diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-06-18 13:45:47 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-18 13:45:47 +0000 |
| commit | 6896410ee29bde89bf25c5f126a76a755a810e94 (patch) | |
| tree | fca597d080e0eaa3ed4775eaaf90033dce3692f5 /src | |
| parent | bd813c8607938e8ff0d8f112987300e22e3dc712 (diff) | |
| download | open-axiom-6896410ee29bde89bf25c5f126a76a755a810e94.tar.gz | |
* algebra/fparfrac.spad.pamphlet (FullPartialFractionExpansion):
Now satisfies DifferentialSpace.
* algebra/gseries.spad.pamphlet (GeneralUnivariatePowerSeries):
Now satisfies an instance of PartialDifferentialDomain.
* algebra/laurent.spad.pamphlet (UnivariateLaurentSeries): Likewise.
* algebra/puiseux.spad.pamphlet (UnivariatePuiseuxSeries): Likewise.
* algebra/suls.spad.pamphlet (SparseUnivariateLaurentSeries): Likewise.
* algebra/supxs.spad.pamphlet (SparseUnivariatePuiseuxSeries):
Likewise.
* algebra/suts.spad.pamphlet (SparseUnivariateTaylorSeries): Likewise.
* algebra/taylor.spad.pamphlet (UnivariateTaylorSeries): Likewise.
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 14 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 11 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 11 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 1 | ||||
| -rw-r--r-- | src/algebra/fparfrac.spad.pamphlet | 12 | ||||
| -rw-r--r-- | src/algebra/gseries.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/laurent.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/puiseux.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/suls.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/supxs.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/suts.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/algebra/taylor.spad.pamphlet | 8 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 596 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1339 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1335 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8848 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 25682 |
17 files changed, 18937 insertions, 18964 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 02bf4cbe..939bb682 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,19 @@ 2010-06-18 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/fparfrac.spad.pamphlet (FullPartialFractionExpansion): + Now satisfies DifferentialSpace. + * algebra/gseries.spad.pamphlet (GeneralUnivariatePowerSeries): + Now satisfies an instance of PartialDifferentialDomain. + * algebra/laurent.spad.pamphlet (UnivariateLaurentSeries): Likewise. + * algebra/puiseux.spad.pamphlet (UnivariatePuiseuxSeries): Likewise. + * algebra/suls.spad.pamphlet (SparseUnivariateLaurentSeries): Likewise. + * algebra/supxs.spad.pamphlet (SparseUnivariatePuiseuxSeries): + Likewise. + * algebra/suts.spad.pamphlet (SparseUnivariateTaylorSeries): Likewise. + * algebra/taylor.spad.pamphlet (UnivariateTaylorSeries): Likewise. + +2010-06-18 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/catdef.spad.pamphlet (DifferentialExtension): Now extends DifferentialSpaceExtension. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index efcfdf48..ebfc81c3 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -770,12 +770,12 @@ axiom_algebra_layer_14_objects = \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_14))) $(OUT)/EXPUPXS.$(FASLEXT): $(OUT)/UPXS.$(FASLEXT) $(OUT)/UPXS.$(FASLEXT): $(OUT)/UPXSCAT.$(FASLEXT) $(OUT)/UPXSCONS.$(FASLEXT) \ - $(OUT)/ULS.$(FASLEXT) + $(OUT)/ULS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT) $(OUT)/UPXSCONS.$(FASLEXT): $(OUT)/UPXSCCA.$(FASLEXT) -$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT) +$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT) $(OUT)/ULSCONS.$(FASLEXT): $(OUT)/ULSCCAT.$(FASLEXT) $(OUT)/ULSCCAT.$(FASLEXT): $(OUT)/UTS.$(FASLEXT) -$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT) +$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_15 = \ DSMP EXPUPXS UPXS UPXSCONS \ @@ -831,6 +831,7 @@ axiom_algebra_layer_18_objects = \ $(addprefix $(OUT)/, \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_18))) $(OUT)/TSETCAT.$(FASLEXT): $(OUT)/PSETCAT.$(FASLEXT) $(OUT)/RPOLCAT.$(FASLEXT) +$(OUT)/FPARFRAC.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) axiom_algebra_layer_19 = \ ACPLOT ANTISYM ATTRBUT \ @@ -869,6 +870,7 @@ axiom_algebra_layer_19_objects = \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_19))) $(OUT)/AN.$(FASLEXT): $(OUT)/IAN.$(FASLEXT) $(OUT)/IAN.$(FASLEXT): $(OUT)/EXPR.$(FASLEXT) +$(OUT)/SUTS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_20 = \ AF ALGFACT ALGFF ALGMANIP ALGMFACT ALGPKG \ @@ -910,6 +912,9 @@ axiom_algebra_layer_20_objects = \ $(addprefix $(OUT)/, \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_20))) $(OUT)/FDIV.$(FASLEXT): $(OUT)/HELLFDIV.$(FASLEXT) +$(OUT)/GSERIES.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) +$(OUT)/SULS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) +$(OUT)/SUPXS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_21 = \ DEFINTEF DFINTTLS DEFINTRF D01TRNS \ diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index a52c8977..29e74be9 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -802,12 +802,12 @@ axiom_algebra_layer_14_objects = \ <<layer15>>= $(OUT)/EXPUPXS.$(FASLEXT): $(OUT)/UPXS.$(FASLEXT) $(OUT)/UPXS.$(FASLEXT): $(OUT)/UPXSCAT.$(FASLEXT) $(OUT)/UPXSCONS.$(FASLEXT) \ - $(OUT)/ULS.$(FASLEXT) + $(OUT)/ULS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT) $(OUT)/UPXSCONS.$(FASLEXT): $(OUT)/UPXSCCA.$(FASLEXT) -$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT) +$(OUT)/ULS.$(FASLEXT): $(OUT)/ULSCONS.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT) $(OUT)/ULSCONS.$(FASLEXT): $(OUT)/ULSCCAT.$(FASLEXT) $(OUT)/ULSCCAT.$(FASLEXT): $(OUT)/UTS.$(FASLEXT) -$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT) +$(OUT)/UTS.$(FASLEXT): $(OUT)/UTSCAT.$(FASLEXT) $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_15 = \ DSMP EXPUPXS UPXS UPXSCONS \ @@ -883,6 +883,7 @@ axiom_algebra_layer_18_objects = \ <<layer19>>= $(OUT)/TSETCAT.$(FASLEXT): $(OUT)/PSETCAT.$(FASLEXT) $(OUT)/RPOLCAT.$(FASLEXT) +$(OUT)/FPARFRAC.$(FASLEXT): $(OUT)/DIFFSPC.$(FASLEXT) axiom_algebra_layer_19 = \ ACPLOT ANTISYM ATTRBUT \ @@ -926,6 +927,7 @@ axiom_algebra_layer_19_objects = \ <<layer20>>= $(OUT)/AN.$(FASLEXT): $(OUT)/IAN.$(FASLEXT) $(OUT)/IAN.$(FASLEXT): $(OUT)/EXPR.$(FASLEXT) +$(OUT)/SUTS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_20 = \ AF ALGFACT ALGFF ALGMANIP ALGMFACT ALGPKG \ @@ -972,6 +974,9 @@ axiom_algebra_layer_20_objects = \ <<layer21>>= $(OUT)/FDIV.$(FASLEXT): $(OUT)/HELLFDIV.$(FASLEXT) +$(OUT)/GSERIES.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) +$(OUT)/SULS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) +$(OUT)/SUPXS.$(FASLEXT): $(OUT)/PDDOM.$(FASLEXT) axiom_algebra_layer_21 = \ DEFINTEF DFINTTLS DEFINTRF D01TRNS \ diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index ea6b06ce..80bb4c66 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -737,6 +737,7 @@ (|PAdicIntegerCategory| . PADICCT) (|PartialDifferentialDomain| . PDDOM) (|PartialDifferentialRing| . PDRING) + (|PartialDifferentialSpace| . PDSPC) (|PartialTranscendentalFunctions| . PTRANFN) (|Patternable| . PATAB) (|PatternMatchable| . PATMAB) diff --git a/src/algebra/fparfrac.spad.pamphlet b/src/algebra/fparfrac.spad.pamphlet index ed7bce9d..b769ba05 100644 --- a/src/algebra/fparfrac.spad.pamphlet +++ b/src/algebra/fparfrac.spad.pamphlet @@ -15,7 +15,7 @@ ++ Full partial fraction expansion of rational functions ++ Author: Manuel Bronstein ++ Date Created: 9 December 1992 -++ Date Last Updated: 6 October 1993 +++ Date Last Updated: June 18, 2010 ++ References: M.Bronstein & B.Salvy, ++ Full Partial Fraction Decomposition of Rational Functions, ++ in Proceedings of ISSAC'93, Kiev, ACM Press. @@ -34,7 +34,7 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where ODF ==> Fraction ODP FPF ==> Record(polyPart: UP, fracPart: List REC) - Exports ==> Join(SetCategory, ConvertibleTo RF) with + Exports ==> Join(SetCategory, DifferentialSpace, ConvertibleTo RF) with +: (UP, $) -> $ ++ p + x returns the sum of p and x fullPartialFraction: RF -> $ @@ -46,14 +46,6 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where ++ fracPart(f) returns the list of summands of the fractional part of f. construct: List REC -> $ ++ construct(l) is the inverse of fracPart. - differentiate: $ -> $ - ++ differentiate(f) returns the derivative of f. - D: $ -> $ - ++ D(f) returns the derivative of f. - differentiate: ($, N) -> $ - ++ differentiate(f, n) returns the n-th derivative of f. - D: ($, NonNegativeInteger) -> $ - ++ D(f, n) returns the n-th derivative of f. Implementation ==> add Rep := FPF diff --git a/src/algebra/gseries.spad.pamphlet b/src/algebra/gseries.spad.pamphlet index d6ea733c..b9085625 100644 --- a/src/algebra/gseries.spad.pamphlet +++ b/src/algebra/gseries.spad.pamphlet @@ -14,7 +14,7 @@ )abbrev domain GSERIES GeneralUnivariatePowerSeries ++ Author: Clifton J. Williamson ++ Date Created: 22 September 1993 -++ Date Last Updated: 23 September 1993 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: ++ Also See: @@ -40,15 +40,13 @@ GeneralUnivariatePowerSeries(Coef,var,cen): Exports == Implementation where EFUPXS ==> ElementaryFunctionsUnivariatePuiseuxSeries FS2UPS ==> FunctionSpaceToUnivariatePowerSeries - Exports ==> UnivariatePuiseuxSeriesCategory Coef with + Exports ==> Join(UnivariatePuiseuxSeriesCategory Coef,_ + PartialDifferentialDomain(%,Variable var)) with coerce: Variable(var) -> % ++ coerce(var) converts the series variable \spad{var} into a ++ Puiseux series. coerce: UPXS(Coef,var,cen) -> % ++ coerce(f) converts a Puiseux series to a general power series. - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} returns the derivative of - ++ \spad{f(x)} with respect to \spad{x}. if Coef has Algebra Fraction Integer then integrate: (%,Variable(var)) -> % ++ \spad{integrate(f(x))} returns an anti-derivative of the power diff --git a/src/algebra/laurent.spad.pamphlet b/src/algebra/laurent.spad.pamphlet index 0a22f478..1bfafeea 100644 --- a/src/algebra/laurent.spad.pamphlet +++ b/src/algebra/laurent.spad.pamphlet @@ -14,7 +14,7 @@ )abbrev category ULSCCAT UnivariateLaurentSeriesConstructorCategory ++ Author: Clifton J. Williamson ++ Date Created: 6 February 1990 -++ Date Last Updated: 10 May 1990 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: ++ Also See: @@ -562,13 +562,11 @@ UnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where I ==> Integer UTS ==> UnivariateTaylorSeries(Coef,var,cen) - Exports ==> UnivariateLaurentSeriesConstructorCategory(Coef,UTS) with + Exports ==> Join(UnivariateLaurentSeriesConstructorCategory(Coef,UTS),_ + PartialDifferentialDomain(%,Variable var)) with coerce: Variable(var) -> % ++ \spad{coerce(var)} converts the series variable \spad{var} into a ++ Laurent series. - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} returns the derivative of - ++ \spad{f(x)} with respect to \spad{x}. if Coef has Algebra Fraction Integer then integrate: (%,Variable(var)) -> % ++ \spad{integrate(f(x))} returns an anti-derivative of the power diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet index fc5321ec..d9104a28 100644 --- a/src/algebra/puiseux.spad.pamphlet +++ b/src/algebra/puiseux.spad.pamphlet @@ -413,7 +413,7 @@ UnivariatePuiseuxSeriesConstructor(Coef,ULS):_ )abbrev domain UPXS UnivariatePuiseuxSeries ++ Author: Clifton J. Williamson ++ Date Created: 28 January 1990 -++ Date Last Updated: 21 September 1993 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: ++ Also See: @@ -442,10 +442,8 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where ULS ==> UnivariateLaurentSeries(Coef,var,cen) Exports ==> Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS),_ + PartialDifferentialDomain(%,Variable var),_ RetractableTo UTS,CoercibleFrom Variable var) with - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} returns the derivative of - ++ \spad{f(x)} with respect to \spad{x}. if Coef has Algebra Fraction Integer then integrate: (%,Variable(var)) -> % ++ \spad{integrate(f(x))} returns an anti-derivative of the power diff --git a/src/algebra/suls.spad.pamphlet b/src/algebra/suls.spad.pamphlet index 2b1db3b9..efd567aa 100644 --- a/src/algebra/suls.spad.pamphlet +++ b/src/algebra/suls.spad.pamphlet @@ -14,7 +14,7 @@ )abbrev domain SULS SparseUnivariateLaurentSeries ++ Author: Clifton J. Williamson ++ Date Created: 11 November 1994 -++ Date Last Updated: 10 March 1995 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: InnerSparseUnivariatePowerSeries, ++ SparseUnivariateTaylorSeries, SparseUnivariatePuiseuxSeries @@ -44,13 +44,11 @@ SparseUnivariateLaurentSeries(Coef,var,cen): Exports == Implementation where SUTS ==> SparseUnivariateTaylorSeries(Coef,var,cen) EFULS ==> ElementaryFunctionsUnivariateLaurentSeries(Coef,SUTS,%) - Exports ==> UnivariateLaurentSeriesConstructorCategory(Coef,SUTS) with + Exports ==> Join(UnivariateLaurentSeriesConstructorCategory(Coef,SUTS),_ + PartialDifferentialDomain(%,Variable var)) with coerce: Variable(var) -> % ++ \spad{coerce(var)} converts the series variable \spad{var} into a ++ Laurent series. - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} returns the derivative of - ++ \spad{f(x)} with respect to \spad{x}. if Coef has Algebra Fraction Integer then integrate: (%,Variable(var)) -> % ++ \spad{integrate(f(x))} returns an anti-derivative of the power diff --git a/src/algebra/supxs.spad.pamphlet b/src/algebra/supxs.spad.pamphlet index a8591584..a911aa38 100644 --- a/src/algebra/supxs.spad.pamphlet +++ b/src/algebra/supxs.spad.pamphlet @@ -14,7 +14,7 @@ )abbrev domain SUPXS SparseUnivariatePuiseuxSeries ++ Author: Clifton J. Williamson ++ Date Created: 11 November 1994 -++ Date Last Updated: 28 February 1995 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: InnerSparseUnivariatePowerSeries, ++ SparseUnivariateTaylorSeries, SparseUnivariateLaurentSeries @@ -43,10 +43,8 @@ SparseUnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where SUPS ==> InnerSparseUnivariatePowerSeries(Coef) Exports ==> Join(UnivariatePuiseuxSeriesConstructorCategory(Coef,SULS),_ + PartialDifferentialDomain(%,Variable var),_ RetractableTo SUTS,CoercibleFrom Variable var) with - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} returns the derivative of - ++ \spad{f(x)} with respect to \spad{x}. if Coef has Algebra Fraction Integer then integrate: (%,Variable(var)) -> % ++ \spad{integrate(f(x))} returns an anti-derivative of the power diff --git a/src/algebra/suts.spad.pamphlet b/src/algebra/suts.spad.pamphlet index 8e5f4106..ecd46bad 100644 --- a/src/algebra/suts.spad.pamphlet +++ b/src/algebra/suts.spad.pamphlet @@ -14,7 +14,7 @@ )abbrev domain SUTS SparseUnivariateTaylorSeries ++ Author: Clifton J. Williamson ++ Date Created: 16 February 1990 -++ Date Last Updated: 10 March 1995 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: InnerSparseUnivariatePowerSeries, ++ SparseUnivariateLaurentSeries, SparseUnivariatePuiseuxSeries @@ -47,7 +47,8 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where ST ==> Stream Term UP ==> UnivariatePolynomial(var,Coef) - Exports ==> UnivariateTaylorSeriesCategory(Coef) with + Exports ==> Join(UnivariateTaylorSeriesCategory(Coef),_ + PartialDifferentialDomain(%,Variable var)) with coerce: UP -> % ++\spad{coerce(p)} converts a univariate polynomial p in the variable ++\spad{var} to a univariate Taylor series in \spad{var}. @@ -57,9 +58,6 @@ SparseUnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where coerce: Variable(var) -> % ++\spad{coerce(var)} converts the series variable \spad{var} into a ++ Taylor series. - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} computes the derivative of - ++ \spad{f(x)} with respect to \spad{x}. if Coef has Algebra Fraction Integer then integrate: (%,Variable(var)) -> % ++ \spad{integrate(f(x),x)} returns an anti-derivative of the power diff --git a/src/algebra/taylor.spad.pamphlet b/src/algebra/taylor.spad.pamphlet index e85c7a85..e3e01da9 100644 --- a/src/algebra/taylor.spad.pamphlet +++ b/src/algebra/taylor.spad.pamphlet @@ -141,7 +141,7 @@ InnerTaylorSeries(Coef): Exports == Implementation where )abbrev domain UTS UnivariateTaylorSeries ++ Author: Clifton J. Williamson ++ Date Created: 21 December 1989 -++ Date Last Updated: 21 September 1993 +++ Date Last Updated: June 18, 2010 ++ Basic Operations: ++ Related Domains: UnivariateLaurentSeries(Coef,var,cen), UnivariatePuiseuxSeries(Coef,var,cen) ++ Also See: @@ -170,7 +170,8 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where STT ==> StreamTaylorSeriesOperations Coef TERM ==> Record(k:NNI,c:Coef) UP ==> UnivariatePolynomial(var,Coef) - Exports ==> UnivariateTaylorSeriesCategory(Coef) with + Exports ==> Join(UnivariateTaylorSeriesCategory(Coef),_ + PartialDifferentialDomain(%,Variable var)) with coerce: UP -> % ++\spad{coerce(p)} converts a univariate polynomial p in the variable ++\spad{var} to a univariate Taylor series in \spad{var}. @@ -180,9 +181,6 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where coerce: Variable(var) -> % ++\spad{coerce(var)} converts the series variable \spad{var} into a ++ Taylor series. - differentiate: (%,Variable(var)) -> % - ++ \spad{differentiate(f(x),x)} computes the derivative of - ++ \spad{f(x)} with respect to \spad{x}. lagrange: % -> % ++\spad{lagrange(g(x))} produces the Taylor series for \spad{f(x)} ++ where \spad{f(x)} is implicitly defined as \spad{f(x) = x*g(f(x))}. diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 969bd427..826b5d14 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2280951 . 