTCAT" 904541 T FORTCAT (NIL) -9 NIL 904603 NIL) (-404 902510 903020 903410 "FORMULA" 904034 T FORMULA (NIL) -8 NIL NIL NIL) (-403 902298 902328 902397 "FORMULA1" 902474 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-402 901821 901873 902046 "FORDER" 902240 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-401 900917 901081 901274 "FOP" 901648 T FOP (NIL) -7 NIL NIL NIL) (-400 899498 900197 900371 "FNLA" 900799 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-399 898227 898642 898670 "FNCAT" 899130 T FNCAT (NIL) -9 NIL 899390 NIL) (-398 897766 898186 898214 "FNAME" 898219 T FNAME (NIL) -8 NIL NIL NIL) (-397 896329 897292 897320 "FMTC" 897325 T FMTC (NIL) -9 NIL 897361 NIL) (-396 895075 896265 896311 "FMONOID" 896316 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-395 891903 893071 893112 "FMONCAT" 894329 NIL FMONCAT (NIL T) -9 NIL 894934 NIL) (-394 891095 891645 891794 "FM" 891799 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 888519 889165 889193 "FMFUN" 890337 T FMFUN (NIL) -9 NIL 891045 NIL) (-392 887788 887969 887997 "FMC" 888287 T FMC (NIL) -9 NIL 888469 NIL) (-391 884867 885727 885781 "FMCAT" 886976 NIL FMCAT (NIL T T) -9 NIL 887471 NIL) (-390 883733 884633 884733 "FM1" 884812 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-389 881507 881923 882417 "FLOATRP" 883284 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-388 875085 879236 879857 "FLOAT" 880906 T FLOAT (NIL) -8 NIL NIL NIL) (-387 872523 873023 873601 "FLOATCP" 874552 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-386 871370 872129 872170 "FLINEXP" 872175 NIL FLINEXP (NIL T) -9 NIL 872268 NIL) (-385 870302 870599 871007 "FLINEXP-" 871012 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-384 869378 869522 869746 "FLASORT" 870154 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-383 866494 867362 867414 "FLALG" 868641 NIL FLALG (NIL T T) -9 NIL 869108 NIL) (-382 860198 863950 863991 "FLAGG" 865253 NIL FLAGG (NIL T) -9 NIL 865905 NIL) (-381 858924 859263 859753 "FLAGG-" 859758 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-380 857966 858109 858336 "FLAGG2" 858777 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-379 854817 855825 855884 "FINRALG" 857012 NIL FINRALG (NIL T T) -9 NIL 857520 NIL) (-378 853977 854206 854545 "FINRALG-" 854550 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-377 853357 853596 853624 "FINITE" 853820 T FINITE (NIL) -9 NIL 853927 NIL) (-376 845714 847901 847941 "FINAALG" 851608 NIL FINAALG (NIL T) -9 NIL 853061 NIL) (-375 841046 842096 843240 "FINAALG-" 844619 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-374 840414 840801 840904 "FILE" 840976 NIL FILE (NIL T) -8 NIL NIL NIL) (-373 839072 839410 839464 "FILECAT" 840148 NIL FILECAT (NIL T T) -9 NIL 840364 NIL) (-372 836788 838316 838344 "FIELD" 838384 T FIELD (NIL) -9 NIL 838464 NIL) (-371 835408 835793 836304 "FIELD-" 836309 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-370 833258 834043 834390 "FGROUP" 835094 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-369 832348 832512 832732 "FGLMICPK" 833090 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-368 828180 832273 832330 "FFX" 832335 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-367 827781 827842 827977 "FFSLPE" 828113 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-366 823771 824553 825349 "FFPOLY" 827017 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-365 823275 823311 823520 "FFPOLY2" 823729 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-364 819121 823194 823257 "FFP" 823262 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-363 814519 819032 819096 "FF" 819101 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-362 809645 813862 814052 "FFNBX" 814373 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-361 804573 808780 809038 "FFNBP" 809499 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-360 799206 803857 804068 "FFNB" 804406 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-359 798038 798236 798551 "FFINTBAS" 799003 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-358 794064 796285 796313 "FFIELDC" 796933 T FFIELDC (NIL) -9 NIL 797309 NIL) (-357 792726 793097 793594 "FFIELDC-" 793599 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-356 792295 792341 792465 "FFHOM" 792668 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-355 789990 790477 790994 "FFF" 791810 NIL FFF (NIL T) -7 NIL NIL NIL) (-354 785608 789732 789833 "FFCGX" 789933 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-353 781230 785340 785447 "FFCGP" 785551 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-352 776413 780957 781065 "FFCG" 781166 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-351 757348 766533 766619 "FFCAT" 771784 NIL FFCAT (NIL T T T) -9 NIL 773235 NIL) (-350 752545 753593 754907 "FFCAT-" 756137 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-349 751956 751999 752234 "FFCAT2" 752496 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-348 741279 744928 746148 "FEXPR" 750808 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-347 740241 740676 740717 "FEVALAB" 740801 NIL FEVALAB (NIL T) -9 NIL 741062 NIL) (-346 739400 739610 739948 "FEVALAB-" 739953 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-345 737966 738783 738986 "FDIV" 739299 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-344 734986 735727 735842 "FDIVCAT" 737410 NIL FDIVCAT (NIL T T T T) -9 NIL 737847 NIL) (-343 734748 734775 734945 "FDIVCAT-" 734950 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-342 733968 734055 734332 "FDIV2" 734655 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 732942 733263 733465 "FCTRDATA" 733786 T FCTRDATA (NIL) -8 NIL NIL NIL) (-340 731628 731887 732176 "FCPAK1" 732673 T FCPAK1 (NIL) -7 NIL NIL NIL) (-339 730727 731128 731269 "FCOMP" 731519 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-338 714432 717877 721415 "FC" 727209 T FC (NIL) -8 NIL NIL NIL) (-337 706711 710739 710779 "FAXF" 712581 NIL FAXF (NIL T) -9 NIL 713273 NIL) (-336 703988 704645 705470 "FAXF-" 705935 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-335 699040 703364 703540 "FARRAY" 703845 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-334 693934 696001 696054 "FAMR" 697077 NIL FAMR (NIL T T) -9 NIL 697537 NIL) (-333 692824 693126 693561 "FAMR-" 693566 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-332 691993 692746 692799 "FAMONOID" 692804 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-331 689779 690489 690542 "FAMONC" 691483 NIL FAMONC (NIL T T) -9 NIL 691869 NIL) (-330 688443 689533 689670 "FAGROUP" 689675 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-329 686238 686557 686960 "FACUTIL" 688124 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-328 685337 685522 685744 "FACTFUNC" 686048 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-327 677759 684640 684839 "EXPUPXS" 685193 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-326 675242 675782 676368 "EXPRTUBE" 677193 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-325 671513 672105 672835 "EXPRODE" 674581 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-324 657232 670162 670591 "EXPR" 671117 NIL EXPR (NIL T) -8 NIL NIL NIL) (-323 651786 652373 653179 "EXPR2UPS" 656530 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-322 651418 651475 651584 "EXPR2" 651723 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-321 642671 650569 650860 "EXPEXPAN" 651254 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-320 642471 642628 642657 "EXIT" 642662 T EXIT (NIL) -8 NIL NIL NIL) (-319 641951 642195 642286 "EXITAST" 642400 T EXITAST (NIL) -8 NIL NIL NIL) (-318 641578 641640 641753 "EVALCYC" 641883 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-317 641119 641237 641278 "EVALAB" 641448 NIL EVALAB (NIL T) -9 NIL 641552 NIL) (-316 640600 640722 640943 "EVALAB-" 640948 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-315 637968 639270 639298 "EUCDOM" 639853 T EUCDOM (NIL) -9 NIL 640203 NIL) (-314 636373 636815 637405 "EUCDOM-" 637410 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-313 623912 626671 629421 "ESTOOLS" 633643 T ESTOOLS (NIL) -7 NIL NIL NIL) (-312 623544 623601 623710 "ESTOOLS2" 623849 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-311 623295 623337 623417 "ESTOOLS1" 623496 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-310 617332 618940 618968 "ES" 621736 T ES (NIL) -9 NIL 623146 NIL) (-309 612279 613566 615383 "ES-" 615547 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 608653 609414 610194 "ESCONT" 611519 T ESCONT (NIL) -7 NIL NIL NIL) (-307 608398 608430 608512 "ESCONT1" 608615 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-306 608073 608123 608223 "ES2" 608342 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-305 607703 607761 607870 "ES1" 608009 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-304 606919 607048 607224 "ERROR" 607547 T ERROR (NIL) -7 NIL NIL NIL) (-303 600311 606778 606869 "EQTBL" 606874 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-302 592814 595625 597074 "EQ" 598895 NIL -2086 (NIL T) -8 NIL NIL NIL) (-301 592446 592503 592612 "EQ2" 592751 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-300 587737 588784 589877 "EP" 591385 NIL EP (NIL T) -7 NIL NIL NIL) (-299 586337 586628 586934 "ENV" 587451 T ENV (NIL) -8 NIL NIL NIL) (-298 585431 585985 586013 "ENTIRER" 586018 T ENTIRER (NIL) -9 NIL 586064 NIL) (-297 582125 583613 583974 "EMR" 585239 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-296 581255 581440 581494 "ELTAGG" 581874 NIL ELTAGG (NIL T T) -9 NIL 582085 NIL) (-295 580974 581036 581177 "ELTAGG-" 581182 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-294 580738 580767 580821 "ELTAB" 580905 NIL ELTAB (NIL T T) -9 NIL 580957 NIL) (-293 579864 580010 580209 "ELFUTS" 580589 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-292 579606 579662 579690 "ELEMFUN" 579795 T ELEMFUN (NIL) -9 NIL NIL NIL) (-291 579476 579497 579565 "ELEMFUN-" 579570 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-290 574290 577546 577587 "ELAGG" 578527 NIL ELAGG (NIL T) -9 NIL 578990 NIL) (-289 572575 573009 573672 "ELAGG-" 573677 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-288 571887 572024 572180 "ELABOR" 572439 T ELABOR (NIL) -8 NIL NIL NIL) (-287 570548 570827 571121 "ELABEXPR" 571613 T ELABEXPR (NIL) -8 NIL NIL NIL) (-286 563412 565215 566042 "EFUPXS" 569824 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-285 556862 558663 559473 "EFULS" 562688 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-284 554347 554705 555177 "EFSTRUC" 556494 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-283 544138 545704 547252 "EF" 552862 NIL EF (NIL T T) -7 NIL NIL NIL) (-282 543212 543623 543772 "EAB" 544009 T EAB (NIL) -8 NIL NIL NIL) (-281 542394 543171 543199 "E04UCFA" 543204 T E04UCFA (NIL) -8 NIL NIL NIL) (-280 541576 542353 542381 "E04NAFA" 542386 T E04NAFA (NIL) -8 NIL NIL NIL) (-279 540758 541535 541563 "E04MBFA" 541568 T E04MBFA (NIL) -8 NIL NIL NIL) (-278 539940 540717 540745 "E04JAFA" 540750 T E04JAFA (NIL) -8 NIL NIL NIL) (-277 539124 539899 539927 "E04GCFA" 539932 T E04GCFA (NIL) -8 NIL NIL NIL) (-276 538308 539083 539111 "E04FDFA" 539116 T E04FDFA (NIL) -8 NIL NIL NIL) (-275 537490 538267 538295 "E04DGFA" 538300 T E04DGFA (NIL) -8 NIL NIL NIL) (-274 531663 533015 534379 "E04AGNT" 536146 T E04AGNT (NIL) -7 NIL NIL NIL) (-273 530434 530977 531017 "DVARCAT" 531358 NIL DVARCAT (NIL T) -9 NIL 531521 NIL) (-272 529638 529850 530164 "DVARCAT-" 530169 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-271 522686 529437 529566 "DSMP" 529571 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-270 517467 518631 519699 "DROPT" 521638 T DROPT (NIL) -8 NIL NIL NIL) (-269 517132 517191 517289 "DROPT1" 517402 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 512247 513373 514510 "DROPT0" 516015 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 510592 510917 511303 "DRAWPT" 511881 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 505179 506102 507181 "DRAW" 509566 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 504812 504865 504983 "DRAWHACK" 505120 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 503543 503812 504103 "DRAWCX" 504541 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 503058 503127 503278 "DRAWCURV" 503469 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 493526 495488 497603 "DRAWCFUN" 500963 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 490290 492219 492260 "DQAGG" 492889 NIL DQAGG (NIL T) -9 NIL 493163 NIL) (-260 478200 484758 484841 "DPOLCAT" 486693 NIL DPOLCAT (NIL T T T T) -9 NIL 487238 NIL) (-259 473037 474385 476343 "DPOLCAT-" 476348 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 467343 472898 472996 "DPMO" 473001 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 461552 467123 467290 "DPMM" 467295 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 461122 461336 461425 "DOMTMPLT" 461483 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 460555 460924 461004 "DOMCTOR" 461062 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 459767 460035 460186 "DOMAIN" 460424 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 453666 459402 459554 "DMP" 459668 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 453266 453322 453466 "DLP" 453604 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 447088 452593 452783 "DLIST" 453108 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 443885 445941 445982 "DLAGG" 446532 NIL DLAGG (NIL T) -9 NIL 446762 NIL) (-249 442561 443225 443253 "DIVRING" 443345 T DIVRING (NIL) -9 NIL 443428 NIL) (-248 441798 441988 442288 "DIVRING-" 442293 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 439900 440257 440663 "DISPLAY" 441412 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 433930 439814 439877 "DIRPROD" 439882 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 432778 432981 433246 "DIRPROD2" 433723 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 422068 427933 427986 "DIRPCAT" 428244 NIL DIRPCAT (NIL NIL T) -9 NIL 429042 NIL) (-243 419172 419876 420837 "DIRPCAT-" 421174 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 418459 418619 418805 "DIOSP" 419006 T DIOSP (NIL) -7 NIL NIL NIL) (-241 415114 417371 417412 "DIOPS" 417846 NIL DIOPS (NIL T) -9 NIL 418075 NIL) (-240 414663 414777 414968 "DIOPS-" 414973 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 413714 414342 414370 "DIFRING" 414375 T DIFRING (NIL) -9 NIL 414397 NIL) (-238 413386 413460 413488 "DIFFSPC" 413607 T DIFFSPC (NIL) -9 NIL 413682 NIL) (-237 413031 413109 413261 "DIFFSPC-" 413266 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 412187 412665 412705 "DIFFMOD" 412710 NIL DIFFMOD (NIL T) -9 NIL 412737 NIL) (-235 411895 411940 411981 "DIFFDOM" 412102 NIL DIFFDOM (NIL T) -9 NIL 412170 NIL) (-234 411748 411772 411856 "DIFFDOM-" 411861 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 409400 410672 410713 "DIFEXT" 411076 NIL DIFEXT (NIL T) -9 NIL 411370 NIL) (-232 407685 408113 408779 "DIFEXT-" 408784 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 404960 407217 407258 "DIAGG" 407263 NIL DIAGG (NIL T) -9 NIL 407283 NIL) (-230 404344 404501 404753 "DIAGG-" 404758 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 399761 403303 403580 "DHMATRIX" 404113 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 395373 396282 397292 "DFSFUN" 398771 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 390453 394304 394616 "DFLOAT" 395081 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 