3485824333) +(2279591 . 3485856132) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3029) +(-32 R -3027) ((|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 -1055) (QUOTE (-575))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -3029 UP UPUP -3486) +(-40 -3027 UP UPUP -1444) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4453 |has| (-418 |#2|) (-373)) (-4458 |has| (-418 |#2|) (-373)) (-4452 |has| (-418 |#2|) (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-418 |#2|) (QUOTE (-146))) (|HasCategory| (-418 |#2|) (QUOTE (-148))) (|HasCategory| (-418 |#2|) (QUOTE (-359))) (-3765 (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-378))) (-3765 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3765 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3765 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-359))))) (-3765 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -650) (QUOTE (-575)))) (-3765 (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) -(-41 R -3029) +((|HasCategory| (-418 |#2|) (QUOTE (-146))) (|HasCategory| (-418 |#2|) (QUOTE (-148))) (|HasCategory| (-418 |#2|) (QUOTE (-359))) (-3763 (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-378))) (-3763 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3763 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3763 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-359))))) (-3763 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -650) (QUOTE (-575)))) (-3763 (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) +(-41 R -3027) ((|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 (-463))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -441) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4460 . T) (-4461 . T)) -((-3765 (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|))))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|))))))) +((-3763 (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|))))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3029) +(-54 |Base| R -3027) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,11 +167,11 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|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}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-61 -1777) ((|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 @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3765 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) +((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -392,7 +392,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -3029 UP) +(-116 -3027 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 @@ -403,7 +403,7 @@ 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}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-924))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-117 |#1|) (QUOTE (-1039))) (|HasCategory| (-117 |#1|) (QUOTE (-831))) (-3765 (|HasCategory| (-117 |#1|) (QUOTE (-831))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (QUOTE (-1169))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -318) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -295) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-316))) (|HasCategory| (-117 |#1|) (QUOTE (-556))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-924)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((|HasCategory| (-117 |#1|) (QUOTE (-924))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-117 |#1|) (QUOTE (-1039))) (|HasCategory| (-117 |#1|) (QUOTE (-831))) (-3763 (|HasCategory| (-117 |#1|) (QUOTE (-831))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (QUOTE (-1169))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -318) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -295) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-316))) (|HasCategory| (-117 |#1|) (QUOTE (-556))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-924)))) (|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 @@ -419,7 +419,7 @@ 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"))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -439,15 +439,15 @@ NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-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."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-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."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130)))))) (-3765 (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1117)))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130)))))) +((-3763 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130)))))) (-3763 (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1117)))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-130) (QUOTE (-1117))) (|HasCategory| (-130) (LIST (QUOTE -318) (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 @@ -472,11 +472,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4462 "*") . T)) NIL -(-136 |minix| -2833 S T$) +(-136 |minix| -2831 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -2833 R) +(-137 |minix| -2831 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -499,7 +499,7 @@ 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}."))) ((-4460 . T) (-4450 . T) (-4461 . T)) -((-3765 (-12 (|HasCategory| (-145) (QUOTE (-378))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-145) (QUOTE (-378))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) +((-3763 (-12 (|HasCategory| (-145) (QUOTE (-378))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-145) (QUOTE (-378))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (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 @@ -524,7 +524,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4457 . T)) NIL -(-149 -3029 UP UPUP) +(-149 -3027 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 @@ -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 -3029) +(-159 R -3027) ((|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 @@ -598,7 +598,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-1220))) (|HasCategory| |#2| (QUOTE (-1077))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4456)) (|HasAttribute| |#2| (QUOTE -4459)) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-567)))) (-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})"))) -((-4453 -3765 (|has| |#1| (-567)) (-12 (|has| |#1| (-316)) (|has| |#1| (-924)))) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4456 |has| |#1| (-6 -4456)) (-4459 |has| |#1| (-6 -4459)) (-3502 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-4453 -3763 (|has| |#1| (-567)) (-12 (|has| |#1| (-316)) (|has| |#1| (-924)))) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4456 |has| |#1| (-6 -4456)) (-4459 |has| |#1| (-6 -4459)) (-3501 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . 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}."))) -((-4453 -3765 (|has| |#1| (-567)) (-12 (|has| |#1| (-316)) (|has| |#1| (-924)))) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4456 |has| |#1| (-6 -4456)) (-4459 |has| |#1| (-6 -4459)) (-3502 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . 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T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . 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(|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -3029) +(-190 R -3027) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -3029 UP UPUP R) +(-217 -3027 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 -3029 FP) +(-218 -3027 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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3765 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) +((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -3029) +(-221 R -3027) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -827,18 +827,18 @@ NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-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}."))) ((-4457 . T)) NIL -(-226 R -3029) +(-226 R -3027) ((|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}."))) -((-3494 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . 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)}.}"))) @@ -847,7 +847,7 @@ 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}"))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-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 @@ -896,22 +896,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-242 S -2833 R) +(-242 S -2831 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 (-373))) (|HasCategory| |#3| (QUOTE (-804))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4457)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-378))) (|HasCategory| |#3| (QUOTE (-737))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (QUOTE (-1117)))) -(-243 -2833 R) +(-243 -2831 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"))) ((-4454 |has| |#2| (-1066)) (-4455 |has| |#2| (-1066)) (-4457 |has| |#2| (-6 -4457)) (-4460 . T)) NIL -(-244 -2833 A B) +(-244 -2831 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 -(-245 -2833 R) +(-245 -2831 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -931,7 +931,7 @@ NIL (-250 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}"))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-251 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 @@ -939,7 +939,7 @@ NIL (-252 |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"))) (((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#2| (QUOTE (-924))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-924))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) (-253) ((|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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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 @@ -1019,7 +1019,7 @@ NIL (-272 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"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#3| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#3| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#3| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#3| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#3| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-273 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 @@ -1064,11 +1064,11 @@ 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 -(-284 R -3029) +(-284 R -3027) ((|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 -(-285 R -3029) +(-285 R -3027) ((|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 @@ -1120,7 +1120,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-298 S R |Mod| -4256 -3794 |exactQuo|) +(-298 S R |Mod| -1745 -4167 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL @@ -1142,21 +1142,21 @@ NIL NIL (-303 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) (-305) ((|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 -(-306 -3029 S) +(-306 -3027 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 -(-307 E -3029) +(-307 E -3027) ((|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 @@ -1204,7 +1204,7 @@ 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 -(-319 -3029) +(-319 -3027) ((|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 @@ -1219,7 +1219,7 @@ NIL (-322 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))}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . 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(LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -318) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (LIST (QUOTE -295) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1271) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-316))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-556))) (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-861))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-924))) (|HasCategory| $ (QUOTE (-146)))) (-3763 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1271 |#1| |#2| |#3| |#4|) (QUOTE (-924))) (|HasCategory| $ (QUOTE (-146)))))) (-323 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 @@ -1230,9 +1230,9 @@ NIL NIL (-325 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."))) -((-4457 -3765 (-12 (|has| |#1| (-567)) (-3765 (|has| |#1| (-1066)) (|has| |#1| (-484)))) (|has| |#1| (-1066)) (|has| |#1| (-484))) (-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) ((-4462 "*") |has| |#1| (-567)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-567)) (-4452 |has| |#1| (-567))) -((-3765 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))))) (|HasCategory| |#1| (QUOTE (-567))) (-3765 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-21))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-1066))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (LIST (QUOTE -650) 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|#1| (-567)) (-4458 |has| |#1| (-567)) (-4452 |has| |#1| (-567))) +((-3763 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (QUOTE (-1066))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))))) (-3763 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-1129)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-1066)))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-1066)))) (-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-1066)))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))))) (-3763 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1129)))) (-3763 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))))) (-3763 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-1066)))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1129))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| $ (QUOTE (-1066))) (|HasCategory| $ (LIST (QUOTE -1055) (QUOTE (-575))))) +(-326 R -3027) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1243,7 +1243,7 @@ NIL (-328 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."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3765 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2883) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4413) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) (-329 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1275,12 +1275,12 @@ NIL (-336 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."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) -(-337 S -3029) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +(-337 S -3027) ((|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 (-378)))) -(-338 -3029) +(-338 -3027) ((|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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL @@ -1304,15 +1304,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-344 S -3029 UP UPUP R) +(-344 S -3027 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 -(-345 -3029 UP UPUP R) +(-345 -3027 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 -(-346 -3029 UP UPUP R) +(-346 -3027 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 @@ -1332,26 +1332,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-351 S -3029 UP UPUP) +(-351 S -3027 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 (-378))) (|HasCategory| |#2| (QUOTE (-373)))) -(-352 -3029 UP UPUP) +(-352 -3027 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."))) ((-4453 |has| (-418 |#2|) (-373)) (-4458 |has| (-418 |#2|) (-373)) (-4452 |has| (-418 |#2|) (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-353 |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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) +((-3763 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) (-354 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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) (-355 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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 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 @@ -1368,31 +1368,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL -(-360 R UP -3029) +(-360 R UP -3027) ((|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 (-361 |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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) +((-3763 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) (-362 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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) (-363 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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 |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}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) +((-3763 (|HasCategory| (-925 |#1|) (QUOTE (-146))) (|HasCategory| (-925 |#1|) (QUOTE (-378)))) (|HasCategory| (-925 |#1|) (QUOTE (-148))) (|HasCategory| (-925 |#1|) (QUOTE (-378))) (|HasCategory| (-925 |#1|) (QUOTE (-146)))) (-365 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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) -(-366 -3029 GF) +((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) +(-366 -3027 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 @@ -1400,14 +1400,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-368 -3029 FP FPP) +(-368 -3027 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 (-369 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}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) +((-3763 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-378)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-146)))) (-370 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 @@ -1486,7 +1486,7 @@ NIL NIL (-389) ((|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}."))) -((-4443 . T) (-4451 . T) (-3494 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-4443 . T) (-4451 . T) (-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-390 |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}."))) @@ -1540,7 +1540,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-403 -3029 UP UPUP R) +(-403 -3027 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 @@ -1568,8 +1568,8 @@ NIL ((|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 -(-410 -3029 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) +(-410 -3027 UP) +((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-411 R) @@ -1590,7 +1590,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4443)) (|HasAttribute| |#1| (QUOTE -4451))) (-415) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3494 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-416 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."))) @@ -1603,7 +1603,7 @@ NIL (-418 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."))) ((-4447 -12 (|has| |#1| (-6 -4458)) (|has| |#1| (-463)) (|has| |#1| (-6 -4447))) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-831))) (-3765 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-861)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839))))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-556))) (-12 (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-463)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (QUOTE (-831))) (-3763 (|HasCategory| |#1| (QUOTE (-831))) (|HasCategory| |#1| (QUOTE (-861)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839))))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-556))) (-12 (|HasAttribute| |#1| (QUOTE -4458)) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#1| (QUOTE (-463)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-419 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1624,11 +1624,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-424 R -3029 UP A) +(-424 R -3027 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4457 . T)) NIL -(-425 R -3029 UP A |ibasis|) +(-425 R -3027 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 -1055) (|devaluate| |#2|)))) @@ -1647,7 +1647,7 @@ NIL (-429 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."))) ((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -318) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -295) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1239))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-1239)))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-463)))) +((|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -318) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -295) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1239))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-1239)))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-463)))) (-430 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 @@ -1676,7 +1676,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4460 . T) (-4450 . T) (-4461 . T)) NIL -(-437 R -3029) +(-437 R -3027) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1684,7 +1684,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4447 -12 (|has| |#1| (-6 -4447)) (|has| |#2| (-6 -4447))) (-4454 . T) (-4455 . T) (-4457 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#2| (QUOTE -4447)))) -(-439 R -3029) +(-439 R -3027) ((|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 @@ -1694,17 +1694,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-1129))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (-441 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}."))) -((-4457 -3765 (|has| |#1| (-1066)) (|has| |#1| (-484))) (-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) ((-4462 "*") |has| |#1| (-567)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-567)) (-4452 |has| |#1| (-567))) +((-4457 -3763 (|has| |#1| (-1066)) (|has| |#1| (-484))) (-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) ((-4462 "*") |has| |#1| (-567)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-567)) (-4452 |has| |#1| (-567))) NIL -(-442 R -3029) +(-442 R -3027) ((|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 -(-443 R -3029) +(-443 R -3027) ((|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)))) -(-444 R -3029) +(-444 R -3027) ((|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 @@ -1712,7 +1712,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-446 R -3029 UP) +(-446 R -3027 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 -1055) (QUOTE (-48))))) @@ -1744,7 +1744,7 @@ 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 -(-454 R UP -3029) +(-454 R UP -3027) ((|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 @@ -1791,7 +1791,7 @@ NIL (-465 |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"))) (((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#2| (QUOTE (-924))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-924))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) (-466 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 @@ -1856,7 +1856,7 @@ 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 -(-482 |lv| -3029 R) +(-482 |lv| -3027 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 @@ -1869,13 +1869,13 @@ NIL ((-4457 . T)) NIL (-485 |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."))) +((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . 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T)) -((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117)))) +((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117)))) (-487 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)}"))) ((-4461 . T) (-4460 . T)) @@ -1891,7 +1891,7 @@ NIL (-490 |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."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) (-491) ((|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 @@ -1899,11 +1899,11 @@ NIL (-492 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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(|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))))) (|HasCategory| (-575) (QUOTE (-861))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194))))) (-3763 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-737)))) (-3763 (|HasCategory| |#2| (QUOTE (-1066))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-1117)))) (|HasAttribute| |#2| (QUOTE -4457)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194))))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))))) (-494) ((|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 @@ -1911,8 +1911,8 @@ NIL (-495 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}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) -(-496 -3029 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +(-496 -3027 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 @@ -1923,7 +1923,7 @@ NIL (-498) ((|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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3765 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) +((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) (-499 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1948,7 +1948,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-505 -3029 UP |AlExt| |AlPol|) +(-505 -3027 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 @@ -1959,16 +1959,16 @@ NIL (-507 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-508 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."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-509 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 -(-510 R UP -3029) +(-510 R UP -3027) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1988,7 +1988,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-515 -3029 |Expon| |VarSet| |DPoly|) +(-515 -3027 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-1194))))) @@ -2039,7 +2039,7 @@ NIL (-527 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-528) ((|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 @@ -2047,15 +2047,15 @@ NIL (-529 |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}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((-3765 (|HasCategory| (-592 |#1|) (QUOTE (-146))) (|HasCategory| (-592 |#1|) (QUOTE (-378)))) (|HasCategory| (-592 |#1|) (QUOTE (-148))) (|HasCategory| (-592 |#1|) (QUOTE (-378))) (|HasCategory| (-592 |#1|) (QUOTE (-146)))) +((-3763 (|HasCategory| (-592 |#1|) (QUOTE (-146))) (|HasCategory| (-592 |#1|) (QUOTE (-378)))) (|HasCategory| (-592 |#1|) (QUOTE (-148))) (|HasCategory| (-592 |#1|) (QUOTE (-378))) (|HasCategory| (-592 |#1|) (QUOTE (-146)))) (-530 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}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-531 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."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-532 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 @@ -2067,7 +2067,7 @@ NIL (-534 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."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-535) ((|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 @@ -2100,7 +2100,7 @@ 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 -(-543 K -3029 |Par|) +(-543 K -3027 |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 @@ -2124,7 +2124,7 @@ 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 -(-549 K -3029 |Par|) +(-549 K -3027 |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 @@ -2175,12 +2175,12 @@ NIL (-561 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) -(-562 R -3029) +((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) +(-562 R -3027) ((|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 -(-563 R0 -3029 UP UPUP R) +(-563 R0 -3027 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 @@ -2190,7 +2190,7 @@ NIL NIL (-565 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."))) -((-3494 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-3493 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-566 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."))) @@ -2200,7 +2200,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL -(-568 R -3029) +(-568 R -3027) ((|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 @@ -2212,7 +2212,7 @@ 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 -(-571 R -3029 L) +(-571 R -3027 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 -667) (|devaluate| |#2|)))) @@ -2220,11 +2220,11 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-573 -3029 UP UPUP R) +(-573 -3027 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 -(-574 -3029 UP) +(-574 -3027 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 @@ -2236,15 +2236,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-577 R -3029 L) +(-577 R -3027 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 -667) (|devaluate| |#2|)))) -(-578 R -3029) +(-578 R -3027) ((|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 -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-1156)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-640))))) -(-579 -3029 UP) +(-579 -3027 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 @@ -2252,27 +2252,27 @@ 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 -(-581 -3029) +(-581 -3027) ((|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 (-582 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."))) -((-3494 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-3493 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-583) ((|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 -(-584 R -3029) +(-584 R -3027) ((|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 -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-293))) (|HasCategory| |#2| (QUOTE (-640))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-293)))) (|HasCategory| |#1| (QUOTE (-567)))) -(-585 -3029 UP) +(-585 -3027 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 -(-586 R -3029) +(-586 R -3027) ((|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 @@ -2304,11 +2304,11 @@ NIL ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-594 R -3029) +(-594 R -3027) ((|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 -(-595 E -3029) +(-595 E -3027) ((|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 @@ -2316,7 +2316,7 @@ 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 -(-597 -3029) +(-597 -3027) ((|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}."))) ((-4455 . T) (-4454 . T)) ((|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-1194))))) @@ -2347,7 +2347,7 @@ NIL (-604 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (-3765 (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117)))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) +((-3763 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (-3763 (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117)))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (-605 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 @@ -2355,7 +2355,7 @@ NIL (-606 |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}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-575)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-575)) (|devaluate| |#1|)))) (|HasCategory| (-575) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -2883) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-575)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-575)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-575)) (|devaluate| |#1|)))) (|HasCategory| (-575) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-575)))))) (-607 |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.