388716 388997 389386 "DFINTTLS" 390161 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 385745 386737 387137 "DERHAM" 388382 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 383546 385520 385609 "DEQUEUE" 385689 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 382800 382933 383116 "DEGRED" 383408 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 379230 379975 380821 "DEFINTRF" 382028 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 376785 377254 377846 "DEFINTEF" 378749 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 376135 376405 376520 "DEFAST" 376690 T DEFAST (NIL) -8 NIL NIL NIL) (-219 370044 375728 375878 "DECIMAL" 376005 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 367556 368014 368520 "DDFACT" 369588 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 367152 367195 367346 "DBLRESP" 367507 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 365020 365382 365743 "DBASE" 366918 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 364262 364500 364646 "DATAARY" 364919 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 363368 364221 364249 "D03FAFA" 364254 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 362475 363327 363355 "D03EEFA" 363360 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 360425 360891 361380 "D03AGNT" 362006 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 359714 360384 360412 "D02EJFA" 360417 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 359003 359673 359701 "D02CJFA" 359706 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 358292 358962 358990 "D02BHFA" 358995 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 357581 358251 358279 "D02BBFA" 358284 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 350778 352367 353973 "D02AGNT" 355995 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 348546 349069 349615 "D01WGTS" 350252 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 347613 348505 348533 "D01TRNS" 348538 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 346681 347572 347600 "D01GBFA" 347605 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 345749 346640 346668 "D01FCFA" 346673 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 344817 345708 345736 "D01ASFA" 345741 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 343885 344776 344804 "D01AQFA" 344809 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 342953 343844 343872 "D01APFA" 343877 T D01APFA (NIL) -8 NIL NIL NIL) (-199 342021 342912 342940 "D01ANFA" 342945 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 341089 341980 342008 "D01AMFA" 342013 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 340157 341048 341076 "D01ALFA" 341081 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 339225 340116 340144 "D01AKFA" 340149 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 338293 339184 339212 "D01AJFA" 339217 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 331588 333141 334702 "D01AGNT" 336752 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 330925 331053 331205 "CYCLOTOM" 331456 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 327658 328373 329100 "CYCLES" 330218 T CYCLES (NIL) -7 NIL NIL NIL) (-191 326970 327104 327275 "CVMP" 327519 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 324811 325069 325438 "CTRIGMNP" 326698 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 324247 324605 324678 "CTOR" 324758 T CTOR (NIL) -8 NIL NIL NIL) (-188 323756 323978 324079 "CTORKIND" 324166 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 323047 323363 323391 "CTORCAT" 323573 T CTORCAT (NIL) -9 NIL 323686 NIL) (-186 322645 322756 322915 "CTORCAT-" 322920 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 322107 322319 322427 "CTORCALL" 322569 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 321481 321580 321733 "CSTTOOLS" 322004 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 317280 317937 318695 "CRFP" 320793 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 316755 317001 317093 "CRCEAST" 317208 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 315802 315987 316215 "CRAPACK" 316559 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 315186 315287 315491 "CPMATCH" 315678 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 314911 314939 315045 "CPIMA" 315152 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 311259 311931 312650 "COORDSYS" 314246 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 310671 310792 310934 "CONTOUR" 311137 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 306562 308674 309166 "CONTFRAC" 310211 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 306442 306463 306491 "CONDUIT" 306528 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 305530 306084 306112 "COMRING" 306117 T COMRING (NIL) -9 NIL 306169 NIL) (-173 304584 304888 305072 "COMPPROP" 305366 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 304245 304280 304408 "COMPLPAT" 304543 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 294447 304054 304163 "COMPLEX" 304168 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 294083 294140 294247 "COMPLEX2" 294384 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 293422 293543 293703 "COMPILER" 293943 T COMPILER (NIL) -8 NIL NIL NIL) (-168 293140 293175 293273 "COMPFACT" 293381 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 276977 287061 287101 "COMPCAT" 288105 NIL COMPCAT (NIL T) -9 NIL 289453 NIL) (-166 266267 269256 272963 "COMPCAT-" 273319 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 265996 266024 266127 "COMMUPC" 266233 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265790 265824 265883 "COMMONOP" 265957 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 265346 265541 265628 "COMM" 265723 T COMM (NIL) -8 NIL NIL NIL) (-162 264922 265150 265225 "COMMAAST" 265291 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 264171 264365 264393 "COMBOPC" 264731 T COMBOPC (NIL) -9 NIL 264906 NIL) (-160 263067 263277 263519 "COMBINAT" 263961 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 259524 260098 260725 "COMBF" 262489 NIL COMBF (NIL T T) -7 NIL NIL NIL) 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T) ((-294 |#2| $) -12 (|has| |#1| (-372)) (|has| |#2| (-294 |#2| |#2|))) ((-294 $ $) |has| (-574) (-1128)) ((-298) -2833 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-315) |has| |#1| (-372)) ((-317 |#2|) -12 (|has| |#1| (-372)) (|has| |#2| (-317 |#2|))) ((-372) |has| |#1| (-372)) ((-347 |#2|) |has| |#1| (-372)) ((-386 |#2|) |has| |#1| (-372)) ((-410 |#2|) |has| |#1| (-372)) ((-462) |has| |#1| (-372)) ((-503) |has| |#1| (-38 (-417 (-574)))) ((-524 (-1193) |#2|) -12 (|has| |#1| (-372)) (|has| |#2| (-524 (-1193) |#2|))) ((-524 |#2| |#2|) -12 (|has| |#1| (-372)) (|has| |#2| (-317 |#2|))) ((-566) -2833 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-656 #1#) -2833 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-656 (-574)) . T) ((-656 |#1|) . T) ((-656 |#2|) |has| |#1| (-372)) ((-656 $) . T) ((-658 #1#) -2833 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-658 #3=(-574)) -12 (|has| |#1| (-372)) (|has| |#2| (-649 (-574)))) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-372)) ((-658 $) . T) ((-650 #1#) -2833 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-650 |#1|) |has| |#1| (-174)) ((-650 |#2|) |has| |#1| (-372)) ((-650 $) -2833 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-649 #3#) -12 (|has| |#1| (-372)) (|has| |#2| (-649 (-574)))) ((-649 |#2|) |has| |#1| (-372)) ((-727 #1#) -2833 (|has| |#1| (-372)) (|has| |#1| (-38 (-417 (-574))))) ((-727 |#1|) |has| |#1| (-174)) ((-727 |#2|) |has| |#1| (-372)) ((-727 $) -2833 (|has| |#1| (-566)) (|has| |#1| (-372))) ((-736) . 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NIL) (-1245 2975138 2975383 2975771 "ULSCCAT-" 2975776 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1244 2964202 2970685 2970728 "ULSCAT" 2971591 NIL ULSCAT (NIL T) -9 NIL 2972322 NIL) (-1243 2963632 2963711 2963890 "ULS2" 2964117 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1242 2962751 2963261 2963368 "UINT8" 2963479 T UINT8 (NIL) -8 NIL NIL 2963564) (-1241 2961869 2962379 2962486 "UINT64" 2962597 T UINT64 (NIL) -8 NIL NIL 2962682) (-1240 2960987 2961497 2961604 "UINT32" 2961715 T UINT32 (NIL) -8 NIL NIL 2961800) (-1239 2960105 2960615 2960722 "UINT16" 2960833 T UINT16 (NIL) -8 NIL NIL 2960918) (-1238 2958408 2959365 2959395 "UFD" 2959607 T UFD (NIL) -9 NIL 2959721 NIL) (-1237 2958202 2958248 2958343 "UFD-" 2958348 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1236 2957284 2957467 2957683 "UDVO" 2958008 T UDVO (NIL) -7 NIL NIL NIL) (-1235 2955100 2955509 2955980 "UDPO" 2956848 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1234 2955033 2955038 2955068 "TYPE" 2955073 T TYPE (NIL) -9 NIL NIL NIL) (-1233 2954793 2954988 2955019 "TYPEAST" 2955024 T TYPEAST (NIL) -8 NIL NIL NIL) (-1232 2953764 2953966 2954206 "TWOFACT" 2954587 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1231 2952787 2953173 2953408 "TUPLE" 2953564 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1230 2950478 2950997 2951536 "TUBETOOL" 2952270 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1229 2949327 2949532 2949773 "TUBE" 2950271 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1228 2944056 2948299 2948582 "TS" 2949079 NIL TS (NIL T) -8 NIL NIL NIL) (-1227 2932696 2936815 2936912 "TSETCAT" 2942181 NIL TSETCAT (NIL T T T T) -9 NIL 2943712 NIL) (-1226 2927428 2929028 2930919 "TSETCAT-" 2930924 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1225 2922067 2922914 2923843 "TRMANIP" 2926564 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1224 2921508 2921571 2921734 "TRIMAT" 2921999 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1223 2919374 2919611 2919968 "TRIGMNIP" 2921257 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1222 2918894 2919007 2919037 "TRIGCAT" 2919250 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1221 2918563 2918642 2918783 "TRIGCAT-" 2918788 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1220 2915408 2917421 2917702 "TREE" 2918317 NIL TREE (NIL T) -8 NIL NIL NIL) (-1219 2914682 2915210 2915240 "TRANFUN" 2915275 T TRANFUN (NIL) -9 NIL 2915341 NIL) (-1218 2913961 2914152 2914432 "TRANFUN-" 2914437 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1217 2913765 2913797 2913858 "TOPSP" 2913922 T TOPSP (NIL) -7 NIL NIL NIL) (-1216 2913113 2913228 2913382 "TOOLSIGN" 2913646 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1215 2911747 2912290 2912529 "TEXTFILE" 2912896 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1214 2909659 2910200 2910629 "TEX" 2911340 T TEX (NIL) -8 NIL NIL NIL) (-1213 2909440 2909471 2909543 "TEX1" 2909622 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1212 2909088 2909151 2909241 "TEMUTL" 2909372 T TEMUTL (NIL) -7 NIL NIL NIL) (-1211 2907242 2907522 2907847 "TBCMPPK" 2908811 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1210 2899019 2905402 2905458 "TBAGG" 2905858 NIL TBAGG (NIL T T) -9 NIL 2906069 NIL) (-1209 2894089 2895577 2897331 "TBAGG-" 2897336 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1208 2893473 2893580 2893725 "TANEXP" 2893978 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1207 2892984 2893248 2893338 "TALGOP" 2893418 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1206 2886374 2892841 2892934 "TABLE" 2892939 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1205 2885786 2885885 2886023 "TABLEAU" 2886271 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1204 2880394 2881614 2882862 "TABLBUMP" 2884572 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1203 2879616 2879763 2879944 "SYSTEM" 2880235 T SYSTEM (NIL) -8 NIL NIL NIL) (-1202 2876075 2876774 2877557 "SYSSOLP" 2878867 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1201 2875873 2876030 2876061 "SYSPTR" 2876066 T SYSPTR (NIL) -8 NIL NIL NIL) (-1200 2874909 2875414 2875533 "SYSNNI" 2875719 NIL SYSNNI (NIL NIL) -8 NIL NIL 2875804) (-1199 2874208 2874667 2874746 "SYSINT" 2874806 NIL SYSINT (NIL NIL) -8 NIL NIL 2874851) (-1198 2870540 2871486 2872196 "SYNTAX" 2873520 T SYNTAX (NIL) -8 NIL NIL NIL) (-1197 2867698 2868300 2868932 "SYMTAB" 2869930 T SYMTAB (NIL) -8 NIL NIL NIL) (-1196 2862947 2863849 2864832 "SYMS" 2866737 T SYMS (NIL) -8 NIL NIL NIL) (-1195 2860182 2862405 2862635 "SYMPOLY" 2862752 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1194 2859699 2859774 2859897 "SYMFUNC" 2860094 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1193 2855719 2857011 2857824 "SYMBOL" 2858908 T SYMBOL (NIL) -8 NIL NIL NIL) (-1192 2849258 2850947 2852667 "SWITCH" 2854021 T SWITCH (NIL) -8 NIL NIL NIL) (-1191 2842492 2848079 2848382 "SUTS" 2849013 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1190 2834558 2841739 2842012 "SUPXS" 2842277 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1189 2826228 2834176 2834302 "SUP" 2834467 NIL SUP (NIL T) -8 NIL NIL NIL) (-1188 2825387 2825514 2825731 "SUPFRACF" 2826096 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1187 2825008 2825067 2825180 "SUP2" 2825322 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1186 2823456 2823730 2824086 "SUMRF" 2824707 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1185 2822791 2822857 2823049 "SUMFS" 2823377 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1184 2806587 2821968 2822219 "SULS" 2822598 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1183 2806189 2806409 2806479 "SUCHTAST" 2806539 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1182 2805484 2805714 2805854 "SUCH" 2806097 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1181 2799351 2800390 2801349 "SUBSPACE" 2804572 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1180 2798781 2798871 2799035 "SUBRESP" 2799239 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1179 2792149 2793446 2794757 "STTF" 2797517 NIL STTF (NIL T) -7 NIL NIL NIL) (-1178 2786322 2787442 2788589 "STTFNC" 2791049 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1177 2777635 2779504 2781298 "STTAYLOR" 2784563 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1176 2770765 2777499 2777582 "STRTBL" 2777587 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1175 2766129 2770720 2770751 "STRING" 2770756 T STRING (NIL) -8 NIL NIL NIL) (-1174 2760958 2765472 2765502 "STRICAT" 2765561 T STRICAT (NIL) -9 NIL 2765623 NIL) (-1173 2753711 2758577 2759188 "STREAM" 2760382 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1172 2753221 2753298 2753442 "STREAM3" 2753628 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1171 2752203 2752386 2752621 "STREAM2" 2753034 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1170 2751891 2751943 2752036 "STREAM1" 2752145 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1169 2750907 2751088 2751319 "STINPROD" 2751707 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1168 2750459 2750669 2750699 "STEP" 2750779 T STEP (NIL) -9 NIL 2750857 NIL) (-1167 2749646 2749948 2750096 "STEPAST" 2750333 T STEPAST (NIL) -8 NIL NIL NIL) (-1166 2743078 2749545 2749622 "STBL" 2749627 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1165 2738173 2742269 2742312 "STAGG" 2742465 NIL STAGG (NIL T) -9 NIL 2742554 NIL) (-1164 2735875 2736477 2737349 "STAGG-" 2737354 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1163 2734022 2735645 2735737 "STACK" 2735818 NIL STACK (NIL T) -8 NIL NIL NIL) (-1162 2726717 2732163 2732619 "SREGSET" 2733652 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1161 2719142 2720511 2722024 "SRDCMPK" 2725323 