}"))) (((-4462 "*") |has| |#1| (-567)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) @@ -2372,7 +2372,7 @@ 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 -(-611 R -3029 FG) +(-611 R -3027 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 @@ -2383,7 +2383,7 @@ NIL (-613 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-614 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2402,8 +2402,8 @@ NIL NIL (-618 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4457 -3765 (-3226 (|has| |#2| (-377 |#1|)) (|has| |#1| (-567))) (-12 (|has| |#2| (-428 |#1|)) (|has| |#1| (-567)))) (-4455 . T) (-4454 . T)) -((-3765 (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) +((-4457 -3763 (-3224 (|has| |#2| (-377 |#1|)) (|has| |#1| (-567))) (-12 (|has| |#2| (-428 |#1|)) (|has| |#1| (-567)))) (-4455 . T) (-4454 . T)) +((-3763 (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-619 |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."))) ((-4460 . T) (-4461 . T)) @@ -2432,7 +2432,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-626 -3029 UP) +(-626 -3027 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2460,7 +2460,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4454 . T) (-4455 . T) (-4457 . T)) ((|HasCategory| |#1| (QUOTE (-859)))) -(-633 R -3029) +(-633 R -3027) ((|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 @@ -2492,18 +2492,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-641 R -3029) +(-641 R -3027) ((|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 -(-642 |lv| -3029) +(-642 |lv| -3027) ((|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 (-643) ((|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."))) ((-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-1176) (QUOTE (-861))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117)))) +((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-1176) (QUOTE (-861))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 (-52))) (QUOTE (-1117)))) (-644 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2514,8 +2514,8 @@ NIL NIL (-646 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4457 -3765 (-3226 (|has| |#2| (-377 |#1|)) (|has| |#1| (-567))) (-12 (|has| |#2| (-428 |#1|)) (|has| |#1| (-567)))) (-4455 . T) (-4454 . T)) -((-3765 (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) +((-4457 -3763 (-3224 (|has| |#2| (-377 |#1|)) (|has| |#1| (-567))) (-12 (|has| |#2| (-428 |#1|)) (|has| |#1| (-567)))) (-4455 . T) (-4454 . T)) +((-3763 (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (LIST (QUOTE -428) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -377) (|devaluate| |#1|)))) (-647 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 @@ -2527,7 +2527,7 @@ NIL (-649 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 -((-3215 (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-373)))) +((-3213 (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-373)))) (-650 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 @@ -2551,7 +2551,7 @@ NIL (-655 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."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-656 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2563,7 +2563,7 @@ NIL (-658 S) ((|substitute| (($ |#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."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-659 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 @@ -2580,7 +2580,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|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 -(-663 R -3029 L) +(-663 R -3027 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 @@ -2600,11 +2600,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4454 . T) (-4455 . T) (-4457 . T)) NIL -(-668 -3029 UP) +(-668 -3027 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)))) -(-669 A -3523) +(-669 A -3902) ((|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}}"))) ((-4454 . T) (-4455 . T) (-4457 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-373)))) @@ -2640,11 +2640,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4461 . T) (-4460 . T)) NIL -(-678 -3029) +(-678 -3027) ((|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 -(-679 -3029 |Row| |Col| M) +(-679 -3027 |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 @@ -2655,7 +2655,7 @@ NIL (-681 |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."))) ((-4457 . T) (-4460 . T) (-4454 . T) (-4455 . T)) -((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-567))) (-3765 (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-567))) (-3763 (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-682) ((|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 @@ -2675,7 +2675,7 @@ NIL (-686 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 -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-687) ((|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 @@ -2731,7 +2731,7 @@ NIL (-700 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."))) ((-4460 . T) (-4461 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-316))) (|HasCategory| |#1| (QUOTE (-567))) (|HasAttribute| |#1| (QUOTE (-4462 "*"))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-701 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 @@ -2740,7 +2740,7 @@ 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 -(-703 S -3029 FLAF FLAS) +(-703 S -3027 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}.")) 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T) (-4459 |has| (-710) (-6 -4459)) (-4456 |has| (-710) (-6 -4456)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . 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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}."))) ((-4461 . T)) @@ -2764,13 +2764,13 @@ 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 -(-709 OV E -3029 PG) +(-709 OV E -3027 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 (-710) ((|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}"))) -((-3494 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) +((-3493 . T) (-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-711 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."))) @@ -2796,7 +2796,7 @@ 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 -(-717 S -3430 I) +(-717 S -3428 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 @@ -2816,14 +2816,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 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T)) NIL (-723 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"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4456 |has| |#1| (-373)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . 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(-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-724 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2832,7 +2832,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4455 |has| |#1| (-174)) (-4454 |has| |#1| (-174)) (-4457 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-726 R |Mod| -4256 -3794 |exactQuo|) +(-726 R |Mod| -1745 -4167 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4457 . T)) NIL @@ -2844,7 +2844,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4455 . T) (-4454 . T)) NIL -(-729 -3029) +(-729 -3027) ((|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]]}."))) ((-4457 . T)) NIL @@ -2880,7 +2880,7 @@ 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 -(-738 -3029 UP) +(-738 -3027 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 @@ -2899,7 +2899,7 @@ NIL (-742 |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."))) (((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#2| (QUOTE (-924))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-924))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-875 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) (-743 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 @@ -3032,11 +3032,11 @@ 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 -(-776 -3029) +(-776 -3027) ((|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 -(-777 P -3029) +(-777 P -3027) ((|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 @@ -3044,7 +3044,7 @@ NIL NIL NIL NIL -(-779 UP -3029) +(-779 UP -3027) ((|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 @@ -3060,7 +3060,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4462 "*") . T)) NIL -(-783 R -3029) +(-783 R -3027) ((|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 @@ -3080,7 +3080,7 @@ 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 -(-788 -3029 |ExtF| |SUEx| |ExtP| |n|) +(-788 -3027 |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 @@ -3095,7 +3095,7 @@ NIL (-791 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."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) 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(-575))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-575))))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-1194)))) (-3213 (|HasCategory| |#1| (LIST (QUOTE -1009) (QUOTE (-575))))))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-792 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3103,7 +3103,7 @@ NIL (-793 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4456 |has| |#1| (-373)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-1169))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-794 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3164,23 +3164,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4454 . T) (-4455 . T) (-4457 . T)) NIL -(-809 -3765 R OS S) +(-809 -3763 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-810 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (-3765 (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3765 (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1077))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (-3763 (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-1077))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1016 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (-811) ((|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 -(-812 R -3029 L) +(-812 R -3027 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 -(-813 R -3029) +(-813 R -3027) ((|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 @@ -3188,7 +3188,7 @@ 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 -(-815 R -3029) +(-815 R -3027) ((|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 @@ -3196,11 +3196,11 @@ 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 -(-817 -3029 UP UPUP R) +(-817 -3027 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 -(-818 -3029 UP L LQ) +(-818 -3027 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 @@ -3208,38 +3208,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-820 -3029 UP L LQ) +(-820 -3027 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 -(-821 -3029 UP) +(-821 -3027 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 -(-822 -3029 L UP A LO) +(-822 -3027 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 -(-823 -3029 UP) +(-823 -3027 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)))) -(-824 -3029 LO) +(-824 -3027 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 -(-825 -3029 LODO) +(-825 -3027 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 -(-826 -2833 S |f|) +(-826 -2831 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}."))) ((-4454 |has| |#2| (-1066)) (-4455 |has| |#2| (-1066)) (-4457 |has| |#2| (-6 -4457)) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-378))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-737))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-804))) (|HasCategory| |#2| (LIST 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(|HasCategory| |#2| (QUOTE (-1066)))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194))))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))))) (-827 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-829 (-1194)) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-828 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4462 "*") |has| |#2| (-373)) (-4453 |has| |#2| (-373)) (-4458 |has| |#2| (-373)) (-4452 |has| |#2| (-373)) (-4457 . T) (-4455 . T) (-4454 . T)) @@ -3307,7 +3307,7 @@ NIL (-844 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."))) ((-4457 |has| |#1| (-859))) -((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3765 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3765 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-556)))) +((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-556)))) (-845 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 @@ -3347,12 +3347,12 @@ NIL (-854 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4457 |has| |#1| (-859))) -((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3765 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3765 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-556)))) +((|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (QUOTE (-21))) (-3763 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#1| (QUOTE (-859))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-556)))) (-855) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-856 -2833 S) +(-856 -2831 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 @@ -3388,11 +3388,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) -(-865 R |sigma| -3594) +(-865 R |sigma| -3592) ((|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."))) ((-4454 . T) (-4455 . T) (-4457 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-373)))) -(-866 |x| R |sigma| -3594) +(-866 |x| R |sigma| -3592) ((|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}."))) ((-4454 . T) (-4455 . T) (-4457 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-373)))) @@ -3459,15 +3459,15 @@ NIL (-882 |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)."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-881 |#1|) (QUOTE (-924))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-148))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-881 |#1|) (QUOTE (-1039))) (|HasCategory| (-881 |#1|) (QUOTE (-831))) (-3765 (|HasCategory| (-881 |#1|) (QUOTE (-831))) (|HasCategory| (-881 |#1|) (QUOTE (-861)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (QUOTE (-1169))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (QUOTE (-237))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (QUOTE (-238))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -318) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -295) (LIST (QUOTE -881) (|devaluate| |#1|)) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (QUOTE (-316))) (|HasCategory| (-881 |#1|) (QUOTE (-556))) (|HasCategory| (-881 |#1|) (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-924)))) (|HasCategory| (-881 |#1|) (QUOTE (-146))))) +((|HasCategory| (-881 |#1|) (QUOTE (-924))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-148))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-881 |#1|) (QUOTE (-1039))) (|HasCategory| (-881 |#1|) (QUOTE (-831))) (-3763 (|HasCategory| (-881 |#1|) (QUOTE (-831))) (|HasCategory| (-881 |#1|) (QUOTE (-861)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (QUOTE (-1169))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| (-881 |#1|) (QUOTE (-237))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (QUOTE (-238))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -525) (QUOTE (-1194)) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -318) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (LIST (QUOTE -295) (LIST (QUOTE -881) (|devaluate| |#1|)) (LIST (QUOTE -881) (|devaluate| |#1|)))) (|HasCategory| (-881 |#1|) (QUOTE (-316))) (|HasCategory| (-881 |#1|) (QUOTE (-556))) (|HasCategory| (-881 |#1|) (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-881 |#1|) (QUOTE (-924)))) (|HasCategory| (-881 |#1|) (QUOTE (-146))))) (-883 |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)}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-831))) (-3765 (|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -295) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-831))) (-3763 (|HasCategory| |#2| (QUOTE (-831))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -295) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-861))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) (-884 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 (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))))) (-885) ((|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 @@ -3527,7 +3527,7 @@ NIL (-899 |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 (-3215 (|HasCategory| |#2| (QUOTE (-1066)))) (-3215 (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (-3215 (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194))))) +((-12 (-3213 (|HasCategory| |#2| (QUOTE (-1066)))) (-3213 (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))))) (-12 (|HasCategory| |#2| (QUOTE (-1066))) (-3213 (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-1194))))) (-900 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 @@ -3536,7 +3536,7 @@ 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 -(-902 R -3430) +(-902 R -3428) ((|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 @@ -3568,7 +3568,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-910 UP -3029) +(-910 UP -3027) ((|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 @@ -3595,7 +3595,7 @@ NIL (-916 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 (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-917 |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 @@ -3611,7 +3611,7 @@ NIL (-920 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."))) ((-4457 . T)) -((-3765 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-861)))) +((-3763 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-861)))) (-921 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 @@ -3632,7 +3632,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-378)))) -(-926 R0 -3029 UP UPUP R) +(-926 R0 -3027 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 @@ -3660,7 +3660,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-933 -3029) +(-933 -3027) ((|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 @@ -3676,11 +3676,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4462 "*") . T)) NIL -(-937 -3029 P) +(-937 -3027 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-938 |xx| -3029) +(-938 |xx| -3027) ((|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 @@ -3704,7 +3704,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-944 R -3029) +(-944 R -3027) ((|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 @@ -3716,7 +3716,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-947 S R -3029) +(-947 S R -3027) ((|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 @@ -3736,11 +3736,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -898) (|devaluate| |#1|)))) -(-952 R -3029 -3430) +(-952 R -3027 -3428) ((|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 -(-953 -3430) +(-953 -3428) ((|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 @@ -3763,7 +3763,7 @@ NIL (-958 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-959 |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 @@ -3788,7 +3788,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) NIL -(-965 E V R P -3029) +(-965 E V R P -3027) ((|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 @@ -3799,8 +3799,8 @@ NIL (-967 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}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-968 E V R P -3029) +((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1194) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-968 E V R P -3027) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-463)))) @@ -3823,12 +3823,12 @@ NIL (-973 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-974) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-975 -3029) +(-975 -3027) ((|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 @@ -3843,11 +3843,11 @@ NIL (-978 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}"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4458))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4458))) (-979 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) ((-4457 -12 (|has| |#2| (-484)) (|has| |#1| (-484)))) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737))))) (-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-378)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737))))) (-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-378)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737)))) (-12 (|HasCategory| |#1| (QUOTE (-804))) (|HasCategory| |#2| (QUOTE (-804))))) (-12 (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#2| (QUOTE (-737)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) (-980) ((|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 @@ -3936,7 +3936,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1002 K R UP -3029) +(-1002 K R UP -3027) ((|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 @@ -3995,11 +3995,11 @@ NIL (-1016 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.}"))) ((-4453 |has| |#1| (-299)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-373))) (-3765 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-1077))) (|HasCategory| |#1| (QUOTE (-556)))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -525) (QUOTE (-1194)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -295) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-1077))) (|HasCategory| |#1| (QUOTE (-556)))) (-1017 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}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-1018 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4008,14 +4008,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1020 -3029 UP UPUP |radicnd| |n|) +(-1020 -3027 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4453 |has| (-418 |#2|) (-373)) (-4458 |has| (-418 |#2|) (-373)) (-4452 |has| (-418 |#2|) (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-418 |#2|) (QUOTE (-146))) (|HasCategory| (-418 |#2|) (QUOTE (-148))) (|HasCategory| (-418 |#2|) (QUOTE (-359))) (-3765 (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-378))) (-3765 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3765 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3765 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-359))))) (-3765 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -650) (QUOTE (-575)))) (-3765 (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) +((|HasCategory| (-418 |#2|) (QUOTE (-146))) (|HasCategory| (-418 |#2|) (QUOTE (-148))) (|HasCategory| (-418 |#2|) (QUOTE (-359))) (-3763 (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))) (|HasCategory| (-418 |#2|) (QUOTE (-378))) (-3763 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3763 (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (QUOTE (-359)))) (-3763 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-359))))) (-3763 (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -650) (QUOTE (-575)))) (-3763 (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 |#2|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-237))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (QUOTE (-238))) (|HasCategory| (-418 |#2|) (QUOTE (-373)))) (-12 (|HasCategory| (-418 |#2|) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-418 |#2|) (QUOTE (-373))))) (-1021 |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."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3765 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) +((|HasCategory| (-575) (QUOTE (-924))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-148))) (|HasCategory| (-575) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-1039))) (|HasCategory| (-575) (QUOTE (-831))) (-3763 (|HasCategory| (-575) (QUOTE (-831))) (|HasCategory| (-575) (QUOTE (-861)))) (|HasCategory| (-575) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-1169))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| (-575) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| (-575) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| (-575) (QUOTE (-237))) (|HasCategory| (-575) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| (-575) (QUOTE (-238))) (|HasCategory| (-575) (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| (-575) (LIST (QUOTE -525) (QUOTE (-1194)) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -318) (QUOTE (-575)))) (|HasCategory| (-575) (LIST (QUOTE -295) (QUOTE (-575)) (QUOTE (-575)))) (|HasCategory| (-575) (QUOTE (-316))) (|HasCategory| (-575) (QUOTE (-556))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-575) (LIST (QUOTE -650) (QUOTE (-575)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-575) (QUOTE (-924)))) (|HasCategory| (-575) (QUOTE (-146))))) (-1022) ((|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 @@ -4048,19 +4048,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4453 . T) (-4458 . T) (-4452 . T) (-4455 . T) (-4454 . T) ((-4462 "*") . T) (-4457 . T)) NIL -(-1030 R -3029) +(-1030 R -3027) ((|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 -(-1031 R -3029) +(-1031 R -3027) ((|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 -(-1032 -3029 UP) +(-1032 -3027 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 -(-1033 -3029 UP) +(-1033 -3027 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 @@ -4095,8 +4095,8 @@ NIL (-1041 |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"))) ((-4453 . T) (-4458 . T) (-4452 . T) (-4455 . T) (-4454 . T) ((-4462 "*") . T) (-4457 . T)) -((-3765 (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (QUOTE (-575))))) -(-1042 -3029 L) +((-3763 (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-418 (-575)) (LIST (QUOTE -1055) (QUOTE (-575))))) +(-1042 -3027 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 @@ -4132,14 +4132,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1051 -3029 |Expon| |VarSet| |FPol| |LFPol|) +(-1051 -3027 |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"))) (((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-1052) ((|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.}"))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1194))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-1194) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1194))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-1194) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873))))) (-1053) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4196,7 +4196,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4457 . T)) NIL -(-1067 |xx| -3029) +(-1067 |xx| -3027) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4215,7 +4215,7 @@ NIL (-1071 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4460 . T) (-4455 . T) (-4454 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-3765 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (QUOTE (-316))) (|HasCategory| |#3| (QUOTE (-567))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-873))))) +((|HasCategory| |#3| (QUOTE (-174))) (-3763 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-373)))) (|HasCategory| |#3| (QUOTE (-373))) (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (QUOTE (-316))) (|HasCategory| |#3| (QUOTE (-567))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-873))))) (-1072 |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 @@ -4251,7 +4251,7 @@ NIL (-1080) ((|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}"))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1194))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-1194) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1194))) (LIST (QUOTE |:|) (QUOTE -3179) (QUOTE (-52))))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-52) (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| (-52) (QUOTE (-1117))) (|HasCategory| (-52) (LIST (QUOTE -318) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (QUOTE (-1117))) (|HasCategory| (-1194) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-52) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (LIST (QUOTE -624) (QUOTE (-873))))) (-1081 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 @@ -4300,11 +4300,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1093 |Base| R -3029) +(-1093 |Base| R -3027) ((|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 -(-1094 |Base| R -3029) +(-1094 |Base| R -3027) ((|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 @@ -4319,7 +4319,7 @@ NIL (-1097 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."))) ((-4453 |has| |#1| (-373)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-359))) (-3765 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-359))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-378))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-359)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))))) (-1098 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 @@ -4347,7 +4347,7 @@ NIL (-1104 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"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-924))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) +((|HasCategory| |#1| (QUOTE (-924))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#1| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1105 (-1194)) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasAttribute| |#1| (QUOTE -4458)) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-924)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1105 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 @@ -4407,7 +4407,7 @@ NIL (-1119 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)}}"))) ((-4460 . T) (-4450 . T) (-4461 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-378))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-1120 |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 ().")) 