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1160 2712027 2716552 2716582 "SRAGG" 2717885 T SRAGG (NIL) -9 NIL 2718493 NIL) (-1159 2711044 2711299 2711678 "SRAGG-" 2711683 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1158 2705415 2709991 2710412 "SQMATRIX" 2710670 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1157 2699100 2702133 2702860 "SPLTREE" 2704760 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1156 2695063 2695756 2696402 "SPLNODE" 2698526 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1155 2694110 2694343 2694373 "SPFCAT" 2694817 T SPFCAT (NIL) -9 NIL NIL NIL) (-1154 2692847 2693057 2693321 "SPECOUT" 2693868 T SPECOUT (NIL) -7 NIL NIL NIL) (-1153 2683957 2685829 2685859 "SPADXPT" 2690535 T SPADXPT (NIL) -9 NIL 2692699 NIL) (-1152 2683718 2683758 2683827 "SPADPRSR" 2683910 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1151 2681767 2683673 2683704 "SPADAST" 2683709 T SPADAST (NIL) -8 NIL NIL NIL) (-1150 2673712 2675485 2675528 "SPACEC" 2679901 NIL SPACEC (NIL T) -9 NIL 2681717 NIL) (-1149 2671842 2673644 2673693 "SPACE3" 2673698 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1148 2670594 2670765 2671056 "SORTPAK" 2671647 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1147 2668686 2668989 2669401 "SOLVETRA" 2670258 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1146 2667736 2667958 2668219 "SOLVESER" 2668459 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1145 2663040 2663928 2664923 "SOLVERAD" 2666788 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1144 2658855 2659464 2660193 "SOLVEFOR" 2662407 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1143 2653125 2658204 2658301 "SNTSCAT" 2658306 NIL SNTSCAT (NIL T T T T) -9 NIL 2658376 NIL) (-1142 2647231 2651448 2651839 "SMTS" 2652815 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1141 2641827 2647119 2647196 "SMP" 2647201 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1140 2639986 2640287 2640685 "SMITH" 2641524 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1139 2632428 2636715 2636818 "SMATCAT" 2638169 NIL SMATCAT (NIL NIL T T T) -9 NIL 2638719 NIL) (-1138 2629146 2630031 2631289 "SMATCAT-" 2631294 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1137 2626812 2628382 2628425 "SKAGG" 2628686 NIL SKAGG (NIL T) -9 NIL 2628821 NIL) (-1136 2623088 2626285 2626469 "SINT" 2626621 T SINT (NIL) -8 NIL NIL 2626783) (-1135 2622860 2622898 2622964 "SIMPAN" 2623044 T SIMPAN (NIL) -7 NIL NIL NIL) (-1134 2622139 2622395 2622535 "SIG" 2622742 T SIG (NIL) -8 NIL NIL NIL) (-1133 2620977 2621198 2621473 "SIGNRF" 2621898 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1132 2619810 2619961 2620245 "SIGNEF" 2620806 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1131 2619116 2619393 2619517 "SIGAST" 2619708 T SIGAST (NIL) -8 NIL NIL NIL) (-1130 2616806 2617260 2617766 "SHP" 2618657 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1129 2610802 2616707 2616783 "SHDP" 2616788 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1128 2610375 2610567 2610597 "SGROUP" 2610690 T SGROUP (NIL) -9 NIL 2610752 NIL) (-1127 2610233 2610259 2610332 "SGROUP-" 2610337 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1126 2607024 2607722 2608445 "SGCF" 2609532 T SGCF (NIL) -7 NIL NIL NIL) (-1125 2601392 2606471 2606568 "SFRTCAT" 2606573 NIL SFRTCAT (NIL T T T T) -9 NIL 2606612 NIL) (-1124 2594813 2595831 2596967 "SFRGCD" 2600375 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1123 2587939 2589012 2590198 "SFQCMPK" 2593746 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1122 2587559 2587648 2587759 "SFORT" 2587880 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1121 2586677 2587399 2587520 "SEXOF" 2587525 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1120 2585784 2586558 2586626 "SEX" 2586631 T SEX (NIL) -8 NIL NIL NIL) (-1119 2581565 2582280 2582375 "SEXCAT" 2584997 NIL SEXCAT (NIL T T T T T) -9 NIL 2585557 NIL) (-1118 2578718 2581499 2581547 "SET" 2581552 NIL SET (NIL T) -8 NIL NIL NIL) (-1117 2576942 2577431 2577736 "SETMN" 2578459 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1116 2576438 2576590 2576620 "SETCAT" 2576796 T SETCAT (NIL) -9 NIL 2576906 NIL) (-1115 2576130 2576208 2576338 "SETCAT-" 2576343 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1114 2572491 2574591 2574634 "SETAGG" 2575504 NIL SETAGG (NIL T) -9 NIL 2575844 NIL) (-1113 2571949 2572065 2572302 "SETAGG-" 2572307 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1112 2571392 2571645 2571746 "SEQAST" 2571870 T SEQAST (NIL) -8 NIL NIL NIL) (-1111 2570591 2570885 2570946 "SEGXCAT" 2571232 NIL SEGXCAT (NIL T T) -9 NIL 2571352 NIL) (-1110 2569597 2570257 2570439 "SEG" 2570444 NIL SEG (NIL T) -8 NIL NIL NIL) (-1109 2568576 2568790 2568833 "SEGCAT" 2569355 NIL SEGCAT (NIL T) -9 NIL 2569576 NIL) (-1108 2567508 2567939 2568147 "SEGBIND" 2568403 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1107 2567129 2567188 2567301 "SEGBIND2" 2567443 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1106 2566702 2566930 2567007 "SEGAST" 2567074 T SEGAST (NIL) -8 NIL NIL NIL) (-1105 2565921 2566047 2566251 "SEG2" 2566546 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1104 2565292 2565856 2565903 "SDVAR" 2565908 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1103 2557730 2565062 2565192 "SDPOL" 2565197 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1102 2556323 2556589 2556908 "SCPKG" 2557445 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1101 2555487 2555659 2555851 "SCOPE" 2556153 T SCOPE (NIL) -8 NIL NIL NIL) (-1100 2554707 2554841 2555020 "SCACHE" 2555342 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1099 2554353 2554539 2554569 "SASTCAT" 2554574 T SASTCAT (NIL) -9 NIL 2554587 NIL) (-1098 2553840 2554188 2554264 "SAOS" 2554299 T SAOS (NIL) -8 NIL NIL NIL) (-1097 2553405 2553440 2553613 "SAERFFC" 2553799 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1096 2547255 2553302 2553382 "SAE" 2553387 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1095 2546848 2546883 2547042 "SAEFACT" 2547214 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1094 2545169 2545483 2545884 "RURPK" 2546514 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1093 2543806 2544112 2544417 "RULESET" 2545003 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1092 2541029 2541559 2542017 "RULE" 2543487 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1091 2540641 2540823 2540906 "RULECOLD" 2540981 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1090 2540431 2540459 2540530 "RTVALUE" 2540592 T RTVALUE (NIL) -8 NIL NIL NIL) (-1089 2539902 2540148 2540242 "RSTRCAST" 2540359 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1088 2534750 2535545 2536465 "RSETGCD" 2539101 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1087 2523980 2529059 2529156 "RSETCAT" 2533275 NIL RSETCAT (NIL T T T T) -9 NIL 2534372 NIL) (-1086 2521907 2522446 2523270 "RSETCAT-" 2523275 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1085 2514293 2515669 2517189 "RSDCMPK" 2520506 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1084 2512272 2512739 2512813 "RRCC" 2513899 NIL RRCC (NIL T T) -9 NIL 2514243 NIL) (-1083 2511623 2511797 2512076 "RRCC-" 2512081 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1082 2511066 2511319 2511420 "RPTAST" 2511544 T RPTAST (NIL) -8 NIL NIL NIL) (-1081 2484729 2494178 2494245 "RPOLCAT" 2504911 NIL RPOLCAT (NIL T T T) -9 NIL 2508071 NIL) (-1080 2476227 2478567 2481689 "RPOLCAT-" 2481694 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1079 2467158 2474438 2474920 "ROUTINE" 2475767 T ROUTINE (NIL) -8 NIL NIL NIL) (-1078 2463905 2466784 2466924 "ROMAN" 2467040 T ROMAN (NIL) -8 NIL NIL NIL) (-1077 2462149 2462765 2463025 "ROIRC" 2463710 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1076 2458381 2460665 2460695 "RNS" 2460999 T RNS (NIL) -9 NIL 2461273 NIL) (-1075 2456890 2457273 2457807 "RNS-" 2457882 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1074 2456293 2456701 2456731 "RNG" 2456736 T RNG (NIL) -9 NIL 2456757 NIL) (-1073 2455296 2455658 2455860 "RNGBIND" 2456144 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1072 2454695 2455083 2455126 "RMODULE" 2455131 NIL RMODULE (NIL T) -9 NIL 2455158 NIL) (-1071 2453531 2453625 2453961 "RMCAT2" 2454596 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1070 2450381 2452877 2453174 "RMATRIX" 2453293 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1069 2443208 2445468 2445583 "RMATCAT" 2448942 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2449924 NIL) (-1068 2442583 2442730 2443037 "RMATCAT-" 2443042 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1067 2441984 2442205 2442248 "RLINSET" 2442442 NIL RLINSET (NIL T) -9 NIL 2442533 NIL) (-1066 2441551 2441626 2441754 "RINTERP" 2441903 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1065 2440609 2441163 2441193 "RING" 2441249 T RING (NIL) -9 NIL 2441341 NIL) (-1064 2440401 2440445 2440542 "RING-" 2440547 NIL RING- (NIL T) -8 NIL NIL NIL) (-1063 2439242 2439479 2439737 "RIDIST" 2440165 T RIDIST (NIL) -7 NIL NIL NIL) (-1062 2430531 2438710 2438916 "RGCHAIN" 2439090 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1061 2429881 2430287 2430328 "RGBCSPC" 2430386 NIL RGBCSPC (NIL T) -9 NIL 2430438 NIL) (-1060 2429039 2429420 2429461 "RGBCMDL" 2429693 NIL RGBCMDL (NIL T) -9 NIL 2429807 NIL) (-1059 2426033 2426647 2427317 "RF" 2428403 NIL RF (NIL T) -7 NIL NIL NIL) (-1058 2425679 2425742 2425845 "RFFACTOR" 2425964 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1057 2425404 2425439 2425536 "RFFACT" 2425638 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1056 2423521 2423885 2424267 "RFDIST" 2425044 T RFDIST (NIL) -7 NIL NIL NIL) (-1055 2422974 2423066 2423229 "RETSOL" 2423423 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1054 2422610 2422690 2422733 "RETRACT" 2422866 NIL RETRACT (NIL T) -9 NIL 2422953 NIL) (-1053 2422459 2422484 2422571 "RETRACT-" 2422576 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1052 2422061 2422281 2422351 "RETAST" 2422411 T RETAST (NIL) -8 NIL NIL NIL) (-1051 2414799 2421714 2421841 "RESULT" 2421956 T RESULT (NIL) -8 NIL NIL NIL) (-1050 2413390 2414068 2414267 "RESRING" 2414702 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1049 2413026 2413075 2413173 "RESLATC" 2413327 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1048 2412731 2412766 2412873 "REPSQ" 2412985 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1047 2410153 2410733 2411335 "REP" 2412151 T REP (NIL) -7 NIL NIL NIL) (-1046 2409850 2409885 2409996 "REPDB" 2410112 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1045 2403750 2405139 2406362 "REP2" 2408662 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1044 2400127 2400808 2401616 "REP1" 2402977 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1043 2392823 2398268 2398724 "REGSET" 2399757 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1042 2391588 2391971 2392221 "REF" 2392608 NIL REF (NIL T) -8 NIL NIL NIL) (-1041 2390965 2391068 2391235 "REDORDER" 2391472 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1040 2386933 2390178 2390405 "RECLOS" 2390793 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1039 2385985 2386166 2386381 "REALSOLV" 2386740 T REALSOLV (NIL) -7 NIL NIL NIL) (-1038 2385831 2385872 2385902 "REAL" 2385907 T REAL (NIL) -9 NIL 2385942 NIL) (-1037 2382314 2383116 2384000 "REAL0Q" 2384996 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1036 2377915 2378903 2379964 "REAL0" 2381295 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1035 2377386 2377632 2377726 "RDUCEAST" 2377843 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1034 2376791 2376863 2377070 "RDIV" 2377308 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1033 2375859 2376033 2376246 "RDIST" 2376613 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1032 2374456 2374743 2375115 "RDETRS" 2375567 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1031 2372268 2372722 2373260 "RDETR" 2373998 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1030 2370893 2371171 2371568 "RDEEFS" 2371984 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1029 2369402 2369708 2370133 "RDEEF" 2370581 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1028 2363463 2366383 2366413 "RCFIELD" 2367708 T RCFIELD (NIL) -9 NIL 2368439 NIL) (-1027 2361527 2362031 2362727 "RCFIELD-" 2362802 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1026 2357796 2359628 2359671 "RCAGG" 2360755 NIL RCAGG (NIL T) -9 NIL 2361220 NIL) (-1025 2357424 2357518 2357681 "RCAGG-" 2357686 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1024 2356759 2356871 2357036 "RATRET" 2357308 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1023 2356312 2356379 2356500 "RATFACT" 2356687 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1022 2355620 2355740 2355892 "RANDSRC" 2356182 T RANDSRC (NIL) -7 NIL NIL NIL) (-1021 2355354 2355398 2355471 "RADUTIL" 2355569 T RADUTIL (NIL) -7 NIL NIL NIL) (-1020 2348375 2354185 2354496 "RADIX" 2355077 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1019 2339891 2348217 2348347 "RADFF" 2348352 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1018 2339538 2339613 2339643 "RADCAT" 2339803 T RADCAT (NIL) -9 NIL NIL NIL) (-1017 2339320 2339368 2339468 "RADCAT-" 2339473 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1016 2337418 2339090 2339182 "QUEUE" 2339263 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1015 2333866 2337351 2337399 "QUAT" 2337404 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1014 2333497 2333540 2333671 "QUATCT2" 2333817 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1013 2326581 2330017 2330059 "QUATCAT" 2330850 NIL QUATCAT (NIL T) -9 NIL 2331616 NIL) (-1012 2322720 2323757 2325147 "QUATCAT-" 2325243 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1011 2320185 2321796 2321839 "QUAGG" 2322220 NIL QUAGG (NIL T) -9 NIL 2322395 NIL) (-1010 2319787 2320007 2320077 "QQUTAST" 2320137 T QQUTAST (NIL) -8 NIL NIL NIL) (-1009 2318800 2319300 2319465 "QFORM" 2319668 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1008 2309524 2314852 2314894 "QFCAT" 2315562 NIL QFCAT (NIL T) -9 NIL 2316563 NIL) (-1007 2304869 2306132 2307806 "QFCAT-" 2307902 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1006 2304500 2304543 2304674 "QFCAT2" 2304820 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1005 2303955 2304065 2304197 "QEQUAT" 2304390 T QEQUAT (NIL) -8 NIL NIL NIL) (-1004 2297081 2298154 2299340 "QCMPACK" 2302888 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1003 2294619 2295067 2295497 "QALGSET" 2296736 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1002 2293854 2294030 2294266 "QALGSET2" 2294437 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1001 2292539 2292763 2293082 "PWFFINTB" 2293627 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1000 2290714 2290882 2291238 "PUSHVAR" 2292353 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-999 2286632 2287686 2287727 "PTRANFN" 2289611 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-998 2285034 2285325 2285647 "PTPACK" 2286343 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-997 2284666 2284723 2284832 "PTFUNC2" 2284971 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-996 2279111 2283508 2283549 "PTCAT" 2283845 NIL PTCAT (NIL T) -9 NIL 2283998 NIL) (-995 2278769 2278804 2278928 "PSQFR" 2279070 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-994 2277364 2277662 2277996 "PSEUDLIN" 2278467 