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(|HasCategory| |#3| (QUOTE (-1066)))) (-12 (|HasCategory| |#3| (QUOTE (-1066))) (|HasCategory| |#3| (LIST (QUOTE -913) (QUOTE (-1194))))) (|HasCategory| |#3| (QUOTE (-861))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#3| (QUOTE (-1117))) (|HasCategory| |#3| (LIST (QUOTE -318) (|devaluate| |#3|))))) (-1131 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 @@ -4460,7 +4460,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1133 R -3029) +(-1133 R -3027) ((|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\".") 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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}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373)))) (-1144 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}"))) ((-4461 . T) (-4460 . T)) NIL -(-1145 UP -3029) +(-1145 UP -3027) ((|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 @@ -4563,11 +4563,11 @@ NIL (-1158 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -318) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117))) (-3765 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -318) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117))))) (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -318) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117))) (-3763 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -318) (LIST (QUOTE -1157) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1157 |#1| |#2|) (QUOTE (-1117))))) (|HasCategory| (-1157 |#1| |#2|) (LIST (QUOTE -624) (QUOTE (-873))))) (-1159 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4457 . T) (-4449 |has| |#2| (-6 (-4462 "*"))) (-4460 . T) (-4454 . T) (-4455 . T)) -((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-373))) (-3765 (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-316))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-373))) (-3763 (|HasAttribute| |#2| (QUOTE (-4462 "*"))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-1160 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4587,7 +4587,7 @@ NIL (-1164 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-1165 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 @@ -4599,7 +4599,7 @@ NIL (-1167 |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."))) ((-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117)))) +((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117)))) (-1168) ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL @@ -4627,7 +4627,7 @@ NIL (-1174 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) ((-4461 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-1175) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4461 . T) (-4460 . T)) @@ -4635,11 +4635,11 @@ NIL (-1176) NIL ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) +((-3763 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| (-145) (QUOTE (-1117))) (|HasCategory| (-145) (LIST (QUOTE -318) (QUOTE (-145)))))) (-1177 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#1|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-1176) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (QUOTE (-1176))) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#1|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (QUOTE (-1117))) (|HasCategory| (-1176) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 (-1176)) (|:| -3179 |#1|)) (LIST (QUOTE -624) (QUOTE (-873))))) (-1178 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 @@ -4669,10 +4669,10 @@ NIL NIL NIL (-1185 |Coef| |var| |cen|) -((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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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}."))) +((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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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}."))) +((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|)))) (|HasCategory| (-782) (QUOTE (-1129))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasSignature| |#1| (LIST (QUOTE -2883) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasCategory| |#1| (QUOTE (-373))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4413) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|)))) (|HasCategory| (-782) (QUOTE (-1129))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) (-1193) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4715,7 +4715,7 @@ NIL (-1196 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-6 -4458)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3765 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| (-988) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasAttribute| |#1| (QUOTE -4458))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3763 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-463))) (-12 (|HasCategory| (-988) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasAttribute| |#1| (QUOTE -4458))) (-1197) ((|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 @@ -4759,7 +4759,7 @@ NIL (-1207 |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}"))) ((-4460 . T) (-4461 . T)) -((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3765 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -318) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4169) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3179) (|devaluate| |#2|)))))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#2| (QUOTE (-1117)))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -625) (QUOTE (-547)))) (-12 (|HasCategory| |#2| (QUOTE (-1117))) (|HasCategory| |#2| (LIST (QUOTE -318) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1117))) (-3763 (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#2| (LIST (QUOTE -624) (QUOTE (-873)))) (|HasCategory| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (LIST (QUOTE -624) (QUOTE (-873))))) (-1208 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 @@ -4815,7 +4815,7 @@ NIL (-1221 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4461 . T) (-4460 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) +((-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1117))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (-1222 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4824,7 +4824,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1224 R -3029) +(-1224 R -3027) ((|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 @@ -4832,7 +4832,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1226 R -3029) +(-1226 R -3027) ((|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 -625) (LIST (QUOTE -904) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -898) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -898) (|devaluate| |#1|))))) @@ -4847,7 +4847,7 @@ NIL (-1229 |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}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-373)))) (-1230 |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 @@ -4860,7 +4860,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) -(-1233 -3029) +(-1233 -3027) ((|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 @@ -4923,11 +4923,11 @@ NIL (-1248 |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)}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . 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|#3|) (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1277 |#1| |#2| |#3|) (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| (-1277 |#1| |#2| |#3|) (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| (-1277 |#1| |#2| |#3|) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1277 |#1| |#2| |#3|) (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-373)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1277 |#1| |#2| |#3|) (QUOTE (-924))) (|HasCategory| |#1| (QUOTE (-373)))) (-12 (|HasCategory| (-1277 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-373)))) (|HasCategory| |#1| (QUOTE (-146))))) (-1250 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4963,7 +4963,7 @@ NIL (-1258 |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}"))) (((-4462 "*") |has| |#2| (-174)) (-4453 |has| |#2| (-567)) (-4456 |has| |#2| (-373)) (-4458 |has| |#2| (-6 -4458)) (-4455 . T) (-4454 . T) (-4457 . T)) -((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3765 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3765 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3765 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) +((|HasCategory| |#2| (QUOTE (-924))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-174))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-567)))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-389)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-389))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -898) (QUOTE (-575)))) (|HasCategory| |#2| (LIST (QUOTE -898) (QUOTE (-575))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-389)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -625) (LIST (QUOTE -904) (QUOTE (-575)))))) (-12 (|HasCategory| (-1099) (LIST (QUOTE -625) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -650) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (QUOTE (-575)))) (-3763 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| |#2| (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (-3763 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-567))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-373))) (|HasCategory| |#2| (QUOTE (-1169))) (|HasCategory| |#2| (LIST (QUOTE -915) (QUOTE (-1194)))) (|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4458)) (|HasCategory| |#2| (QUOTE (-463))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (-3763 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-924)))) (|HasCategory| |#2| (QUOTE (-146))))) (-1259 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 @@ -4979,7 +4979,7 @@ NIL (-1262 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 (-1194)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1129))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2883) (LIST (|devaluate| |#2|) (QUOTE (-1194)))))) +((|HasCategory| |#2| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1129))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2882) (LIST (|devaluate| |#2|) (QUOTE (-1194)))))) (-1263 |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."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) @@ -5007,15 +5007,15 @@ NIL (-1269 |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)}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3765 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2883) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4413) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) +((|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-1270 |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}."))) +((|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."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4458 |has| |#1| (-373)) (-4452 |has| |#1| (-373)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3765 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2883) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4413) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (|HasCategory| |#1| (QUOTE (-174))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575))) (|devaluate| |#1|)))) (|HasCategory| (-418 (-575)) (QUOTE (-1129))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-3763 (|HasCategory| |#1| (QUOTE (-373))) (|HasCategory| |#1| (QUOTE (-567)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -418) (QUOTE (-575)))))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) (-1271 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))}."))) (((-4462 "*") |has| (-1270 |#2| |#3| |#4|) (-174)) (-4453 |has| (-1270 |#2| |#3| |#4|) (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-174))) (-3765 (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-373))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-463))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-567)))) +((|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-174))) (-3763 (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575)))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| (-1270 |#2| |#3| |#4|) (LIST (QUOTE -1055) (QUOTE (-575)))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-373))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-463))) (|HasCategory| (-1270 |#2| |#3| |#4|) (QUOTE (-567)))) (-1272 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5031,20 +5031,20 @@ NIL (-1275 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-575)))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-1220))) (|HasSignature| |#2| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4413) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1194))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-1220))) (|HasSignature| |#2| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4388) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1194))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#2| (QUOTE (-373)))) (-1276 |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."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) NIL (-1277 |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}."))) +((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4462 "*") |has| |#1| (-174)) (-4453 |has| |#1| (-567)) (-4454 . T) (-4455 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3765 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|)))) (|HasCategory| (-782) (QUOTE (-1129))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasSignature| |#1| (LIST (QUOTE -2883) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasCategory| |#1| (QUOTE (-373))) (-3765 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4413) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasCategory| |#1| (QUOTE (-567))) (-3763 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -913) (QUOTE (-1194)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-782)) (|devaluate| |#1|)))) (|HasCategory| (-782) (QUOTE (-1129))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasSignature| |#1| (LIST (QUOTE -2882) (LIST (|devaluate| |#1|) (QUOTE (-1194)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-782))))) (|HasCategory| |#1| (QUOTE (-373))) (-3763 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-575)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-1220))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -418) (QUOTE (-575))))) (|HasSignature| |#1| (LIST (QUOTE -4388) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1194))))) (|HasSignature| |#1| (LIST (QUOTE -1606) (LIST (LIST (QUOTE -655) (QUOTE (-1194))) (|devaluate| |#1|))))))) (-1278 |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 -(-1279 -3029 UP L UTS) +(-1279 -3027 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 (-567)))) @@ -5071,7 +5071,7 @@ NIL (-1285 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."))) ((-4461 . T) (-4460 . T)) -((-3765 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3765 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3765 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) +((-3763 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-3763 (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-547)))) (-3763 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-575) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-737))) (|HasCategory| |#1| (QUOTE (-1066))) (-12 (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-1066)))) (|HasCategory| |#1| (LIST (QUOTE -624) (QUOTE (-873)))) (-12 (|HasCategory| |#1| (QUOTE (-1117))) (|HasCategory| |#1| (LIST (QUOTE -318) (|devaluate| |#1|))))) (-1286) ((|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 @@ -5104,7 +5104,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1294 K R UP -3029) +(-1294 K R UP -3027) ((|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 @@ -5140,11 +5140,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4453 |has| |#2| (-6 -4453)) (-4455 . T) (-4454 . T) (-4457 . T)) NIL -(-1303 S -3029) +(-1303 S -3027) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-378))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1304 -3029) +(-1304 -3027) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4452 . T) (-4458 . T) (-4453 . T) ((-4462 "*") . T) (-4454 . T) (-4455 . T) (-4457 . T)) NIL @@ -5204,4 +5204,4 @@ NIL NIL NIL NIL -((-3 NIL 2280931 2280936 2280941 2280946) (-2 NIL 2280911 2280916 2280921 2280926) (-1 NIL 2280891 2280896 2280901 2280906) (0 NIL 2280871 2280876 2280881 2280886) (-1314 "ZMOD.spad" 2280680 2280693 2280809 2280866) (-1313 "ZLINDEP.spad" 2279746 2279757 2280670 2280675) (-1312 "ZDSOLVE.spad" 2269691 2269713 2279736 2279741) (-1311 "YSTREAM.spad" 2269186 2269197 2269681 2269686) (-1310 "YDIAGRAM.spad" 2268820 2268829 2269176 2269181) (-1309 "XRPOLY.spad" 2268040 2268060 2268676 2268745) (-1308 "XPR.spad" 2265835 2265848 2267758 2267857) (-1307 "XPOLY.spad" 2265390 2265401 2265691 2265760) (-1306 "XPOLYC.spad" 2264709 2264725 2265316 2265385) (-1305 "XPBWPOLY.spad" 2263146 2263166 2264489 2264558) (-1304 "XF.spad" 2261609 2261624 2263048 2263141) (-1303 "XF.spad" 2260052 2260069 2261493 2261498) (-1302 "XFALG.spad" 2257100 2257116 2259978 2260047) (-1301 "XEXPPKG.spad" 2256351 2256377 2257090 2257095) (-1300 "XDPOLY.spad" 2255965 2255981 2256207 2256276) (-1299 "XALG.spad" 2255625 2255636 2255921 2255960) (-1298 "WUTSET.spad" 2251464 2251481 2255271 2255298) (-1297 "WP.spad" 2250663 2250707 2251322 2251389) (-1296 "WHILEAST.spad" 2250461 2250470 2250653 2250658) (-1295 "WHEREAST.spad" 2250132 2250141 2250451 2250456) (-1294 "WFFINTBS.spad" 2247795 2247817 2250122 2250127) (-1293 "WEIER.spad" 2246017 2246028 2247785 2247790) (-1292 "VSPACE.spad" 2245690 2245701 2245985 2246012) (-1291 "VSPACE.spad" 2245383 2245396 2245680 2245685) (-1290 "VOID.spad" 2245060 2245069 2245373 2245378) (-1289 "VIEW.spad" 2242740 2242749 2245050 2245055) (-1288 "VIEWDEF.spad" 2237941 2237950 2242730 2242735) (-1287 "VIEW3D.spad" 2221902 2221911 2237931 2237936) (-1286 "VIEW2D.spad" 2209793 2209802 2221892 2221897) (-1285 "VECTOR.spad" 2208467 2208478 2208718 2208745) (-1284 "VECTOR2.spad" 2207106 2207119 2208457 2208462) (-1283 "VECTCAT.spad" 2205010 2205021 2207074 2207101) (-1282 "VECTCAT.spad" 2202721 2202734 2204787 2204792) (-1281 "VARIABLE.spad" 2202501 2202516 2202711 2202716) (-1280 "UTYPE.spad" 2202145 2202154 2202491 2202496) (-1279 "UTSODETL.spad" 2201440 2201464 2202101 2202106) (-1278 "UTSODE.spad" 2199656 2199676 2201430 2201435) (-1277 "UTS.spad" 2194460 2194488 2198123 2198220) (-1276 "UTSCAT.spad" 2191939 2191955 2194358 2194455) (-1275 "UTSCAT.spad" 2189062 2189080 2191483 2191488) (-1274 "UTS2.spad" 2188657 2188692 2189052 2189057) (-1273 "URAGG.spad" 2183330 2183341 2188647 2188652) (-1272 "URAGG.spad" 2177967 2177980 2183286 2183291) (-1271 "UPXSSING.spad" 2175612 2175638 2177048 2177181) (-1270 "UPXS.spad" 2172766 2172794 2173744 2173893) (-1269 "UPXSCONS.spad" 2170525 2170545 2170898 2171047) (-1268 "UPXSCCA.spad" 2169096 2169116 2170371 2170520) (-1267 "UPXSCCA.spad" 2167809 2167831 2169086 2169091) (-1266 "UPXSCAT.spad" 2166398 2166414 2167655 2167804) (-1265 "UPXS2.spad" 2165941 2165994 2166388 2166393) (-1264 "UPSQFREE.spad" 2164355 2164369 2165931 2165936) (-1263 "UPSCAT.spad" 2162142 2162166 2164253 2164350) (-1262 "UPSCAT.spad" 2159635 2159661 2161748 2161753) (-1261 "UPOLYC.spad" 2154675 2154686 2159477 2159630) (-1260 "UPOLYC.spad" 2149607 2149620 2154411 2154416) (-1259 "UPOLYC2.spad" 2149078 2149097 2149597 2149602) (-1258 "UP.spad" 2146184 2146199 2146571 2146724) (-1257 "UPMP.spad" 2145084 2145097 2146174 2146179) (-1256 "UPDIVP.spad" 2144649 2144663 2145074 2145079) (-1255 "UPDECOMP.spad" 2142894 2142908 2144639 2144644) (-1254 "UPCDEN.spad" 2142103 2142119 2142884 2142889) (-1253 "UP2.spad" 2141467 2141488 2142093 2142098) (-1252 "UNISEG.spad" 2140820 2140831 2141386 2141391) (-1251 "UNISEG2.spad" 2140317 2140330 2140776 2140781) (-1250 "UNIFACT.spad" 2139420 2139432 2140307 2140312) (-1249 "ULS.spad" 2129062 2129090 2130149 2130578) (-1248 "ULSCONS.spad" 2120196 2120216 2120566 2120715) (-1247 "ULSCCAT.spad" 2117933 2117953 2120042 2120191) (-1246 "ULSCCAT.spad" 2115778 2115800 2117889 2117894) (-1245 "ULSCAT.spad" 2114010 2114026 2115624 2115773) (-1244 "ULS2.spad" 2113524 2113577 2114000 2114005) (-1243 "UINT8.spad" 2113401 2113410 2113514 2113519) (-1242 "UINT64.spad" 2113277 2113286 2113391 2113396) (-1241 "UINT32.spad" 2113153 2113162 2113267 2113272) (-1240 "UINT16.spad" 2113029 2113038 2113143 2113148) (-1239 "UFD.spad" 2112094 2112103 2112955 2113024) (-1238 "UFD.spad" 2111221 2111232 2112084 2112089) (-1237 "UDVO.spad" 2110102 2110111 2111211 2111216) (-1236 "UDPO.spad" 2107595 2107606 2110058 2110063) (-1235 "TYPE.spad" 2107527 2107536 2107585 2107590) (-1234 "TYPEAST.spad" 2107446 2107455 2107517 2107522) (-1233 "TWOFACT.spad" 2106098 2106113 2107436 2107441) (-1232 "TUPLE.spad" 2105584 2105595 2105997 2106002) (-1231 "TUBETOOL.spad" 2102451 2102460 2105574 2105579) (-1230 "TUBE.spad" 2101098 2101115 2102441 2102446) (-1229 "TS.spad" 2099697 2099713 2100663 2100760) (-1228 "TSETCAT.spad" 2086824 2086841 2099665 2099692) (-1227 "TSETCAT.spad" 2073937 2073956 2086780 2086785) (-1226 "TRMANIP.spad" 2068303 2068320 2073643 2073648) (-1225 "TRIMAT.spad" 2067266 2067291 2068293 2068298) (-1224 "TRIGMNIP.spad" 2065793 2065810 2067256 2067261) (-1223 "TRIGCAT.spad" 2065305 2065314 2065783 2065788) (-1222 "TRIGCAT.spad" 2064815 2064826 2065295 2065300) (-1221 "TREE.spad" 2063390 2063401 2064422 2064449) (-1220 "TRANFUN.spad" 2063229 2063238 2063380 2063385) (-1219 "TRANFUN.spad" 2063066 2063077 2063219 2063224) (-1218 "TOPSP.spad" 2062740 2062749 2063056 2063061) (-1217 "TOOLSIGN.spad" 2062403 2062414 2062730 2062735) (-1216 "TEXTFILE.spad" 2060964 2060973 2062393 2062398) (-1215 "TEX.spad" 2058110 2058119 2060954 2060959) (-1214 "TEX1.spad" 2057666 2057677 2058100 2058105) (-1213 "TEMUTL.spad" 2057221 2057230 2057656 2057661) (-1212 "TBCMPPK.spad" 2055314 2055337 2057211 2057216) (-1211 "TBAGG.spad" 2054364 2054387 2055294 2055309) (-1210 "TBAGG.spad" 2053422 2053447 2054354 2054359) (-1209 "TANEXP.spad" 2052830 2052841 2053412 2053417) (-1208 "TALGOP.spad" 2052554 2052565 2052820 2052825) (-1207 "TABLE.spad" 2050965 2050988 2051235 2051262) (-1206 "TABLEAU.spad" 2050446 2050457 2050955 2050960) (-1205 "TABLBUMP.spad" 2047249 2047260 2050436 2050441) (-1204 "SYSTEM.spad" 2046477 2046486 2047239 2047244) (-1203 "SYSSOLP.spad" 2043960 2043971 2046467 2046472) (-1202 "SYSPTR.spad" 2043859 2043868 2043950 2043955) (-1201 "SYSNNI.spad" 2043041 2043052 2043849 2043854) (-1200 "SYSINT.spad" 2042445 2042456 2043031 2043036) (-1199 "SYNTAX.spad" 2038651 2038660 2042435 2042440) (-1198 "SYMTAB.spad" 2036719 2036728 2038641 2038646) (-1197 "SYMS.spad" 2032742 2032751 2036709 2036714) (-1196 "SYMPOLY.spad" 2031749 2031760 2031831 2031958) (-1195 "SYMFUNC.spad" 2031250 2031261 2031739 2031744) (-1194 "SYMBOL.spad" 2028753 2028762 2031240 2031245) (-1193 "SWITCH.spad" 2025524 2025533 2028743 2028748) (-1192 "SUTS.spad" 2022429 2022457 2023991 2024088) (-1191 "SUPXS.spad" 2019570 2019598 2020561 2020710) (-1190 "SUP.spad" 2016290 2016301 2017063 2017216) (-1189 "SUPFRACF.spad" 2015395 2015413 2016280 2016285) (-1188 "SUP2.spad" 2014787 2014800 2015385 2015390) (-1187 "SUMRF.spad" 2013761 2013772 2014777 2014782) (-1186 "SUMFS.spad" 2013398 2013415 2013751 2013756) (-1185 "SULS.spad" 2003027 2003055 2004127 2004556) (-1184 "SUCHTAST.spad" 2002796 2002805 2003017 2003022) (-1183 "SUCH.spad" 2002478 2002493 2002786 2002791) (-1182 "SUBSPACE.spad" 1994593 1994608 2002468 2002473) (-1181 "SUBRESP.spad" 1993763 1993777 1994549 1994554) (-1180 "STTF.spad" 1989862 1989878 1993753 1993758) (-1179 "STTFNC.spad" 1986330 1986346 1989852 1989857) (-1178 "STTAYLOR.spad" 1978965 1978976 1986211 1986216) (-1177 "STRTBL.spad" 1977470 1977487 1977619 1977646) (-1176 "STRING.spad" 1976879 1976888 1976893 1976920) (-1175 "STRICAT.spad" 1976667 1976676 1976847 1976874) (-1174 "STREAM.spad" 1973585 1973596 1976192 1976207) (-1173 "STREAM3.spad" 1973158 1973173 1973575 1973580) (-1172 "STREAM2.spad" 1972286 1972299 1973148 1973153) (-1171 "STREAM1.spad" 1971992 1972003 1972276 1972281) (-1170 "STINPROD.spad" 1970928 1970944 1971982 1971987) (-1169 "STEP.spad" 1970129 1970138 1970918 1970923) (-1168 "STEPAST.spad" 1969363 1969372 1970119 1970124) (-1167 "STBL.spad" 1967889 1967917 1968056 1968071) (-1166 "STAGG.spad" 1966964 1966975 1967879 1967884) (-1165 "STAGG.spad" 1966037 1966050 1966954 1966959) (-1164 "STACK.spad" 1965394 1965405 1965644 1965671) (-1163 "SREGSET.spad" 1963098 1963115 1965040 1965067) (-1162 "SRDCMPK.spad" 1961659 1961679 1963088 1963093) (-1161 "SRAGG.spad" 1956802 1956811 1961627 1961654) (-1160 "SRAGG.spad" 1951965 1951976 1956792 1956797) (-1159 "SQMATRIX.spad" 1949544 1949562 1950460 1950547) (-1158 "SPLTREE.spad" 1944096 1944109 1948980 1949007) (-1157 "SPLNODE.spad" 1940684 1940697 1944086 1944091) (-1156 "SPFCAT.spad" 1939493 1939502 1940674 1940679) (-1155 "SPECOUT.spad" 1938045 1938054 1939483 1939488) (-1154 "SPADXPT.spad" 1929640 1929649 1938035 1938040) (-1153 "spad-parser.spad" 1929105 1929114 1929630 1929635) (-1152 "SPADAST.spad" 1928806 1928815 1929095 1929100) (-1151 "SPACEC.spad" 1913005 1913016 1928796 1928801) (-1150 "SPACE3.spad" 1912781 1912792 1912995 1913000) (-1149 "SORTPAK.spad" 1912330 1912343 1912737 1912742) (-1148 "SOLVETRA.spad" 1910093 1910104 1912320 1912325) (-1147 "SOLVESER.spad" 1908621 1908632 1910083 1910088) (-1146 "SOLVERAD.spad" 1904647 1904658 1908611 1908616) (-1145 "SOLVEFOR.spad" 1903109 1903127 1904637 1904642) (-1144 "SNTSCAT.spad" 1902709 1902726 1903077 1903104) (-1143 "SMTS.spad" 1900981 1901007 1902274 1902371) (-1142 "SMP.spad" 1898456 1898476 1898846 1898973) (-1141 "SMITH.spad" 1897301 1897326 1898446 1898451) (-1140 "SMATCAT.spad" 1895411 1895441 1897245 1897296) (-1139 "SMATCAT.spad" 1893453 1893485 1895289 1895294) (-1138 "SKAGG.spad" 1892416 1892427 1893421 1893448) (-1137 "SINT.spad" 1891356 1891365 1892282 1892411) (-1136 "SIMPAN.spad" 1891084 1891093 1891346 1891351) (-1135 "SIG.spad" 1890414 1890423 1891074 1891079) (-1134 "SIGNRF.spad" 1889532 1889543 1890404 1890409) (-1133 "SIGNEF.spad" 1888811 1888828 1889522 1889527) (-1132 "SIGAST.spad" 1888196 1888205 1888801 1888806) (-1131 "SHP.spad" 1886124 1886139 1888152 1888157) (-1130 "SHDP.spad" 1874327 1874354 1874836 1874935) (-1129 "SGROUP.spad" 1873935 1873944 1874317 1874322) (-1128 "SGROUP.spad" 1873541 1873552 1873925 1873930) (-1127 "SGCF.spad" 1866680 1866689 1873531 1873536) (-1126 "SFRTCAT.spad" 1865610 1865627 1866648 1866675) (-1125 "SFRGCD.spad" 1864673 1864693 1865600 1865605) (-1124 "SFQCMPK.spad" 1859310 1859330 1864663 1864668) (-1123 "SFORT.spad" 1858749 1858763 1859300 1859305) (-1122 "SEXOF.spad" 1858592 1858632 1858739 1858744) (-1121 "SEX.spad" 1858484 1858493 1858582 1858587) (-1120 "SEXCAT.spad" 1856265 1856305 1858474 1858479) (-1119 "SET.spad" 1854589 1854600 1855686 1855725) (-1118 "SETMN.spad" 1853039 1853056 1854579 1854584) (-1117 "SETCAT.spad" 1852361 1852370 1853029 1853034) (-1116 "SETCAT.spad" 1851681 1851692 1852351 1852356) (-1115 "SETAGG.spad" 1848230 1848241 1851661 1851676) (-1114 "SETAGG.spad" 1844787 1844800 1848220 1848225) (-1113 "SEQAST.spad" 1844490 1844499 1844777 1844782) (-1112 "SEGXCAT.spad" 1843646 1843659 1844480 1844485) (-1111 "SEG.spad" 1843459 1843470 1843565 1843570) (-1110 "SEGCAT.spad" 1842384 1842395 1843449 1843454) (-1109 "SEGBIND.spad" 1842142 1842153 1842331 1842336) (-1108 "SEGBIND2.spad" 1841840 1841853 1842132 1842137) (-1107 "SEGAST.spad" 1841554 1841563 1841830 1841835) (-1106 "SEG2.spad" 1840989 1841002 1841510 1841515) (-1105 "SDVAR.spad" 1840265 1840276 1840979 1840984) (-1104 "SDPOL.spad" 1837598 1837609 1837889 1838016) (-1103 "SCPKG.spad" 1835687 1835698 1837588 1837593) (-1102 "SCOPE.spad" 1834840 1834849 1835677 1835682) (-1101 "SCACHE.spad" 1833536 1833547 1834830 1834835) (-1100 "SASTCAT.spad" 1833445 1833454 1833526 1833531) (-1099 "SAOS.spad" 1833317 1833326 1833435 1833440) (-1098 "SAERFFC.spad" 1833030 1833050 1833307 1833312) (-1097 "SAE.spad" 1830500 1830516 1831111 1831246) (-1096 "SAEFACT.spad" 1830201 1830221 1830490 1830495) (-1095 "RURPK.spad" 1827860 1827876 1830191 1830196) (-1094 "RULESET.spad" 1827313 1827337 1827850 1827855) (-1093 "RULE.spad" 1825553 1825577 1827303 1827308) (-1092 "RULECOLD.spad" 1825405 1825418 1825543 1825548) (-1091 "RTVALUE.spad" 1825140 1825149 1825395 1825400) (-1090 "RSTRCAST.spad" 1824857 1824866 1825130 1825135) (-1089 "RSETGCD.spad" 1821235 1821255 1824847 1824852) (-1088 "RSETCAT.spad" 1811171 1811188 1821203 1821230) (-1087 "RSETCAT.spad" 1801127 1801146 1811161 1811166) (-1086 "RSDCMPK.spad" 1799579 1799599 1801117 1801122) (-1085 "RRCC.spad" 1797963 1797993 1799569 1799574) (-1084 "RRCC.spad" 1796345 1796377 1797953 1797958) (-1083 "RPTAST.spad" 1796047 1796056 1796335 1796340) (-1082 "RPOLCAT.spad" 1775407 1775422 1795915 1796042) (-1081 "RPOLCAT.spad" 1754480 1754497 1774990 1774995) (-1080 "ROUTINE.spad" 1750363 1750372 1753127 1753154) (-1079 "ROMAN.spad" 1749691 1749700 1750229 1750358) (-1078 "ROIRC.spad" 1748771 1748803 1749681 1749686) (-1077 "RNS.spad" 1747674 1747683 1748673 1748766) (-1076 "RNS.spad" 1746663 1746674 1747664 1747669) (-1075 "RNG.spad" 1746398 1746407 1746653 1746658) (-1074 "RNGBIND.spad" 1745558 1745572 1746353 1746358) (-1073 "RMODULE.spad" 1745323 1745334 1745548 1745553) (-1072 "RMCAT2.spad" 1744743 1744800 1745313 1745318) (-1071 "RMATRIX.spad" 1743567 1743586 1743910 1743949) (-1070 "RMATCAT.spad" 1739146 1739177 1743523 1743562) (-1069 "RMATCAT.spad" 1734615 1734648 1738994 1738999) (-1068 "RLINSET.spad" 1734170 1734181 1734605 1734610) (-1067 "RINTERP.spad" 1734058 1734078 1734160 1734165) (-1066 "RING.spad" 1733528 1733537 1734038 1734053) (-1065 "RING.spad" 1733006 1733017 1733518 1733523) (-1064 "RIDIST.spad" 1732398 1732407 1732996 1733001) (-1063 "RGCHAIN.spad" 1730981 1730997 1731883 1731910) (-1062 "RGBCSPC.spad" 1730762 1730774 1730971 1730976) (-1061 "RGBCMDL.spad" 1730292 1730304 1730752 1730757) (-1060 "RF.spad" 1727934 1727945 1730282 1730287) (-1059 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1568802 1568929) (-966 "POLYLIFT.spad" 1567552 1567575 1568277 1568282) (-965 "POLYCATQ.spad" 1565670 1565692 1567542 1567547) (-964 "POLYCAT.spad" 1559140 