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-993 2264127 2266498 2268822 "PSETPK" 2275124 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-992 2257145 2259885 2259981 "PSETCAT" 2263002 NIL PSETCAT (NIL T T T T) -9 NIL 2263816 NIL) (-991 2254981 2255615 2256436 "PSETCAT-" 2256441 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-990 2254330 2254495 2254523 "PSCURVE" 2254791 T PSCURVE (NIL) -9 NIL 2254958 NIL) (-989 2250328 2251844 2251909 "PSCAT" 2252753 NIL PSCAT (NIL T T T) -9 NIL 2252993 NIL) (-988 2249391 2249607 2250007 "PSCAT-" 2250012 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-987 2247750 2248460 2248723 "PRTITION" 2249148 T PRTITION (NIL) -8 NIL NIL NIL) (-986 2247225 2247471 2247563 "PRTDAST" 2247678 T PRTDAST (NIL) -8 NIL NIL NIL) (-985 2236315 2238529 2240717 "PRS" 2245087 NIL PRS (NIL T T) -7 NIL NIL NIL) (-984 2234126 2235665 2235705 "PRQAGG" 2235888 NIL PRQAGG (NIL T) -9 NIL 2235990 NIL) (-983 2233462 2233767 2233795 "PROPLOG" 2233934 T PROPLOG (NIL) -9 NIL 2234049 NIL) (-982 2233066 2233123 2233246 "PROPFUN2" 2233385 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-981 2232381 2232502 2232674 "PROPFUN1" 2232927 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-980 2230562 2231128 2231425 "PROPFRML" 2232117 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-979 2230031 2230138 2230266 "PROPERTY" 2230454 T PROPERTY (NIL) -8 NIL NIL NIL) (-978 2224089 2228197 2229017 "PRODUCT" 2229257 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-977 2221367 2223547 2223781 "PR" 2223900 NIL PR (NIL T T) -8 NIL NIL NIL) (-976 2221163 2221195 2221254 "PRINT" 2221328 T PRINT (NIL) -7 NIL NIL NIL) (-975 2220503 2220620 2220772 "PRIMES" 2221043 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-974 2218568 2218969 2219435 "PRIMELT" 2220082 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-973 2218297 2218346 2218374 "PRIMCAT" 2218498 T PRIMCAT (NIL) -9 NIL NIL NIL) (-972 2214412 2218235 2218280 "PRIMARR" 2218285 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-971 2213419 2213597 2213825 "PRIMARR2" 2214230 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-970 2213062 2213118 2213229 "PREASSOC" 2213357 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-969 2212537 2212670 2212698 "PPCURVE" 2212903 T PPCURVE (NIL) -9 NIL 2213039 NIL) (-968 2212132 2212332 2212415 "PORTNUM" 2212474 T PORTNUM (NIL) -8 NIL NIL NIL) (-967 2209491 2209890 2210482 "POLYROOT" 2211713 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-966 2203584 2209095 2209255 "POLY" 2209364 NIL POLY (NIL T) -8 NIL NIL NIL) (-965 2202967 2203025 2203259 "POLYLIFT" 2203520 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-964 2199242 2199691 2200320 "POLYCATQ" 2202512 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-963 2185771 2190989 2191054 "POLYCAT" 2194568 NIL POLYCAT (NIL T T T) -9 NIL 2196446 NIL) (-962 2178998 2180922 2183386 "POLYCAT-" 2183391 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2178585 2178653 2178773 "POLY2UP" 2178924 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-960 2178217 2178274 2178383 "POLY2" 2178522 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-959 2176902 2177141 2177417 "POLUTIL" 2177991 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-958 2175257 2175534 2175865 "POLTOPOL" 2176624 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-957 2170722 2175193 2175239 "POINT" 2175244 NIL POINT (NIL T) -8 NIL NIL NIL) (-956 2168909 2169266 2169641 "PNTHEORY" 2170367 T PNTHEORY (NIL) -7 NIL NIL NIL) (-955 2167367 2167664 2168063 "PMTOOLS" 2168607 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-954 2166960 2167038 2167155 "PMSYM" 2167283 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-953 2166468 2166537 2166712 "PMQFCAT" 2166885 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-952 2165823 2165933 2166089 "PMPRED" 2166345 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-951 2165216 2165302 2165464 "PMPREDFS" 2165724 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-950 2163880 2164088 2164466 "PMPLCAT" 2164978 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-949 2163412 2163491 2163643 "PMLSAGG" 2163795 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-948 2162885 2162961 2163143 "PMKERNEL" 2163330 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-947 2162502 2162577 2162690 "PMINS" 2162804 NIL PMINS (NIL T) -7 NIL NIL NIL) (-946 2161944 2162013 2162222 "PMFS" 2162427 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-945 2161172 2161290 2161495 "PMDOWN" 2161821 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-944 2160339 2160497 2160678 "PMASS" 2161011 T PMASS (NIL) -7 NIL NIL NIL) (-943 2159612 2159722 2159885 "PMASSFS" 2160226 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-942 2159267 2159335 2159429 "PLOTTOOL" 2159538 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-941 2153874 2155078 2156226 "PLOT" 2158139 T PLOT (NIL) -8 NIL NIL NIL) (-940 2149678 2150722 2151643 "PLOT3D" 2152973 T PLOT3D (NIL) -8 NIL NIL NIL) (-939 2148590 2148767 2149002 "PLOT1" 2149482 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-938 2123981 2128656 2133507 "PLEQN" 2143856 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-937 2123299 2123421 2123601 "PINTERP" 2123846 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-936 2122992 2123039 2123142 "PINTERPA" 2123246 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-935 2122208 2122756 2122843 "PI" 2122883 T PI (NIL) -8 NIL NIL 2122950) (-934 2120505 2121480 2121508 "PID" 2121690 T PID (NIL) -9 NIL 2121824 NIL) (-933 2120256 2120293 2120368 "PICOERCE" 2120462 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-932 2119576 2119715 2119891 "PGROEB" 2120112 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-931 2115163 2115977 2116882 "PGE" 2118691 T PGE (NIL) -7 NIL NIL NIL) (-930 2113286 2113533 2113899 "PGCD" 2114880 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-929 2112624 2112727 2112888 "PFRPAC" 2113170 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-928 2109264 2111172 2111525 "PFR" 2112303 NIL PFR (NIL T) -8 NIL NIL NIL) (-927 2107653 2107897 2108222 "PFOTOOLS" 2109011 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-926 2106186 2106425 2106776 "PFOQ" 2107410 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-925 2104687 2104899 2105255 "PFO" 2105970 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-924 2101240 2104576 2104645 "PF" 2104650 NIL PF (NIL NIL) -8 NIL NIL NIL) (-923 2098574 2099845 2099873 "PFECAT" 2100458 T PFECAT (NIL) -9 NIL 2100842 NIL) (-922 2098019 2098173 2098387 "PFECAT-" 2098392 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-921 2096622 2096874 2097175 "PFBRU" 2097768 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-920 2094488 2094840 2095272 "PFBR" 2096273 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-919 2090534 2092000 2092647 "PERM" 2093874 NIL PERM (NIL T) -8 NIL NIL NIL) (-918 2085768 2086741 2087611 "PERMGRP" 2089697 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-917 2083887 2084847 2084888 "PERMCAT" 2085288 NIL PERMCAT (NIL T) -9 NIL 2085586 NIL) (-916 2083540 2083581 2083705 "PERMAN" 2083840 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-915 2081028 2083205 2083327 "PENDTREE" 2083451 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-914 2079957 2080172 2080213 "PDSPC" 2080746 NIL PDSPC (NIL T) -9 NIL 2080991 NIL) (-913 2079060 2079278 2079640 "PDSPC-" 2079645 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-912 2077942 2078710 2078751 "PDRING" 2078756 NIL PDRING (NIL T) -9 NIL 2078784 NIL) (-911 2075157 2075935 2076603 "PDEPROB" 2077294 T PDEPROB (NIL) -8 NIL NIL NIL) (-910 2072702 2073206 2073761 "PDEPACK" 2074622 T PDEPACK (NIL) -7 NIL NIL NIL) (-909 2071614 2071804 2072055 "PDECOMP" 2072501 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-908 2069193 2070036 2070064 "PDECAT" 2070851 T PDECAT (NIL) -9 NIL 2071564 NIL) (-907 2068822 2068877 2068931 "PDDOM" 2069096 NIL PDDOM (NIL T T) -9 NIL 2069176 NIL) (-906 2068641 2068671 2068778 "PDDOM-" 2068783 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-905 2068392 2068425 2068515 "PCOMP" 2068602 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-904 2066570 2067193 2067490 "PBWLB" 2068121 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-903 2059043 2060643 2061981 "PATTERN" 2065253 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-902 2058675 2058732 2058841 "PATTERN2" 2058980 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-901 2056432 2056820 2057277 "PATTERN1" 2058264 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-900 2053800 2054381 2054862 "PATRES" 2055997 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-899 2053364 2053431 2053563 "PATRES2" 2053727 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-898 2051247 2051652 2052059 "PATMATCH" 2053031 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-897 2050757 2050966 2051007 "PATMAB" 2051114 NIL PATMAB (NIL T) -9 NIL 2051197 NIL) (-896 2049275 2049611 2049869 "PATLRES" 2050562 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-895 2048821 2048944 2048985 "PATAB" 2048990 NIL PATAB (NIL T) -9 NIL 2049162 NIL) (-894 2047003 2047398 2047821 "PARTPERM" 2048418 T PARTPERM (NIL) -7 NIL NIL NIL) (-893 2046624 2046687 2046789 "PARSURF" 2046934 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-892 2046256 2046313 2046422 "PARSU2" 2046561 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-891 2046020 2046060 2046127 "PARSER" 2046209 T PARSER (NIL) -7 NIL NIL NIL) (-890 2045641 2045704 2045806 "PARSCURV" 2045951 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-889 2045273 2045330 2045439 "PARSC2" 2045578 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-888 2044912 2044970 2045067 "PARPCURV" 2045209 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-887 2044544 2044601 2044710 "PARPC2" 2044849 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-886 2043605 2043917 2044099 "PARAMAST" 2044382 T PARAMAST (NIL) -8 NIL NIL NIL) (-885 2043125 2043211 2043330 "PAN2EXPR" 2043506 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-884 2041902 2042246 2042474 "PALETTE" 2042917 T PALETTE (NIL) -8 NIL NIL NIL) (-883 2040295 2040907 2041267 "PAIR" 2041588 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-882 2034074 2039552 2039747 "PADICRC" 2040149 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-881 2027198 2033418 2033603 "PADICRAT" 2033921 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-880 2025513 2027135 2027180 "PADIC" 2027185 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-879 2022623 2024187 2024227 "PADICCT" 2024808 NIL PADICCT (NIL NIL) -9 NIL 2025090 NIL) (-878 2021580 2021780 2022048 "PADEPAC" 2022410 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-877 2020792 2020925 2021131 "PADE" 2021442 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-876 2019179 2020000 2020280 "OWP" 2020596 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-875 2018672 2018885 2018982 "OVERSET" 2019102 T OVERSET (NIL) -8 NIL NIL NIL) (-874 2017718 2018277 2018449 "OVAR" 2018540 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-873 2016982 2017103 2017264 "OUT" 2017577 T OUT (NIL) -7 NIL NIL NIL) (-872 2005854 2008091 2010291 "OUTFORM" 2014802 T OUTFORM (NIL) -8 NIL NIL NIL) (-871 2005190 2005451 2005578 "OUTBFILE" 2005747 T OUTBFILE (NIL) -8 NIL NIL NIL) (-870 2004497 2004662 2004690 "OUTBCON" 2005008 T OUTBCON (NIL) -9 NIL 2005174 NIL) (-869 2004098 2004210 2004367 "OUTBCON-" 2004372 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-868 2003478 2003827 2003916 "OSI" 2004029 T OSI (NIL) -8 NIL NIL NIL) (-867 2003008 2003346 2003374 "OSGROUP" 2003379 T OSGROUP (NIL) -9 NIL 2003401 NIL) (-866 2001753 2001980 2002265 "ORTHPOL" 2002755 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-865 1999304 2001588 2001709 "OREUP" 2001714 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-864 1996707 1998995 1999122 "ORESUP" 1999246 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-863 1994235 1994735 1995296 "OREPCTO" 1996196 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-862 1987921 1990122 1990163 "OREPCAT" 1992511 NIL OREPCAT (NIL T) -9 NIL 1993615 NIL) (-861 1985068 1985850 1986908 "OREPCAT-" 1986913 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-860 1984219 1984517 1984545 "ORDSET" 1984854 T ORDSET (NIL) -9 NIL 1985018 NIL) (-859 1983650 1983798 1984022 "ORDSET-" 1984027 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-858 1982215 1983006 1983034 "ORDRING" 1983236 T ORDRING (NIL) -9 NIL 1983361 NIL) (-857 1981860 1981954 1982098 "ORDRING-" 1982103 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-856 1981240 1981703 1981731 "ORDMON" 1981736 T ORDMON (NIL) -9 NIL 1981757 NIL) (-855 1980402 1980549 1980744 "ORDFUNS" 1981089 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-854 1979740 1980159 1980187 "ORDFIN" 1980252 T ORDFIN (NIL) -9 NIL 1980326 NIL) (-853 1976299 1978326 1978735 "ORDCOMP" 1979364 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-852 1975565 1975692 1975878 "ORDCOMP2" 1976159 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-851 1972146 1973056 1973870 "OPTPROB" 1974771 T OPTPROB (NIL) -8 NIL NIL NIL) (-850 1968948 1969587 1970291 "OPTPACK" 1971462 T OPTPACK (NIL) -7 NIL NIL NIL) (-849 1966635 1967401 1967429 "OPTCAT" 1968248 T OPTCAT (NIL) -9 NIL 1968898 NIL) (-848 1966019 1966312 1966417 "OPSIG" 1966550 T OPSIG (NIL) -8 NIL NIL NIL) (-847 1965787 1965826 1965892 "OPQUERY" 1965973 T OPQUERY (NIL) -7 NIL NIL NIL) (-846 1962918 1964098 1964602 "OP" 1965316 NIL OP (NIL T) -8 NIL NIL NIL) (-845 1962292 1962518 1962559 "OPERCAT" 1962771 NIL OPERCAT (NIL T) -9 NIL 1962868 NIL) (-844 1962047 1962103 1962220 "OPERCAT-" 1962225 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-843 1958860 1960844 1961213 "ONECOMP" 1961711 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-842 1958165 1958280 1958454 "ONECOMP2" 1958732 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1957584 1957690 1957820 "OMSERVER" 1958055 T OMSERVER (NIL) -7 NIL NIL NIL) (-840 1954446 1957024 1957064 "OMSAGG" 1957125 NIL OMSAGG (NIL T) -9 NIL 1957189 NIL) (-839 1953069 1953332 1953614 "OMPKG" 1954184 T OMPKG (NIL) -7 NIL NIL NIL) (-838 1952499 1952602 1952630 "OM" 1952929 T OM (NIL) -9 NIL NIL NIL) (-837 1951046 1952048 1952217 "OMLO" 1952380 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-836 1950006 1950153 1950373 "OMEXPR" 1950872 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-835 1949297 1949552 1949688 "OMERR" 1949890 T OMERR (NIL) -8 NIL NIL NIL) (-834 1948448 1948718 1948878 "OMERRK" 1949157 T OMERRK (NIL) -8 NIL NIL NIL) (-833 1947899 1948125 1948233 "OMENC" 1948360 T OMENC (NIL) -8 NIL NIL NIL) (-832 1941794 1942979 1944150 "OMDEV" 1946748 T OMDEV (NIL) -8 NIL NIL NIL) (-831 1940863 1941034 1941228 "OMCONN" 1941620 T OMCONN (NIL) -8 NIL NIL NIL) (-830 1939384 1940360 1940388 "OINTDOM" 1940393 T OINTDOM (NIL) -9 NIL 1940414 NIL) (-829 1936722 1938072 1938409 "OFMONOID" 1939079 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-828 1936094 1936659 1936704 "ODVAR" 1936709 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-827 1933517 1935839 1935994 "ODR" 1935999 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-826 1926009 1933293 1933419 "ODPOL" 1933424 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-825 1919975 1925881 1925986 "ODP" 1925991 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-824 1918741 1918956 1919231 "ODETOOLS" 1919749 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-823 1915708 1916366 1917082 "ODESYS" 1918074 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-822 1910590 1911498 1912523 "ODERTRIC" 1914783 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-821 1910016 1910098 1910292 "ODERED" 1910502 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-820 1906904 1907452 1908129 "ODERAT" 1909439 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-819 1903863 1904328 1904925 "ODEPRRIC" 1906433 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-818 1901806 1902402 1902888 "ODEPROB" 1903397 T ODEPROB (NIL) -8 NIL NIL NIL) (-817 1898326 1898811 1899458 "ODEPRIM" 1901285 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-816 1897575 1897677 1897937 "ODEPAL" 1898218 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-815 1893737 1894528 1895392 "ODEPACK" 1896731 T ODEPACK (NIL) -7 NIL NIL NIL) (-814 1892798 1892905 1893127 "ODEINT" 1893626 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-813 1886899 1888324 1889771 "ODEIFTBL" 1891371 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-812 1882297 1883083 1884035 "ODEEF" 1886058 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-811 1881646 1881735 1881958 "ODECONST" 1882202 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-810 1879771 1880432 1880460 "ODECAT" 1881065 T ODECAT (NIL) -9 NIL 1881596 NIL) (-809 1876626 1879476 1879598 "OCT" 1879681 NIL OCT (NIL T) -8 NIL NIL NIL) (-808 1876264 1876307 1876434 "OCTCT2" 1876577 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-807 1870875 1873310 1873350 "OC" 1874447 NIL OC (NIL T) -9 NIL 1875305 NIL) (-806 1868102 1868850 1869840 "OC-" 1869934 NIL OC- (NIL T T) -8 NIL NIL NIL) (-805 1867454 1867922 1867950 "OCAMON" 1867955 T OCAMON (NIL) -9 NIL 1867976 NIL) (-804 1866985 1867326 1867354 "OASGP" 1867359 T OASGP (NIL) -9 NIL 1867379 NIL) (-803 1866246 1866735 1866763 "OAMONS" 1866803 T OAMONS (NIL) -9 NIL 1866846 NIL) (-802 1865660 1866093 1866121 "OAMON" 1866126 T OAMON (NIL) -9 NIL 1866146 NIL) (-801 1864918 1865436 1865464 "OAGROUP" 1865469 T OAGROUP (NIL) -9 NIL 1865489 NIL) (-800 1864608 1864658 1864746 "NUMTUBE" 1864862 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-799 1858181 1859699 1861235 "NUMQUAD" 1863092 T NUMQUAD (NIL) -7 NIL NIL NIL) (-798 1853937 1854925 1855950 "NUMODE" 1857176 T NUMODE (NIL) -7 NIL NIL NIL) (-797 1851292 1852172 1852200 "NUMINT" 1853123 T NUMINT (NIL) -9 NIL 1853887 NIL) (-796 1850240 1850437 1850655 "NUMFMT" 1851094 T NUMFMT (NIL) -7 NIL NIL NIL) (-795 1836599 1839544 1842076 "NUMERIC" 1847747 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-794 1830969 1836048 1836143 "NTSCAT" 1836148 NIL NTSCAT (NIL T T T T) -9 NIL 1836187 NIL) (-793 1830163 1830328 1830521 "NTPOLFN" 1830808 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-792 1818151 1826988 1827800 "NSUP" 1829384 NIL NSUP (NIL T) -8 NIL NIL NIL) (-791 1817783 1817840 1817949 "NSUP2" 1818088 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-790 1807920 1817557 1817690 "NSMP" 1817695 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-789 1806352 1806653 1807010 "NREP" 1807608 NIL NREP (NIL T) -7 NIL NIL NIL) (-788 1804943 1805195 1805553 "NPCOEF" 1806095 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-787 1804009 1804124 1804340 "NORMRETR" 1804824 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-786 1802050 1802340 1802749 "NORMPK" 1803717 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-785 1801735 1801763 1801887 "NORMMA" 1802016 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-784 1801535 1801692 1801721 "NONE" 1801726 T NONE (NIL) -8 NIL NIL NIL) (-783 1801324 1801353 1801422 "NONE1" 1801499 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-782 1800821 1800883 1801062 "NODE1" 1801256 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-781 1799102 1799953 1800208 "NNI" 1800555 T NNI (NIL) -8 NIL NIL 1800790) (-780 1797522 1797835 1798199 "NLINSOL" 1798770 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-779 1793763 1794758 1795657 "NIPROB" 1796643 T NIPROB (NIL) -8 NIL NIL NIL) (-778 1792520 1792754 1793056 "NFINTBAS" 1793525 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-777 1791694 1792170 1792211 "NETCLT" 1792383 NIL NETCLT (NIL T) -9 NIL 1792465 NIL) (-776 1790402 1790633 1790914 "NCODIV" 1791462 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-775 1790164 1790201 1790276 "NCNTFRAC" 1790359 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-774 1788344 1788708 1789128 "NCEP" 1789789 NIL NCEP (NIL T) -7 NIL NIL NIL) (-773 1787195 1787968 1787996 "NASRING" 1788106 T NASRING (NIL) -9 NIL 1788186 NIL) (-772 1786990 1787034 1787128 "NASRING-" 1787133 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-771 1786097 1786622 1786650 "NARNG" 1786767 T NARNG (NIL) -9 NIL 1786858 NIL) (-770 1785789 1785856 1785990 "NARNG-" 1785995 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-769 1784668 1784875 1785110 "NAGSP" 1785574 T NAGSP (NIL) -7 NIL NIL NIL) (-768 1775940 1777624 1779297 "NAGS" 1783015 T NAGS (NIL) -7 NIL NIL NIL) (-767 1774488 1774796 1775127 "NAGF07" 1775629 T NAGF07 (NIL) -7 NIL NIL NIL) (-766 1769026 1770317 1771624 "NAGF04" 1773201 T NAGF04 (NIL) -7 NIL NIL NIL) (-765 1761994 1763608 1765241 "NAGF02" 1767413 T NAGF02 (NIL) -7 NIL NIL NIL) (-764 1757218 1758318 1759435 "NAGF01" 1760897 T NAGF01 (NIL) -7 NIL NIL NIL) (-763 1750846 1752412 1753997 "NAGE04" 1755653 T NAGE04 (NIL) -7 NIL NIL NIL) (-762 1742015 1744136 1746266 "NAGE02" 1748736 T NAGE02 (NIL) -7 NIL NIL NIL) (-761 1737968 1738915 1739879 "NAGE01" 1741071 T NAGE01 (NIL) -7 NIL NIL NIL) (-760 1735763 1736297 1736855 "NAGD03" 1737430 T NAGD03 (NIL) -7 NIL NIL NIL) (-759 1727513 1729441 1731395 "NAGD02" 1733829 T NAGD02 (NIL) -7 NIL NIL NIL) (-758 1721324 1722749 1724189 "NAGD01" 1726093 T NAGD01 (NIL) -7 NIL NIL NIL) (-757 1717533 1718355 1719192 "NAGC06" 1720507 T NAGC06 (NIL) -7 NIL NIL NIL) (-756 1715998 1716330 1716686 "NAGC05" 1717197 T NAGC05 (NIL) -7 NIL NIL NIL) (-755 1715374 1715493 1715637 "NAGC02" 1715874 T NAGC02 (NIL) -7 NIL NIL NIL) (-754 1714333 1714916 1714956 "NAALG" 1715035 NIL NAALG (NIL T) -9 NIL 1715096 NIL) (-753 1714168 1714197 1714287 "NAALG-" 1714292 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-752 1708118 1709226 1710413 "MULTSQFR" 1713064 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-751 1707437 1707512 1707696 "MULTFACT" 1708030 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-750 1700108 1704022 1704075 "MTSCAT" 1705145 NIL MTSCAT (NIL T T) -9 NIL 1705660 NIL) (-749 1699820 1699874 1699966 "MTHING" 1700048 NIL MTHING (NIL T) -7 NIL NIL NIL) (-748 1699612 1699645 1699705 "MSYSCMD" 1699780 T MSYSCMD (NIL) -7 NIL NIL NIL) (-747 1695694 1698367 1698687 "MSET" 1699325 NIL MSET (NIL T) -8 NIL NIL NIL) (-746 1692763 1695255 1695296 "MSETAGG" 1695301 NIL MSETAGG (NIL T) -9 NIL 1695335 NIL) (-745 1688605 1690142 1690887 "MRING" 1692063 NIL MRING (NIL T T) -8 NIL NIL NIL) (-744 1688171 1688238 1688369 "MRF2" 1688532 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-743 1687789 1687824 1687968 "MRATFAC" 1688130 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-742 1685401 1685696 1686127 "MPRFF" 1687494 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-741 1679609 1685255 1685352 "MPOLY" 1685357 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-740 1679099 1679134 1679342 "MPCPF" 1679568 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-739 1678613 1678656 1678840 "MPC3" 1679050 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-738 1677808 1677889 1678110 "MPC2" 1678528 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-737 1676109 1676446 1676836 "MONOTOOL" 1677468 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-736 1675334 1675651 1675679 "MONOID" 1675898 T MONOID (NIL) -9 NIL 1676045 NIL) (-735 1674880 1674999 1675180 "MONOID-" 1675185 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-734 1664788 1670830 1670889 "MONOGEN" 1671563 NIL MONOGEN (NIL T T) -9 NIL 1672019 NIL) (-733 1662006 1662741 1663741 "MONOGEN-" 1663860 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-732 1660839 1661285 1661313 "MONADWU" 1661705 T MONADWU (NIL) -9 NIL 1661943 NIL) (-731 1660211 1660370 1660618 "MONADWU-" 1660623 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-730 1659570 1659814 1659842 "MONAD" 1660049 T MONAD (NIL) -9 NIL 1660161 NIL) (-729 1659255 1659333 1659465 "MONAD-" 1659470 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-728 1657544 1658168 1658447 "MOEBIUS" 1659008 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-727 1656822 1657226 1657266 "MODULE" 1657271 NIL MODULE (NIL T) -9 NIL 1657310 NIL) (-726 1656390 1656486 1656676 "MODULE-" 1656681 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-725 1654070 1654754 1655081 "MODRING" 1656214 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-724 1651014 1652175 1652696 "MODOP" 1653599 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-723 1649602 1650081 1650358 "MODMONOM" 1650877 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-722 1639557 1647893 1648307 "MODMON" 1649239 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-721 1636713 1638401 1638677 "MODFIELD" 1639432 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-720 1635690 1635994 1636184 "MMLFORM" 1636543 T MMLFORM (NIL) -8 NIL NIL NIL) (-719 1635216 1635259 1635438 "MMAP" 1635641 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-718 1633295 1634062 1634103 "MLO" 1634526 NIL MLO (NIL T) -9 NIL 1634768 NIL) (-717 1630661 1631177 1631779 "MLIFT" 1632776 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-716 1630052 1630136 1630290 "MKUCFUNC" 1630572 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-715 1629651 1629721 1629844 "MKRECORD" 1629975 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-714 1628698 1628860 1629088 "MKFUNC" 1629462 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-713 1628086 1628190 1628346 "MKFLCFN" 1628581 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-712 1627363 1627465 1627650 "MKBCFUNC" 1627979 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-711 1624038 1626917 1627053 "MINT" 1627247 T MINT (NIL) -8 NIL NIL NIL) (-710 1622850 1623093 1623370 "MHROWRED" 1623793 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-709 1618230 1621385 1621790 "MFLOAT" 1622465 T MFLOAT (NIL) -8 NIL NIL NIL) (-708 1617587 1617663 1617834 "MFINFACT" 1618142 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-707 1613902 1614750 1615634 "MESH" 1616723 T MESH (NIL) -7 NIL NIL NIL) (-706 1612292 1612604 1612957 "MDDFACT" 1613589 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-705 1609087 1611451 1611492 "MDAGG" 1611747 NIL MDAGG (NIL T) -9 NIL 1611890 NIL) (-704 1598734 1608380 1608587 "MCMPLX" 1608900 T MCMPLX (NIL) -8 NIL NIL NIL) (-703 1597871 1598017 1598218 "MCDEN" 1598583 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-702 1595761 1596031 1596411 "MCALCFN" 1597601 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-701 1594686 1594926 1595159 "MAYBE" 1595567 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-700 1592298 1592821 1593383 "MATSTOR" 1594157 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-699 1588255 1591670 1591918 "MATRIX" 1592083 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-698 1584021 1584728 1585464 "MATLIN" 1587612 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-697 1574127 1577313 1577390 "MATCAT" 1582270 NIL MATCAT (NIL T T T) -9 NIL 1583687 NIL) (-696 1570483 1571504 1572860 "MATCAT-" 1572865 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-695 1569077 1569230 1569563 "MATCAT2" 1570318 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-694 1567189 1567513 1567897 "MAPPKG3" 1568752 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-693 1566170 1566343 1566565 "MAPPKG2" 1567013 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-692 1564669 1564953 1565280 "MAPPKG1" 1565876 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-691 1563748 1564075 1564252 "MAPPAST" 1564512 T MAPPAST (NIL) -8 NIL NIL NIL) (-690 1563359 1563417 1563540 "MAPHACK3" 1563684 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-689 1562951 1563012 1563126 "MAPHACK2" 1563291 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-688 1562389 1562492 1562634 "MAPHACK1" 1562842 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-687 1560468 1561089 1561393 "MAGMA" 1562117 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-686 1559947 1560192 1560283 "MACROAST" 1560397 T MACROAST (NIL) -8 NIL NIL NIL) (-685 1556365 1558186 1558647 "M3D" 1559519 NIL M3D (NIL T) -8 NIL NIL NIL) (-684 1550440 1554704 1554745 "LZSTAGG" 1555527 NIL LZSTAGG (NIL T) -9 NIL 1555822 NIL) (-683 1546398 1547571 1549028 "LZSTAGG-" 1549033 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-682 1543485 1544289 1544776 "LWORD" 1545943 NIL LWORD (NIL T) -8 NIL NIL NIL) (-681 1543061 1543289 1543364 "LSTAST" 1543430 T LSTAST (NIL) -8 NIL NIL NIL) (-680 1536138 1542832 1542966 "LSQM" 1542971 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-679 1535362 1535501 1535729 "LSPP" 1535993 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-678 1533174 1533475 1533931 "LSMP" 1535051 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-677 1529953 1530627 1531357 "LSMP1" 1532476 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-676 1523799 1529090 1529131 "LSAGG" 1529193 NIL LSAGG (NIL T) -9 NIL 1529271 NIL) (-675 1520494 1521418 1522631 "LSAGG-" 1522636 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-674 1518093 1519638 1519887 "LPOLY" 1520289 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-673 1517675 1517760 1517883 "LPEFRAC" 1518002 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-672 1515996 1516769 1517022 "LO" 1517507 NIL LO (NIL T T T) -8 NIL NIL NIL) (-671 1515648 1515760 1515788 "LOGIC" 1515899 T LOGIC (NIL) -9 NIL 1515980 NIL) (-670 1515510 1515533 1515604 "LOGIC-" 1515609 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-669 1514703 1514843 1515036 "LODOOPS" 1515366 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-668 1512126 1514619 1514685 "LODO" 1514690 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-667 1510664 1510899 1511252 "LODOF" 1511873 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-666 1506868 1509299 1509340 "LODOCAT" 1509778 NIL LODOCAT (NIL T) -9 NIL 1509989 NIL) (-665 1506601 1506659 1506786 "LODOCAT-" 1506791 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-664 1503921 1506442 1506560 "LODO2" 1506565 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-663 1501356 1503858 1503903 "LODO1" 1503908 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-662 1500237 1500402 1500707 "LODEEF" 1501179 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-661 1495540 1498431 1498472 "LNAGG" 1499334 NIL LNAGG (NIL T) -9 NIL 1499769 NIL) (-660 1494687 1494901 1495243 "LNAGG-" 1495248 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-659 1490823 1491612 1492251 "LMOPS" 1494102 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-658 1490226 1490614 1490655 "LMODULE" 1490660 NIL LMODULE (NIL T) -9 NIL 1490686 NIL) (-657 1487424 1489871 1489994 "LMDICT" 1490136 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-656 1486830 1487051 1487092 "LLINSET" 1487283 NIL LLINSET (NIL T) -9 NIL 1487374 NIL) (-655 1486529 1486738 1486798 "LITERAL" 1486803 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-654 1479692 1485463 1485767 "LIST" 1486258 NIL LIST (NIL T) -8 NIL NIL NIL) (-653 1479217 1479291 1479430 "LIST3" 1479612 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-652 1478224 1478402 1478630 "LIST2" 1479035 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-651 1476358 1476670 1477069 "LIST2MAP" 1477871 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-650 1475954 1476191 1476232 "LINSET" 1476237 NIL LINSET (NIL T) -9 NIL 1476271 NIL) (-649 1474683 1475216 1475257 "LINEXP" 1475608 NIL LINEXP (NIL T) -9 NIL 1475799 NIL) (-648 1473260 1473520 1473831 "LINDEP" 1474435 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-647 1470027 1470746 1471523 "LIMITRF" 1472515 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-646 1468330 1468626 1469035 "LIMITPS" 1469722 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-645 1462758 1467841 1468069 "LIE" 1468151 NIL LIE (NIL T T) -8 NIL NIL NIL) (-644 1461706 1462175 1462215 "LIECAT" 1462355 NIL LIECAT (NIL T) -9 NIL 1462506 NIL) (-643 1461547 1461574 1461662 "LIECAT-" 1461667 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-642 1454134 1461087 1461243 "LIB" 1461411 T LIB (NIL) -8 NIL NIL NIL) (-641 1449769 1450652 1451587 "LGROBP" 1453251 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-640 1447767 1448041 1448391 "LF" 1449490 NIL LF (NIL T T) -7 NIL NIL NIL) (-639 1446607 1447299 1447327 "LFCAT" 1447534 T LFCAT (NIL) -9 NIL 1447673 NIL) (-638 1443509 1444139 1444827 "LEXTRIPK" 1445971 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-637 1440253 1441079 1441582 "LEXP" 1443089 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-636 1439729 1439974 1440066 "LETAST" 1440181 T LETAST (NIL) -8 NIL NIL NIL) (-635 1438127 1438440 1438841 "LEADCDET" 1439411 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-634 1437317 1437391 1437620 "LAZM3PK" 1438048 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-633 1432234 1435394 1435932 "LAUPOL" 1436829 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-632 1431813 1431857 1432018 "LAPLACE" 1432184 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-631 1429752 1430914 1431165 "LA" 1431646 NIL LA (NIL T T T) -8 NIL NIL NIL) (-630 1428746 1429330 1429371 "LALG" 1429433 NIL LALG (NIL T) -9 NIL 1429492 NIL) (-629 1428460 1428519 1428655 "LALG-" 1428660 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-628 1428295 1428319 1428360 "KVTFROM" 1428422 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-627 1427218 1427662 1427847 "KTVLOGIC" 1428130 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-626 1427053 1427077 1427118 "KRCFROM" 1427180 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-625 1425957 1426144 1426443 "KOVACIC" 1426853 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-624 1425792 1425816 1425857 "KONVERT" 1425919 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-623 1425627 1425651 1425692 "KOERCE" 1425754 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-622 1423458 1424220 1424597 "KERNEL" 1425283 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-621 1422954 1423035 1423167 "KERNEL2" 1423372 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-620 1416724 1421493 1421547 "KDAGG" 1421924 NIL KDAGG (NIL T T) -9 NIL 1422130 NIL) (-619 1416253 1416377 1416582 "KDAGG-" 1416587 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-618 1409401 1415914 1416069 "KAFILE" 1416131 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-617 1403829 1408912 1409140 "JORDAN" 1409222 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-616 1403208 1403478 1403599 "JOINAST" 1403728 T JOINAST (NIL) -8 NIL NIL NIL) (-615 1403054 1403113 1403168 "JAVACODE" 1403173 T JAVACODE (NIL) -8 NIL NIL NIL) (-614 1399306 1401259 1401313 "IXAGG" 1402242 NIL IXAGG (NIL T T) -9 NIL 1402701 NIL) (-613 1398225 1398531 1398950 "IXAGG-" 1398955 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-612 1393755 1398147 1398206 "IVECTOR" 1398211 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-611 1392521 1392758 1393024 "ITUPLE" 1393522 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-610 1391023 1391200 1391495 "ITRIGMNP" 1392343 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-609 1389768 1389972 1390255 "ITFUN3" 1390799 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-608 1389400 1389457 1389566 "ITFUN2" 1389705 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-607 1388559 1388880 1389054 "ITFORM" 1389246 T ITFORM (NIL) -8 NIL NIL NIL) (-606 1386520 1387579 1387857 "ITAYLOR" 1388314 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-605 1375465 1380657 1381820 "ISUPS" 1385390 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-604 1374569 1374709 1374945 "ISUMP" 1375312 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-603 1369944 1374514 1374555 "ISTRING" 1374560 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-602 1369420 1369665 1369757 "ISAST" 1369872 T ISAST (NIL) -8 NIL NIL NIL) (-601 1368629 1368711 1368927 "IRURPK" 1369334 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-600 1367565 1367766 1368006 "IRSN" 1368409 T IRSN (NIL) -7 NIL NIL NIL) (-599 1365636 1365991 1366420 "IRRF2F" 1367203 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-598 1365383 1365421 1365497 "IRREDFFX" 1365592 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-597 1363998 1364257 1364556 "IROOT" 1365116 NIL IROOT (NIL T) -7 NIL NIL NIL) (-596 1360602 1361682 1362374 "IR" 1363338 NIL IR (NIL T) -8 NIL NIL NIL) (-595 1359807 1360095 1360246 "IRFORM" 1360471 T IRFORM (NIL) -8 NIL NIL NIL) (-594 1357420 1357915 1358481 "IR2" 1359285 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-593 1356520 1356633 1356847 "IR2F" 1357303 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-592 1356311 1356345 1356405 "IPRNTPK" 1356480 T IPRNTPK (NIL) -7 NIL NIL NIL) (-591 1352892 1356200 1356269 "IPF" 1356274 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-590 1351219 1352817 1352874 "IPADIC" 1352879 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-589 1350531 1350779 1350909 "IP4ADDR" 1351109 T IP4ADDR (NIL) -8 NIL NIL NIL) (-588 1349905 1350160 1350292 "IOMODE" 1350419 T IOMODE (NIL) -8 NIL NIL NIL) (-587 1348978 1349502 1349629 "IOBFILE" 1349798 T IOBFILE (NIL) -8 NIL NIL NIL) (-586 1348466 1348882 1348910 "IOBCON" 1348915 T IOBCON (NIL) -9 NIL 1348936 NIL) (-585 1347977 1348035 1348218 "INVLAPLA" 1348402 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-584 1337625 1339979 1342365 "INTTR" 1345641 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-583 1333960 1334702 1335567 "INTTOOLS" 1336810 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-582 1333546 1333637 1333754 "INTSLPE" 1333863 T INTSLPE (NIL) -7 NIL NIL NIL) (-581 1331499 1333469 1333528 "INTRVL" 1333533 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-580 1329101 1329613 1330188 "INTRF" 1330984 NIL INTRF (NIL T) -7 NIL NIL NIL) (-579 1328512 1328609 1328751 "INTRET" 1328999 NIL INTRET (NIL T) -7 NIL NIL NIL) (-578 1326509 1326898 1327368 "INTRAT" 1328120 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-577 1323772 1324355 1324974 "INTPM" 1325994 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-576 1320517 1321116 1321854 "INTPAF" 1323158 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-575 1315696 1316658 1317709 "INTPACK" 1319486 T INTPACK (NIL) -7 NIL NIL NIL) (-574 1312594 1315493 1315602 "INT" 1315607 T INT (NIL) -8 NIL NIL NIL) (-573 1311846 1311998 1312206 "INTHERTR" 1312436 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-572 1311285 1311365 1311553 "INTHERAL" 1311760 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-571 1309131 1309574 1310031 "INTHEORY" 1310848 T INTHEORY (NIL) -7 NIL NIL NIL) (-570 1300537 1302158 1303930 "INTG0" 1307483 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-569 1281110 1285900 1290710 "INTFTBL" 1295747 T INTFTBL (NIL) -8 NIL NIL NIL) (-568 1280359 1280497 1280670 "INTFACT" 1280969 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-567 1277786 1278232 1278789 "INTEF" 1279913 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-566 1276153 1276892 1276920 "INTDOM" 1277221 T INTDOM (NIL) -9 NIL 1277428 NIL) (-565 1275522 1275696 1275938 "INTDOM-" 1275943 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-564 1271910 1273838 1273892 "INTCAT" 1274691 NIL INTCAT (NIL T) -9 NIL 1275012 NIL) (-563 1271382 1271485 1271613 "INTBIT" 1271802 T INTBIT (NIL) -7 NIL NIL NIL) (-562 1270081 1270235 1270542 "INTALG" 1271227 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-561 1269564 1269654 1269811 "INTAF" 1269985 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-560 1262907 1269374 1269514 "INTABL" 1269519 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-559 1262240 1262706 1262771 "INT8" 1262805 T INT8 (NIL) -8 NIL NIL 1262850) (-558 1261572 1262038 1262103 "INT64" 1262137 T INT64 (NIL) -8 NIL NIL 1262182) (-557 1260904 1261370 1261435 "INT32" 1261469 T INT32 (NIL) -8 NIL NIL 1261514) (-556 1260236 1260702 1260767 "INT16" 1260801 T INT16 (NIL) -8 NIL NIL 1260846) (-555 1255031 1257797 1257825 "INS" 1258759 T INS (NIL) -9 NIL 1259424 NIL) (-554 1252271 1253042 1254016 "INS-" 1254089 NIL INS- (NIL T) -8 NIL NIL NIL) (-553 1251046 1251273 1251571 "INPSIGN" 1252024 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-552 1250164 1250281 1250478 "INPRODPF" 1250926 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-551 1249058 1249175 1249412 "INPRODFF" 1250044 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-550 1248058 1248210 1248470 "INNMFACT" 1248894 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-549 1247255 1247352 1247540 "INMODGCD" 1247957 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-548 1245763 1246008 1246332 "INFSP" 1247000 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-547 1244947 1245064 1245247 "INFPROD0" 1245643 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-546 1241802 1243012 1243527 "INFORM" 1244440 T INFORM (NIL) -8 NIL NIL NIL) (-545 1241412 1241472 1241570 "INFORM1" 1241737 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-544 1240935 1241024 1241138 "INFINITY" 1241318 T INFINITY (NIL) -7 NIL NIL NIL) (-543 1240111 1240655 1240756 "INETCLTS" 1240854 T INETCLTS (NIL) -8 NIL NIL NIL) (-542 1238727 1238977 1239298 "INEP" 1239859 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-541 1237976 1238624 1238689 "INDE" 1238694 NIL INDE (NIL T) -8 NIL NIL NIL) (-540 1237540 1237608 1237725 "INCRMAPS" 1237903 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-539 1236358 1236809 1237015 "INBFILE" 1237354 T INBFILE (NIL) -8 NIL NIL NIL) (-538 1231657 1232594 1233538 "INBFF" 1235446 NIL INBFF (NIL T) -7 NIL NIL NIL) (-537 1230565 1230834 1230862 "INBCON" 1231375 T INBCON (NIL) -9 NIL 1231641 NIL) (-536 1229817 1230040 1230316 "INBCON-" 1230321 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-535 1229296 1229541 1229632 "INAST" 1229746 T INAST (NIL) -8 NIL NIL NIL) (-534 1228723 1228975 1229081 "IMPTAST" 1229210 T IMPTAST (NIL) -8 NIL NIL NIL) (-533 1225169 1228567 1228671 "IMATRIX" 1228676 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-532 1223877 1224000 1224316 "IMATQF" 1225025 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-531 1222097 1222324 1222661 "IMATLIN" 1223633 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-530 1216675 1222021 1222079 "ILIST" 1222084 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-529 1214580 1216535 1216648 "IIARRAY2" 1216653 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-528 1209978 1214491 1214555 "IFF" 1214560 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-527 1209325 1209595 1209711 "IFAST" 1209882 T IFAST (NIL) -8 NIL NIL NIL) (-526 1204320 1208617 1208805 "IFARRAY" 1209182 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-525 1203500 1204224 1204297 "IFAMON" 1204302 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-524 1203084 1203149 1203203 "IEVALAB" 1203410 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-523 1202759 1202827 1202987 "IEVALAB-" 1202992 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-522 1202390 1202673 1202736 "IDPO" 1202741 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-521 1201640 1202279 1202354 "IDPOAMS" 1202359 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-520 1200947 1201529 1201604 "IDPOAM" 1201609 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-519 1200006 1200282 1200335 "IDPC" 1200748 NIL IDPC (NIL T T) -9 NIL 1200897 NIL) (-518 1199475 1199898 1199971 "IDPAM" 1199976 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-517 1198851 1199367 1199440 "IDPAG" 1199445 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-516 1198496 1198687 1198762 "IDENT" 1198796 T IDENT (NIL) -8 NIL NIL NIL) (-515 1194751 1195599 1196494 "IDECOMP" 1197653 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-514 1187588 1188674 1189721 "IDEAL" 1193787 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-513 1186748 1186860 1187060 "ICDEN" 1187472 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-512 1185819 1186228 1186375 "ICARD" 1186621 T ICARD (NIL) -8 NIL NIL NIL) (-511 1183879 1184192 1184597 "IBPTOOLS" 1185496 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-510 1179486 1183499 1183612 "IBITS" 1183798 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-509 1176209 1176785 1177480 "IBATOOL" 1178903 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-508 1173988 1174450 1174983 "IBACHIN" 1175744 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-507 1171817 1173834 1173937 "IARRAY2" 1173942 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-506 1167923 1171743 1171800 "IARRAY1" 1171805 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-505 1161961 1166335 1166816 "IAN" 1167462 T IAN (NIL) -8 NIL NIL NIL) (-504 1161472 1161529 1161702 "IALGFACT" 1161898 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-503 1161000 1161113 1161141 "HYPCAT" 1161348 T HYPCAT (NIL) -9 NIL NIL NIL) (-502 1160538 1160655 1160841 "HYPCAT-" 1160846 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-501 1160133 1160333 1160416 "HOSTNAME" 1160475 T HOSTNAME (NIL) -8 NIL NIL NIL) (-500 1159978 1160015 1160056 "HOMOTOP" 1160061 NIL HOMOTOP (NIL T) -9 NIL 1160094 NIL) (-499 1156610 1157988 1158029 "HOAGG" 1159010 NIL HOAGG (NIL T) -9 NIL 1159689 NIL) (-498 1155204 1155603 1156129 "HOAGG-" 1156134 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-497 1149113 1154797 1154947 "HEXADEC" 1155074 T HEXADEC (NIL) -8 NIL NIL NIL) (-496 1147861 1148083 1148346 "HEUGCD" 1148890 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-495 1146937 1147698 1147828 "HELLFDIV" 1147833 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-494 1145116 1146714 1146802 "HEAP" 1146881 NIL HEAP (NIL T) -8 NIL NIL NIL) (-493 1144379 1144668 1144802 "HEADAST" 1145002 T HEADAST (NIL) -8 NIL NIL NIL) (-492 1138389 1144294 1144356 "HDP" 1144361 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-491 1132288 1138024 1138176 "HDMP" 1138290 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-490 1131612 1131752 1131916 "HB" 1132144 T HB (NIL) -7 NIL NIL NIL) (-489 1124998 1131458 1131562 "HASHTBL" 1131567 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-488 1124474 1124719 1124811 "HASAST" 1124926 T HASAST (NIL) -8 NIL NIL NIL) (-487 1122252 1124096 1124278 "HACKPI" 1124312 T HACKPI (NIL) -8 NIL NIL NIL) (-486 1117920 1122105 1122218 "GTSET" 1122223 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-485 1111335 1117798 1117896 "GSTBL" 1117901 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-484 1103613 1110366 1110631 "GSERIES" 1111126 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-483 1102754 1103171 1103199 "GROUP" 1103402 T GROUP (NIL) -9 NIL 1103536 NIL) (-482 1102120 1102279 1102530 "GROUP-" 1102535 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-481 1100487 1100808 1101195 "GROEBSOL" 1101797 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-480 1099401 1099689 1099740 "GRMOD" 1100269 NIL GRMOD (NIL T T) -9 NIL 1100437 NIL) (-479 1099169 1099205 1099333 "GRMOD-" 1099338 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-478 1094459 1095523 1096523 "GRIMAGE" 1098189 T GRIMAGE (NIL) -8 NIL NIL NIL) (-477 1092925 1093186 1093510 "GRDEF" 1094155 T GRDEF (NIL) -7 NIL NIL NIL) (-476 1092369 1092485 1092626 "GRAY" 1092804 T GRAY (NIL) -7 NIL NIL NIL) (-475 1091556 1091962 1092013 "GRALG" 1092166 NIL GRALG (NIL T T) -9 NIL 1092259 NIL) (-474 1091217 1091290 1091453 "GRALG-" 1091458 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-473 1087994 1090802 1090980 "GPOLSET" 1091124 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-472 1087348 1087405 1087663 "GOSPER" 1087931 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-471 1083080 1083786 1084312 "GMODPOL" 1087047 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-470 1082085 1082269 1082507 "GHENSEL" 1082892 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-469 1076241 1077084 1078104 "GENUPS" 1081169 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-468 1075938 1075989 1076078 "GENUFACT" 1076184 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-467 1075350 1075427 1075592 "GENPGCD" 1075856 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-466 1074824 1074859 1075072 "GENMFACT" 1075309 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-465 1073390 1073647 1073954 "GENEEZ" 1074567 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-464 1067449 1073001 1073163 "GDMP" 1073313 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-463 1056792 1061220 1062326 "GCNAALG" 1066432 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-462 1055119 1055981 1056009 "GCDDOM" 1056264 T GCDDOM (NIL) -9 NIL 1056421 NIL) (-461 1054589 1054716 1054931 "GCDDOM-" 1054936 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-460 1053261 1053446 1053750 "GB" 1054368 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-459 1041877 1044207 1046599 "GBINTERN" 1050952 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-458 1039714 1040006 1040427 "GBF" 1041552 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-457 1038495 1038660 1038927 "GBEUCLID" 1039530 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-456 1037844 1037969 1038118 "GAUSSFAC" 1038366 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-455 1036211 1036513 1036827 "GALUTIL" 1037563 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-454 1034519 1034793 1035117 "GALPOLYU" 1035938 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-453 1031884 1032174 1032581 "GALFACTU" 1034216 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-452 1023690 1025189 1026797 "GALFACT" 1030316 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-451 1021078 1021736 1021764 "FVFUN" 1022920 T FVFUN (NIL) -9 NIL 1023640 NIL) (-450 1020344 1020526 1020554 "FVC" 1020845 T FVC (NIL) -9 NIL 1021028 NIL) (-449 1019987 1020169 1020237 "FUNDESC" 1020296 T FUNDESC (NIL) -8 NIL NIL NIL) (-448 1019602 1019784 1019865 "FUNCTION" 1019939 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-447 1017346 1017924 1018390 "FT" 1019156 T FT (NIL) -8 NIL NIL NIL) (-446 1016137 1016647 1016850 "FTEM" 1017163 T FTEM (NIL) -8 NIL NIL NIL) (-445 1014428 1014717 1015114 "FSUPFACT" 1015828 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-444 1012825 1013114 1013446 "FST" 1014116 T FST (NIL) -8 NIL NIL NIL) (-443 1012024 1012130 1012318 "FSRED" 1012707 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-442 1010723 1010979 1011326 "FSPRMELT" 1011739 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-441 1008029 1008467 1008953 "FSPECF" 1010286 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-440 989331 997803 997844 "FS" 1001728 NIL FS (NIL T) -9 NIL 1004017 NIL) (-439 977974 980967 985024 "FS-" 985324 NIL FS- (NIL T T) -8 NIL NIL NIL) (-438 977502 977556 977726 "FSINT" 977915 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-437 975794 976495 976798 "FSERIES" 977281 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-436 974836 974952 975176 "FSCINT" 975674 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-435 971044 973780 973821 "FSAGG" 974191 NIL FSAGG (NIL T) -9 NIL 974450 NIL) (-434 968806 969407 970203 "FSAGG-" 970298 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-433 967848 967991 968218 "FSAGG2" 968659 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-432 965530 965810 966357 "FS2UPS" 967566 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-431 965164 965207 965336 "FS2" 965481 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-430 964042 964213 964515 "FS2EXPXP" 964989 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-429 963468 963583 963735 "FRUTIL" 963922 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-428 954881 958963 960321 "FR" 962142 NIL FR (NIL T) -8 NIL NIL NIL) (-427 949895 952570 952610 "FRNAALG" 953930 NIL FRNAALG (NIL T) -9 NIL 954528 NIL) (-426 945568 946644 947919 "FRNAALG-" 948669 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-425 945206 945249 945376 "FRNAAF2" 945519 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-424 943581 944055 944351 "FRMOD" 945018 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-423 941324 941956 942274 "FRIDEAL" 943372 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-422 940515 940602 940893 "FRIDEAL2" 941231 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-421 939648 940062 940103 "FRETRCT" 940108 NIL FRETRCT (NIL T) -9 NIL 940284 NIL) (-420 938760 938991 939342 "FRETRCT-" 939347 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-419 935848 937058 937117 "FRAMALG" 937999 NIL FRAMALG (NIL T T) -9 NIL 938291 NIL) (-418 933982 934437 935067 "FRAMALG-" 935290 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-417 927812 933455 933732 "FRAC" 933737 NIL FRAC (NIL T) -8 NIL NIL NIL) (-416 927448 927505 927612 "FRAC2" 927749 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-415 927084 927141 927248 "FR2" 927385 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-414 921597 924490 924518 "FPS" 925637 T FPS (NIL) -9 NIL 926194 NIL) (-413 921046 921155 921319 "FPS-" 921465 NIL FPS- (NIL T) -8 NIL NIL NIL) (-412 918348 920017 920045 "FPC" 920270 T FPC (NIL) -9 NIL 920412 NIL) (-411 918141 918181 918278 "FPC-" 918283 NIL FPC- (NIL T) -8 NIL NIL NIL) (-410 916931 917629 917670 "FPATMAB" 917675 NIL FPATMAB (NIL T) -9 NIL 917827 NIL) (-409 914604 915107 915533 "FPARFRAC" 916568 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-408 909998 910496 911178 "FORTRAN" 914036 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-407 907714 908214 908753 "FORT" 909479 T FORT (NIL) -7 NIL NIL NIL) (-406 905390 905952 905980 "FORTFN" 907040 T FORTFN (NIL) -9 NIL 907664 NIL) (-405 905154 905204 905232 "FORTCAT" 905291 T FORTCAT (NIL) -9 NIL 905353 NIL) (-404 903260 903770 904160 "FORMULA" 904784 T FORMULA (NIL) -8 NIL NIL NIL) (-403 903048 903078 903147 "FORMULA1" 903224 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-402 902571 902623 902796 "FORDER" 902990 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-401 901667 901831 902024 "FOP" 902398 T FOP (NIL) -7 NIL NIL NIL) (-400 900248 900947 901121 "FNLA" 901549 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-399 898977 899392 899420 "FNCAT" 899880 T FNCAT (NIL) -9 NIL 900140 NIL) (-398 898516 898936 898964 "FNAME" 898969 T FNAME (NIL) -8 NIL NIL NIL) (-397 897079 898042 898070 "FMTC" 898075 T FMTC (NIL) -9 NIL 898111 NIL) (-396 895825 897015 897061 "FMONOID" 897066 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-395 892653 893821 893862 "FMONCAT" 895079 NIL FMONCAT (NIL T) -9 NIL 895684 NIL) (-394 891845 892395 892544 "FM" 892549 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 889269 889915 889943 "FMFUN" 891087 T FMFUN (NIL) -9 NIL 891795 NIL) (-392 888538 888719 888747 "FMC" 889037 T FMC (NIL) -9 NIL 889219 NIL) (-391 885617 886477 886531 "FMCAT" 887726 NIL FMCAT (NIL T T) -9 NIL 888221 NIL) (-390 884483 885383 885483 "FM1" 885562 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-389 882257 882673 883167 "FLOATRP" 884034 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-388 875835 879986 880607 "FLOAT" 881656 T FLOAT (NIL) -8 NIL NIL NIL) (-387 873273 873773 874351 "FLOATCP" 875302 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-386 872120 872879 872920 "FLINEXP" 872925 NIL FLINEXP (NIL T) -9 NIL 873018 NIL) (-385 871052 871349 871757 "FLINEXP-" 871762 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-384 870128 870272 870496 "FLASORT" 870904 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-383 867244 868112 868164 "FLALG" 869391 NIL FLALG (NIL T T) -9 NIL 869858 NIL) (-382 860948 864700 864741 "FLAGG" 866003 NIL FLAGG (NIL T) -9 NIL 866655 NIL) (-381 859674 860013 860503 "FLAGG-" 860508 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-380 858716 858859 859086 "FLAGG2" 859527 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-379 855567 856575 856634 "FINRALG" 857762 NIL FINRALG (NIL T T) -9 NIL 858270 NIL) (-378 854727 854956 855295 "FINRALG-" 855300 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-377 854107 854346 854374 "FINITE" 854570 T FINITE (NIL) -9 NIL 854677 NIL) (-376 846464 848651 848691 "FINAALG" 852358 NIL FINAALG (NIL T) -9 NIL 853811 NIL) (-375 841796 842846 843990 "FINAALG-" 845369 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-374 841164 841551 841654 "FILE" 841726 NIL FILE (NIL T) -8 NIL NIL NIL) (-373 839822 840160 840214 "FILECAT" 840898 NIL FILECAT (NIL T T) -9 NIL 841114 NIL) (-372 837538 839066 839094 "FIELD" 839134 T FIELD (NIL) -9 NIL 839214 NIL) (-371 836158 836543 837054 "FIELD-" 837059 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-370 834008 834793 835140 "FGROUP" 835844 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-369 833098 833262 833482 "FGLMICPK" 833840 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-368 828930 833023 833080 "FFX" 833085 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-367 828531 828592 828727 "FFSLPE" 828863 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-366 824521 825303 826099 "FFPOLY" 827767 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-365 824025 824061 824270 "FFPOLY2" 824479 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-364 819871 823944 824007 "FFP" 824012 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-363 815269 819782 819846 "FF" 819851 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-362 810395 814612 814802 "FFNBX" 815123 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-361 805323 809530 809788 "FFNBP" 810249 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-360 799956 804607 804818 "FFNB" 805156 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-359 798788 798986 799301 "FFINTBAS" 799753 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-358 794814 797035 797063 "FFIELDC" 797683 T FFIELDC (NIL) -9 NIL 798059 NIL) (-357 793476 793847 794344 "FFIELDC-" 794349 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-356 793045 793091 793215 "FFHOM" 793418 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-355 790740 791227 791744 "FFF" 792560 NIL FFF (NIL T) -7 NIL NIL NIL) (-354 786358 790482 790583 "FFCGX" 790683 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-353 781980 786090 786197 "FFCGP" 786301 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-352 777163 781707 781815 "FFCG" 781916 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-351 757866 767052 767138 "FFCAT" 772303 NIL FFCAT (NIL T T T) -9 NIL 773754 NIL) (-350 753063 754111 755425 "FFCAT-" 756655 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-349 752474 752517 752752 "FFCAT2" 753014 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-348 741797 745446 746666 "FEXPR" 751326 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-347 740759 741194 741235 "FEVALAB" 741319 NIL FEVALAB (NIL T) -9 NIL 741580 NIL) (-346 739918 740128 740466 "FEVALAB-" 740471 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-345 738484 739301 739504 "FDIV" 739817 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-344 735504 736245 736360 "FDIVCAT" 737928 NIL FDIVCAT (NIL T T T T) -9 NIL 738365 NIL) (-343 735266 735293 735463 "FDIVCAT-" 735468 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-342 734486 734573 734850 "FDIV2" 735173 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 733460 733781 733983 "FCTRDATA" 734304 T FCTRDATA (NIL) -8 NIL NIL NIL) (-340 732146 732405 732694 "FCPAK1" 733191 T FCPAK1 (NIL) -7 NIL NIL NIL) (-339 731245 731646 731787 "FCOMP" 732037 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-338 714950 718395 721933 "FC" 727727 T FC (NIL) -8 NIL NIL NIL) (-337 707229 711257 711297 "FAXF" 713099 NIL FAXF (NIL T) -9 NIL 713791 NIL) (-336 704506 705163 705988 "FAXF-" 706453 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-335 699558 703882 704058 "FARRAY" 704363 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-334 694452 696519 696572 "FAMR" 697595 NIL FAMR (NIL T T) -9 NIL 698055 NIL) (-333 693342 693644 694079 "FAMR-" 694084 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-332 692511 693264 693317 "FAMONOID" 693322 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-331 690297 691007 691060 "FAMONC" 692001 NIL FAMONC (NIL T T) -9 NIL 692387 NIL) (-330 688961 690051 690188 "FAGROUP" 690193 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-329 686756 687075 687478 "FACUTIL" 688642 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-328 685855 686040 686262 "FACTFUNC" 686566 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-327 678277 685158 685357 "EXPUPXS" 685711 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-326 675760 676300 676886 "EXPRTUBE" 677711 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-325 672031 672623 673353 "EXPRODE" 675099 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-324 657750 670680 671109 "EXPR" 671635 NIL EXPR (NIL T) -8 NIL NIL NIL) (-323 652304 652891 653697 "EXPR2UPS" 657048 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-322 651936 651993 652102 "EXPR2" 652241 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-321 643189 651087 651378 "EXPEXPAN" 651772 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-320 642989 643146 643175 "EXIT" 643180 T EXIT (NIL) -8 NIL NIL NIL) (-319 642469 642713 642804 "EXITAST" 642918 T EXITAST (NIL) -8 NIL NIL NIL) (-318 642096 642158 642271 "EVALCYC" 642401 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-317 641637 641755 641796 "EVALAB" 641966 NIL EVALAB (NIL T) -9 NIL 642070 NIL) (-316 641118 641240 641461 "EVALAB-" 641466 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-315 638486 639788 639816 "EUCDOM" 640371 T EUCDOM (NIL) -9 NIL 640721 NIL) (-314 636891 637333 637923 "EUCDOM-" 637928 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-313 624430 627189 629939 "ESTOOLS" 634161 T ESTOOLS (NIL) -7 NIL NIL NIL) (-312 624062 624119 624228 "ESTOOLS2" 624367 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-311 623813 623855 623935 "ESTOOLS1" 624014 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-310 617850 619458 619486 "ES" 622254 T ES (NIL) -9 NIL 623664 NIL) (-309 612797 614084 615901 "ES-" 616065 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 609171 609932 610712 "ESCONT" 612037 T ESCONT (NIL) -7 NIL NIL NIL) (-307 608916 608948 609030 "ESCONT1" 609133 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-306 608591 608641 608741 "ES2" 608860 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-305 608221 608279 608388 "ES1" 608527 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-304 607437 607566 607742 "ERROR" 608065 T ERROR (NIL) -7 NIL NIL NIL) (-303 600829 607296 607387 "EQTBL" 607392 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-302 593332 596143 597592 "EQ" 599413 NIL -2085 (NIL T) -8 NIL NIL NIL) (-301 592964 593021 593130 "EQ2" 593269 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-300 588255 589302 590395 "EP" 591903 NIL EP (NIL T) -7 NIL NIL NIL) (-299 586855 587146 587452 "ENV" 587969 T ENV (NIL) -8 NIL NIL NIL) (-298 585949 586503 586531 "ENTIRER" 586536 T ENTIRER (NIL) -9 NIL 586582 NIL) (-297 582643 584131 584492 "EMR" 585757 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-296 581773 581958 582012 "ELTAGG" 582392 NIL ELTAGG (NIL T T) -9 NIL 582603 NIL) (-295 581492 581554 581695 "ELTAGG-" 581700 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-294 581256 581285 581339 "ELTAB" 581423 NIL ELTAB (NIL T T) -9 NIL 581475 NIL) (-293 580382 580528 580727 "ELFUTS" 581107 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-292 580124 580180 580208 "ELEMFUN" 580313 T ELEMFUN (NIL) -9 NIL NIL NIL) (-291 579994 580015 580083 "ELEMFUN-" 580088 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-290 574808 578064 578105 "ELAGG" 579045 NIL ELAGG (NIL T) -9 NIL 579508 NIL) (-289 573093 573527 574190 "ELAGG-" 574195 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-288 572405 572542 572698 "ELABOR" 572957 T ELABOR (NIL) -8 NIL NIL NIL) (-287 571066 571345 571639 "ELABEXPR" 572131 T ELABEXPR (NIL) -8 NIL NIL NIL) (-286 563930 565733 566560 "EFUPXS" 570342 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-285 557380 559181 559991 "EFULS" 563206 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-284 554865 555223 555695 "EFSTRUC" 557012 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-283 544656 546222 547770 "EF" 553380 NIL EF (NIL T T) -7 NIL NIL NIL) (-282 543730 544141 544290 "EAB" 544527 T EAB (NIL) -8 NIL NIL NIL) (-281 542912 543689 543717 "E04UCFA" 543722 T E04UCFA (NIL) -8 NIL NIL NIL) (-280 542094 542871 542899 "E04NAFA" 542904 T E04NAFA (NIL) -8 NIL NIL NIL) (-279 541276 542053 542081 "E04MBFA" 542086 T E04MBFA (NIL) -8 NIL NIL NIL) (-278 540458 541235 541263 "E04JAFA" 541268 T E04JAFA (NIL) -8 NIL NIL NIL) (-277 539642 540417 540445 "E04GCFA" 540450 T E04GCFA (NIL) -8 NIL NIL NIL) (-276 538826 539601 539629 "E04FDFA" 539634 T E04FDFA (NIL) -8 NIL NIL NIL) (-275 538008 538785 538813 "E04DGFA" 538818 T E04DGFA (NIL) -8 NIL NIL NIL) (-274 532181 533533 534897 "E04AGNT" 536664 T E04AGNT (NIL) -7 NIL NIL NIL) (-273 530952 531495 531535 "DVARCAT" 531876 NIL DVARCAT (NIL T) -9 NIL 532039 NIL) (-272 530156 530368 530682 "DVARCAT-" 530687 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-271 523204 529955 530084 "DSMP" 530089 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-270 517985 519149 520217 "DROPT" 522156 T DROPT (NIL) -8 NIL NIL NIL) (-269 517650 517709 517807 "DROPT1" 517920 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 512765 513891 515028 "DROPT0" 516533 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 511110 511435 511821 "DRAWPT" 512399 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 505697 506620 507699 "DRAW" 510084 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 505330 505383 505501 "DRAWHACK" 505638 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 504061 504330 504621 "DRAWCX" 505059 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 503576 503645 503796 "DRAWCURV" 503987 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 494044 496006 498121 "DRAWCFUN" 501481 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 490808 492737 492778 "DQAGG" 493407 NIL DQAGG (NIL T) -9 NIL 493681 NIL) (-260 478610 485169 485252 "DPOLCAT" 487104 NIL DPOLCAT (NIL T T T T) -9 NIL 487649 NIL) (-259 473447 474795 476753 "DPOLCAT-" 476758 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 467753 473308 473406 "DPMO" 473411 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 461962 467533 467700 "DPMM" 467705 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 461532 461746 461835 "DOMTMPLT" 461893 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 460965 461334 461414 "DOMCTOR" 461472 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 460177 460445 460596 "DOMAIN" 460834 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 454076 459812 459964 "DMP" 460078 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 453676 453732 453876 "DLP" 454014 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 447498 453003 453193 "DLIST" 453518 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 444295 446351 446392 "DLAGG" 446942 NIL DLAGG (NIL T) -9 NIL 447172 NIL) (-249 442971 443635 443663 "DIVRING" 443755 T DIVRING (NIL) -9 NIL 443838 NIL) (-248 442208 442398 442698 "DIVRING-" 442703 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 440310 440667 441073 "DISPLAY" 441822 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 434340 440224 440287 "DIRPROD" 440292 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 433188 433391 433656 "DIRPROD2" 434133 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 422340 428206 428259 "DIRPCAT" 428517 NIL DIRPCAT (NIL NIL T) -9 NIL 429315 NIL) (-243 419444 420148 421109 "DIRPCAT-" 421446 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 418731 418891 419077 "DIOSP" 419278 T DIOSP (NIL) -7 NIL NIL NIL) (-241 415386 417643 417684 "DIOPS" 418118 NIL DIOPS (NIL T) -9 NIL 418347 NIL) (-240 414935 415049 415240 "DIOPS-" 415245 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 413986 414614 414642 "DIFRING" 414647 T DIFRING (NIL) -9 NIL 414669 NIL) (-238 413658 413732 413760 "DIFFSPC" 413879 T DIFFSPC (NIL) -9 NIL 413954 NIL) (-237 413303 413381 413533 "DIFFSPC-" 413538 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 412459 412937 412977 "DIFFMOD" 412982 NIL DIFFMOD (NIL T) -9 NIL 413009 NIL) (-235 412167 412212 412253 "DIFFDOM" 412374 NIL DIFFDOM (NIL T) -9 NIL 412442 NIL) (-234 412020 412044 412128 "DIFFDOM-" 412133 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 409553 410825 410866 "DIFEXT" 411229 NIL DIFEXT (NIL T) -9 NIL 411523 NIL) (-232 407838 408266 408932 "DIFEXT-" 408937 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-231 405113 407370 407411 "DIAGG" 407416 NIL DIAGG (NIL T) -9 NIL 407436 NIL) (-230 404497 404654 404906 "DIAGG-" 404911 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 399914 403456 403733 "DHMATRIX" 404266 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 395526 396435 397445 "DFSFUN" 398924 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 390606 394457 394769 "DFLOAT" 395234 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 388869 389150 389539 "DFINTTLS" 390314 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 385898 386890 387290 "DERHAM" 388535 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 383699 385673 385762 "DEQUEUE" 385842 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 382953 383086 383269 "DEGRED" 383561 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 379383 380128 380974 "DEFINTRF" 382181 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 376938 377407 377999 "DEFINTEF" 378902 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 376288 376558 376673 "DEFAST" 376843 T DEFAST (NIL) -8 NIL NIL NIL) (-219 370197 375881 376031 "DECIMAL" 376158 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 367709 368167 368673 "DDFACT" 369741 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 367305 367348 367499 "DBLRESP" 367660 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 365173 365535 365896 "DBASE" 367071 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 364415 364653 364799 "DATAARY" 365072 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 363521 364374 364402 "D03FAFA" 364407 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 362628 363480 363508 "D03EEFA" 363513 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 360578 361044 361533 "D03AGNT" 362159 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 359867 360537 360565 "D02EJFA" 360570 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 359156 359826 359854 "D02CJFA" 359859 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 358445 359115 359143 "D02BHFA" 359148 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 357734 358404 358432 "D02BBFA" 358437 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 350931 352520 354126 "D02AGNT" 356148 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 348699 349222 349768 "D01WGTS" 350405 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 347766 348658 348686 "D01TRNS" 348691 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 346834 347725 347753 "D01GBFA" 347758 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 345902 346793 346821 "D01FCFA" 346826 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 344970 345861 345889 "D01ASFA" 345894 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 344038 344929 344957 "D01AQFA" 344962 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 343106 343997 344025 "D01APFA" 344030 T D01APFA (NIL) -8 NIL NIL NIL) (-199 342174 343065 343093 "D01ANFA" 343098 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 341242 342133 342161 "D01AMFA" 342166 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 340310 341201 341229 "D01ALFA" 341234 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 339378 340269 340297 "D01AKFA" 340302 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 338446 339337 339365 "D01AJFA" 339370 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 331741 333294 334855 "D01AGNT" 336905 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 331078 331206 331358 "CYCLOTOM" 331609 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 327811 328526 329253 "CYCLES" 330371 T CYCLES (NIL) -7 NIL NIL NIL) (-191 327123 327257 327428 "CVMP" 327672 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 324964 325222 325591 "CTRIGMNP" 326851 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 324400 324758 324831 "CTOR" 324911 T CTOR (NIL) -8 NIL NIL NIL) (-188 323909 324131 324232 "CTORKIND" 324319 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 323200 323516 323544 "CTORCAT" 323726 T CTORCAT (NIL) -9 NIL 323839 NIL) (-186 322798 322909 323068 "CTORCAT-" 323073 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 322260 322472 322580 "CTORCALL" 322722 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 321634 321733 321886 "CSTTOOLS" 322157 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 317433 318090 318848 "CRFP" 320946 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 316908 317154 317246 "CRCEAST" 317361 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 315955 316140 316368 "CRAPACK" 316712 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 315339 315440 315644 "CPMATCH" 315831 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 315064 315092 315198 "CPIMA" 315305 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 311412 312084 312803 "COORDSYS" 314399 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 310824 310945 311087 "CONTOUR" 311290 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 306715 308827 309319 "CONTFRAC" 310364 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 306595 306616 306644 "CONDUIT" 306681 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 305683 306237 306265 "COMRING" 306270 T COMRING (NIL) -9 NIL 306322 NIL) (-173 304737 305041 305225 "COMPPROP" 305519 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 304398 304433 304561 "COMPLPAT" 304696 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 294600 304207 304316 "COMPLEX" 304321 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 294236 294293 294400 "COMPLEX2" 294537 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 293575 293696 293856 "COMPILER" 294096 T COMPILER (NIL) -8 NIL NIL NIL) (-168 293293 293328 293426 "COMPFACT" 293534 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 277046 287131 287171 "COMPCAT" 288175 NIL COMPCAT (NIL T) -9 NIL 289523 NIL) (-166 266336 269325 273032 "COMPCAT-" 273388 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 266065 266093 266196 "COMMUPC" 266302 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 265859 265893 265952 "COMMONOP" 266026 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 265415 265610 265697 "COMM" 265792 T COMM (NIL) -8 NIL NIL NIL) (-162 264991 265219 265294 "COMMAAST" 265360 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 264240 264434 264462 "COMBOPC" 264800 T COMBOPC (NIL) -9 NIL 264975 NIL) (-160 263136 263346 263588 "COMBINAT" 264030 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 259593 260167 260794 "COMBF" 262558 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 258351 258709 258944 "COLOR" 259378 T COLOR (NIL) -8 NIL NIL NIL) (-157 257827 258072 258164 "COLONAST" 258279 T COLONAST (NIL) -8 NIL NIL NIL) (-156 257467 257514 257639 "CMPLXRT" 257774 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 256915 257167 257266 "CLLCTAST" 257388 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 252417 253445 254525 "CLIP" 255855 T CLIP (NIL) -7 NIL NIL NIL) (-153 250758 251518 251758 "CLIF" 252244 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 246933 248904 248945 "CLAGG" 249874 NIL CLAGG (NIL T) -9 NIL 250410 NIL) (-151 245355 245812 246395 "CLAGG-" 246400 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 244899 244984 245124 "CINTSLPE" 245264 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 242400 242871 243419 "CHVAR" 244427 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 241574 242128 242156 "CHARZ" 242161 T CHARZ (NIL) -9 NIL 242176 NIL) (-147 241328 241368 241446 "CHARPOL" 241528 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 240386 240973 241001 "CHARNZ" 241048 T CHARNZ (NIL) -9 NIL 241104 NIL) (-145 238292 239040 239393 "CHAR" 240053 T CHAR (NIL) -8 NIL NIL NIL) (-144 238018 238079 238107 "CFCAT" 238218 T CFCAT (NIL) -9 NIL NIL NIL) (-143 237259 237370 237553 "CDEN" 237902 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 233224 236412 236692 "CCLASS" 236999 T CCLASS (NIL) -8 NIL NIL NIL) (-141 232475 232632 232809 "CATEGORY" 233067 T -10 (NIL) -8 NIL NIL NIL) (-140 232048 232394 232442 "CATCTOR" 232447 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 231499 231751 231849 "CATAST" 231970 T CATAST (NIL) -8 NIL NIL NIL) (-138 230975 231220 231312 "CASEAST" 231427 T CASEAST (NIL) -8 NIL NIL NIL) (-137 226113 227132 227876 "CARTEN" 230287 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 225221 225369 225590 "CARTEN2" 225960 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 223537 224371 224628 "CARD" 224984 T CARD (NIL) -8 NIL NIL NIL) (-134 223113 223341 223416 "CAPSLAST" 223482 T CAPSLAST 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\ No newline at end of file |