1559161 1565538 1565665) (-963 "POLYCAT.spad" 1551948 1551971 1558348 1558353) (-962 "POLY2UP.spad" 1551400 1551414 1551938 1551943) (-961 "POLY2.spad" 1550997 1551009 1551390 1551395) (-960 "POLUTIL.spad" 1549938 1549967 1550953 1550958) (-959 "POLTOPOL.spad" 1548686 1548701 1549928 1549933) (-958 "POINT.spad" 1547524 1547534 1547611 1547638) (-957 "PNTHEORY.spad" 1544226 1544234 1547514 1547519) (-956 "PMTOOLS.spad" 1543001 1543015 1544216 1544221) (-955 "PMSYM.spad" 1542550 1542560 1542991 1542996) (-954 "PMQFCAT.spad" 1542141 1542155 1542540 1542545) (-953 "PMPRED.spad" 1541620 1541634 1542131 1542136) (-952 "PMPREDFS.spad" 1541074 1541096 1541610 1541615) (-951 "PMPLCAT.spad" 1540154 1540172 1541006 1541011) (-950 "PMLSAGG.spad" 1539739 1539753 1540144 1540149) (-949 "PMKERNEL.spad" 1539318 1539330 1539729 1539734) (-948 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(-835 "OMERRK.spad" 1365915 1365923 1366871 1366876) (-834 "OMENC.spad" 1365259 1365267 1365905 1365910) (-833 "OMDEV.spad" 1359568 1359576 1365249 1365254) (-832 "OMCONN.spad" 1358977 1358985 1359558 1359563) (-831 "OINTDOM.spad" 1358740 1358748 1358903 1358972) (-830 "OFMONOID.spad" 1356863 1356873 1358696 1358701) (-829 "ODVAR.spad" 1356124 1356134 1356853 1356858) (-828 "ODR.spad" 1355768 1355794 1355936 1356085) (-827 "ODPOL.spad" 1353057 1353067 1353397 1353524) (-826 "ODP.spad" 1341396 1341416 1341769 1341868) (-825 "ODETOOLS.spad" 1340045 1340064 1341386 1341391) (-824 "ODESYS.spad" 1337739 1337756 1340035 1340040) (-823 "ODERTRIC.spad" 1333748 1333765 1337696 1337701) (-822 "ODERED.spad" 1333147 1333171 1333738 1333743) (-821 "ODERAT.spad" 1330762 1330779 1333137 1333142) (-820 "ODEPRRIC.spad" 1327799 1327821 1330752 1330757) (-819 "ODEPROB.spad" 1327056 1327064 1327789 1327794) (-818 "ODEPRIM.spad" 1324390 1324412 1327046 1327051) (-817 "ODEPAL.spad" 1323776 1323800 1324380 1324385) (-816 "ODEPACK.spad" 1310442 1310450 1323766 1323771) (-815 "ODEINT.spad" 1309877 1309893 1310432 1310437) (-814 "ODEIFTBL.spad" 1307272 1307280 1309867 1309872) (-813 "ODEEF.spad" 1302763 1302779 1307262 1307267) (-812 "ODECONST.spad" 1302300 1302318 1302753 1302758) (-811 "ODECAT.spad" 1300898 1300906 1302290 1302295) (-810 "OCT.spad" 1299034 1299044 1299748 1299787) (-809 "OCTCT2.spad" 1298680 1298701 1299024 1299029) (-808 "OC.spad" 1296476 1296486 1298636 1298675) (-807 "OC.spad" 1293997 1294009 1296159 1296164) (-806 "OCAMON.spad" 1293845 1293853 1293987 1293992) (-805 "OASGP.spad" 1293660 1293668 1293835 1293840) (-804 "OAMONS.spad" 1293182 1293190 1293650 1293655) (-803 "OAMON.spad" 1293043 1293051 1293172 1293177) (-802 "OAGROUP.spad" 1292905 1292913 1293033 1293038) (-801 "NUMTUBE.spad" 1292496 1292512 1292895 1292900) (-800 "NUMQUAD.spad" 1280472 1280480 1292486 1292491) (-799 "NUMODE.spad" 1271826 1271834 1280462 1280467) (-798 "NUMINT.spad" 1269392 1269400 1271816 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(-159 "COMBF.spad" 178393 178409 181001 181006) (-158 "COLOR.spad" 177230 177238 178383 178388) (-157 "COLONAST.spad" 176896 176904 177220 177225) (-156 "CMPLXRT.spad" 176607 176624 176886 176891) (-155 "CLLCTAST.spad" 176269 176277 176597 176602) (-154 "CLIP.spad" 172377 172385 176259 176264) (-153 "CLIF.spad" 171032 171048 172333 172372) (-152 "CLAGG.spad" 167537 167547 171022 171027) (-151 "CLAGG.spad" 163913 163925 167400 167405) (-150 "CINTSLPE.spad" 163244 163257 163903 163908) (-149 "CHVAR.spad" 161382 161404 163234 163239) (-148 "CHARZ.spad" 161297 161305 161362 161377) (-147 "CHARPOL.spad" 160807 160817 161287 161292) (-146 "CHARNZ.spad" 160560 160568 160787 160802) (-145 "CHAR.spad" 158434 158442 160550 160555) (-144 "CFCAT.spad" 157762 157770 158424 158429) (-143 "CDEN.spad" 156958 156972 157752 157757) (-142 "CCLASS.spad" 155107 155115 156369 156408) (-141 "CATEGORY.spad" 154149 154157 155097 155102) (-140 "CATCTOR.spad" 154040 154048 154139 154144) (-139 "CATAST.spad" 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133011) (-118 "BPADICRT.spad" 129828 129840 130083 130176) (-117 "BPADIC.spad" 129492 129504 129754 129823) (-116 "BOUNDZRO.spad" 129148 129165 129482 129487) (-115 "BOP.spad" 124330 124338 129138 129143) (-114 "BOP1.spad" 121796 121806 124320 124325) (-113 "BOOLE.spad" 121446 121454 121786 121791) (-112 "BOOLEAN.spad" 120884 120892 121436 121441) (-111 "BMODULE.spad" 120596 120608 120852 120879) (-110 "BITS.spad" 120017 120025 120232 120259) (-109 "BINDING.spad" 119430 119438 120007 120012) (-108 "BINARY.spad" 117444 117452 117800 117893) (-107 "BGAGG.spad" 116649 116659 117424 117439) (-106 "BGAGG.spad" 115862 115874 116639 116644) (-105 "BFUNCT.spad" 115426 115434 115842 115857) (-104 "BEZOUT.spad" 114566 114593 115376 115381) (-103 "BBTREE.spad" 111411 111421 114173 114200) (-102 "BASTYPE.spad" 111083 111091 111401 111406) (-101 "BASTYPE.spad" 110753 110763 111073 111078) (-100 "BALFACT.spad" 110212 110225 110743 110748) (-99 "AUTOMOR.spad" 109663 109672 110192 110207) (-98 "ATTREG.spad" 106386 106393 109415 109658) (-97 "ATTRBUT.spad" 102409 102416 106366 106381) (-96 "ATTRAST.spad" 102126 102133 102399 102404) (-95 "ATRIG.spad" 101596 101603 102116 102121) (-94 "ATRIG.spad" 101064 101073 101586 101591) (-93 "ASTCAT.spad" 100968 100975 101054 101059) (-92 "ASTCAT.spad" 100870 100879 100958 100963) (-91 "ASTACK.spad" 100209 100218 100477 100504) (-90 "ASSOCEQ.spad" 99035 99046 100165 100170) (-89 "ASP9.spad" 98116 98129 99025 99030) (-88 "ASP8.spad" 97159 97172 98106 98111) (-87 "ASP80.spad" 96481 96494 97149 97154) (-86 "ASP7.spad" 95641 95654 96471 96476) (-85 "ASP78.spad" 95092 95105 95631 95636) (-84 "ASP77.spad" 94461 94474 95082 95087) (-83 "ASP74.spad" 93553 93566 94451 94456) (-82 "ASP73.spad" 92824 92837 93543 93548) (-81 "ASP6.spad" 91691 91704 92814 92819) (-80 "ASP55.spad" 90200 90213 91681 91686) (-79 "ASP50.spad" 88017 88030 90190 90195) (-78 "ASP4.spad" 87312 87325 88007 88012) (-77 "ASP49.spad" 86311 86324 87302 87307) (-76 "ASP42.spad" 84718 84757 86301 86306) (-75 "ASP41.spad" 83297 83336 84708 84713) (-74 "ASP35.spad" 82285 82298 83287 83292) (-73 "ASP34.spad" 81586 81599 82275 82280) (-72 "ASP33.spad" 81146 81159 81576 81581) (-71 "ASP31.spad" 80286 80299 81136 81141) (-70 "ASP30.spad" 79178 79191 80276 80281) (-69 "ASP29.spad" 78644 78657 79168 79173) (-68 "ASP28.spad" 69917 69930 78634 78639) (-67 "ASP27.spad" 68814 68827 69907 69912) (-66 "ASP24.spad" 67901 67914 68804 68809) (-65 "ASP20.spad" 67365 67378 67891 67896) (-64 "ASP1.spad" 66746 66759 67355 67360) (-63 "ASP19.spad" 61432 61445 66736 66741) (-62 "ASP12.spad" 60846 60859 61422 61427) (-61 "ASP10.spad" 60117 60130 60836 60841) (-60 "ARRAY2.spad" 59477 59486 59724 59751) (-59 "ARRAY1.spad" 58314 58323 58660 58687) (-58 "ARRAY12.spad" 57027 57038 58304 58309) (-57 "ARR2CAT.spad" 52801 52822 56995 57022) (-56 "ARR2CAT.spad" 48595 48618 52791 52796) (-55 "ARITY.spad" 47967 47974 48585 48590) (-54 "APPRULE.spad" 47227 47249 47957 47962) (-53 "APPLYORE.spad" 46846 46859 47217 47222) (-52 "ANY.spad" 45705 45712 46836 46841) (-51 "ANY1.spad" 44776 44785 45695 45700) (-50 "ANTISYM.spad" 43221 43237 44756 44771) (-49 "ANON.spad" 42914 42921 43211 43216) (-48 "AN.spad" 41223 41230 42730 42823) (-47 "AMR.spad" 39408 39419 41121 41218) (-46 "AMR.spad" 37430 37443 39145 39150) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2279571 2279576 2279581 2279586) (-2 NIL 2279551 2279556 2279561 2279566) (-1 NIL 2279531 2279536 2279541 2279546) (0 NIL 2279511 2279516 2279521 2279526) (-1314 "ZMOD.spad" 2279320 2279333 2279449 2279506) (-1313 "ZLINDEP.spad" 2278386 2278397 2279310 2279315) (-1312 "ZDSOLVE.spad" 2268331 2268353 2278376 2278381) (-1311 "YSTREAM.spad" 2267826 2267837 2268321 2268326) (-1310 "YDIAGRAM.spad" 2267460 2267469 2267816 2267821) (-1309 "XRPOLY.spad" 2266680 2266700 2267316 2267385) (-1308 "XPR.spad" 2264475 2264488 2266398 2266497) (-1307 "XPOLY.spad" 2264030 2264041 2264331 2264400) (-1306 "XPOLYC.spad" 2263349 2263365 2263956 2264025) (-1305 "XPBWPOLY.spad" 2261786 2261806 2263129 2263198) (-1304 "XF.spad" 2260249 2260264 2261688 2261781) (-1303 "XF.spad" 2258692 2258709 2260133 2260138) (-1302 "XFALG.spad" 2255740 2255756 2258618 2258687) (-1301 "XEXPPKG.spad" 2254991 2255017 2255730 2255735) (-1300 "XDPOLY.spad" 2254605 2254621 2254847 2254916) (-1299 "XALG.spad" 2254265 2254276 2254561 2254600) (-1298 "WUTSET.spad" 2250104 2250121 2253911 2253938) (-1297 "WP.spad" 2249303 2249347 2249962 2250029) (-1296 "WHILEAST.spad" 2249101 2249110 2249293 2249298) (-1295 "WHEREAST.spad" 2248772 2248781 2249091 2249096) (-1294 "WFFINTBS.spad" 2246435 2246457 2248762 2248767) (-1293 "WEIER.spad" 2244657 2244668 2246425 2246430) (-1292 "VSPACE.spad" 2244330 2244341 2244625 2244652) (-1291 "VSPACE.spad" 2244023 2244036 2244320 2244325) (-1290 "VOID.spad" 2243700 2243709 2244013 2244018) (-1289 "VIEW.spad" 2241380 2241389 2243690 2243695) (-1288 "VIEWDEF.spad" 2236581 2236590 2241370 2241375) (-1287 "VIEW3D.spad" 2220542 2220551 2236571 2236576) (-1286 "VIEW2D.spad" 2208433 2208442 2220532 2220537) (-1285 "VECTOR.spad" 2207107 2207118 2207358 2207385) (-1284 "VECTOR2.spad" 2205746 2205759 2207097 2207102) (-1283 "VECTCAT.spad" 2203650 2203661 2205714 2205741) (-1282 "VECTCAT.spad" 2201361 2201374 2203427 2203432) (-1281 "VARIABLE.spad" 2201141 2201156 2201351 2201356) (-1280 "UTYPE.spad" 2200785 2200794 2201131 2201136) (-1279 "UTSODETL.spad" 2200080 2200104 2200741 2200746) (-1278 "UTSODE.spad" 2198296 2198316 2200070 2200075) (-1277 "UTS.spad" 2193243 2193271 2196763 2196860) (-1276 "UTSCAT.spad" 2190722 2190738 2193141 2193238) (-1275 "UTSCAT.spad" 2187845 2187863 2190266 2190271) (-1274 "UTS2.spad" 2187440 2187475 2187835 2187840) (-1273 "URAGG.spad" 2182113 2182124 2187430 2187435) (-1272 "URAGG.spad" 2176750 2176763 2182069 2182074) (-1271 "UPXSSING.spad" 2174395 2174421 2175831 2175964) (-1270 "UPXS.spad" 2171691 2171719 2172527 2172676) (-1269 "UPXSCONS.spad" 2169450 2169470 2169823 2169972) (-1268 "UPXSCCA.spad" 2168021 2168041 2169296 2169445) (-1267 "UPXSCCA.spad" 2166734 2166756 2168011 2168016) (-1266 "UPXSCAT.spad" 2165323 2165339 2166580 2166729) (-1265 "UPXS2.spad" 2164866 2164919 2165313 2165318) (-1264 "UPSQFREE.spad" 2163280 2163294 2164856 2164861) (-1263 "UPSCAT.spad" 2161067 2161091 2163178 2163275) (-1262 "UPSCAT.spad" 2158560 2158586 2160673 2160678) (-1261 "UPOLYC.spad" 2153600 2153611 2158402 2158555) (-1260 "UPOLYC.spad" 2148532 2148545 2153336 2153341) (-1259 "UPOLYC2.spad" 2148003 2148022 2148522 2148527) (-1258 "UP.spad" 2145109 2145124 2145496 2145649) (-1257 "UPMP.spad" 2144009 2144022 2145099 2145104) (-1256 "UPDIVP.spad" 2143574 2143588 2143999 2144004) (-1255 "UPDECOMP.spad" 2141819 2141833 2143564 2143569) (-1254 "UPCDEN.spad" 2141028 2141044 2141809 2141814) (-1253 "UP2.spad" 2140392 2140413 2141018 2141023) (-1252 "UNISEG.spad" 2139745 2139756 2140311 2140316) (-1251 "UNISEG2.spad" 2139242 2139255 2139701 2139706) (-1250 "UNIFACT.spad" 2138345 2138357 2139232 2139237) (-1249 "ULS.spad" 2128129 2128157 2129074 2129503) (-1248 "ULSCONS.spad" 2119263 2119283 2119633 2119782) (-1247 "ULSCCAT.spad" 2117000 2117020 2119109 2119258) (-1246 "ULSCCAT.spad" 2114845 2114867 2116956 2116961) (-1245 "ULSCAT.spad" 2113077 2113093 2114691 2114840) (-1244 "ULS2.spad" 2112591 2112644 2113067 2113072) (-1243 "UINT8.spad" 2112468 2112477 2112581 2112586) (-1242 "UINT64.spad" 2112344 2112353 2112458 2112463) (-1241 "UINT32.spad" 2112220 2112229 2112334 2112339) (-1240 "UINT16.spad" 2112096 2112105 2112210 2112215) (-1239 "UFD.spad" 2111161 2111170 2112022 2112091) (-1238 "UFD.spad" 2110288 2110299 2111151 2111156) (-1237 "UDVO.spad" 2109169 2109178 2110278 2110283) (-1236 "UDPO.spad" 2106662 2106673 2109125 2109130) (-1235 "TYPE.spad" 2106594 2106603 2106652 2106657) (-1234 "TYPEAST.spad" 2106513 2106522 2106584 2106589) (-1233 "TWOFACT.spad" 2105165 2105180 2106503 2106508) (-1232 "TUPLE.spad" 2104651 2104662 2105064 2105069) (-1231 "TUBETOOL.spad" 2101518 2101527 2104641 2104646) (-1230 "TUBE.spad" 2100165 2100182 2101508 2101513) (-1229 "TS.spad" 2098764 2098780 2099730 2099827) (-1228 "TSETCAT.spad" 2085891 2085908 2098732 2098759) (-1227 "TSETCAT.spad" 2073004 2073023 2085847 2085852) (-1226 "TRMANIP.spad" 2067370 2067387 2072710 2072715) (-1225 "TRIMAT.spad" 2066333 2066358 2067360 2067365) (-1224 "TRIGMNIP.spad" 2064860 2064877 2066323 2066328) (-1223 "TRIGCAT.spad" 2064372 2064381 2064850 2064855) (-1222 "TRIGCAT.spad" 2063882 2063893 2064362 2064367) (-1221 "TREE.spad" 2062457 2062468 2063489 2063516) (-1220 "TRANFUN.spad" 2062296 2062305 2062447 2062452) (-1219 "TRANFUN.spad" 2062133 2062144 2062286 2062291) (-1218 "TOPSP.spad" 2061807 2061816 2062123 2062128) (-1217 "TOOLSIGN.spad" 2061470 2061481 2061797 2061802) (-1216 "TEXTFILE.spad" 2060031 2060040 2061460 2061465) (-1215 "TEX.spad" 2057177 2057186 2060021 2060026) (-1214 "TEX1.spad" 2056733 2056744 2057167 2057172) (-1213 "TEMUTL.spad" 2056288 2056297 2056723 2056728) (-1212 "TBCMPPK.spad" 2054381 2054404 2056278 2056283) (-1211 "TBAGG.spad" 2053431 2053454 2054361 2054376) (-1210 "TBAGG.spad" 2052489 2052514 2053421 2053426) (-1209 "TANEXP.spad" 2051897 2051908 2052479 2052484) (-1208 "TALGOP.spad" 2051621 2051632 2051887 2051892) (-1207 "TABLE.spad" 2050032 2050055 2050302 2050329) (-1206 "TABLEAU.spad" 2049513 2049524 2050022 2050027) (-1205 "TABLBUMP.spad" 2046316 2046327 2049503 2049508) (-1204 "SYSTEM.spad" 2045544 2045553 2046306 2046311) (-1203 "SYSSOLP.spad" 2043027 2043038 2045534 2045539) (-1202 "SYSPTR.spad" 2042926 2042935 2043017 2043022) (-1201 "SYSNNI.spad" 2042108 2042119 2042916 2042921) (-1200 "SYSINT.spad" 2041512 2041523 2042098 2042103) (-1199 "SYNTAX.spad" 2037718 2037727 2041502 2041507) (-1198 "SYMTAB.spad" 2035786 2035795 2037708 2037713) (-1197 "SYMS.spad" 2031809 2031818 2035776 2035781) (-1196 "SYMPOLY.spad" 2030816 2030827 2030898 2031025) (-1195 "SYMFUNC.spad" 2030317 2030328 2030806 2030811) (-1194 "SYMBOL.spad" 2027820 2027829 2030307 2030312) (-1193 "SWITCH.spad" 2024591 2024600 2027810 2027815) (-1192 "SUTS.spad" 2021639 2021667 2023058 2023155) (-1191 "SUPXS.spad" 2018922 2018950 2019771 2019920) (-1190 "SUP.spad" 2015642 2015653 2016415 2016568) (-1189 "SUPFRACF.spad" 2014747 2014765 2015632 2015637) (-1188 "SUP2.spad" 2014139 2014152 2014737 2014742) (-1187 "SUMRF.spad" 2013113 2013124 2014129 2014134) (-1186 "SUMFS.spad" 2012750 2012767 2013103 2013108) (-1185 "SULS.spad" 2002521 2002549 2003479 2003908) (-1184 "SUCHTAST.spad" 2002290 2002299 2002511 2002516) (-1183 "SUCH.spad" 2001972 2001987 2002280 2002285) (-1182 "SUBSPACE.spad" 1994087 1994102 2001962 2001967) (-1181 "SUBRESP.spad" 1993257 1993271 1994043 1994048) (-1180 "STTF.spad" 1989356 1989372 1993247 1993252) (-1179 "STTFNC.spad" 1985824 1985840 1989346 1989351) (-1178 "STTAYLOR.spad" 1978459 1978470 1985705 1985710) (-1177 "STRTBL.spad" 1976964 1976981 1977113 1977140) (-1176 "STRING.spad" 1976373 1976382 1976387 1976414) (-1175 "STRICAT.spad" 1976161 1976170 1976341 1976368) (-1174 "STREAM.spad" 1973079 1973090 1975686 1975701) (-1173 "STREAM3.spad" 1972652 1972667 1973069 1973074) (-1172 "STREAM2.spad" 1971780 1971793 1972642 1972647) (-1171 "STREAM1.spad" 1971486 1971497 1971770 1971775) (-1170 "STINPROD.spad" 1970422 1970438 1971476 1971481) (-1169 "STEP.spad" 1969623 1969632 1970412 1970417) (-1168 "STEPAST.spad" 1968857 1968866 1969613 1969618) (-1167 "STBL.spad" 1967383 1967411 1967550 1967565) (-1166 "STAGG.spad" 1966458 1966469 1967373 1967378) (-1165 "STAGG.spad" 1965531 1965544 1966448 1966453) (-1164 "STACK.spad" 1964888 1964899 1965138 1965165) (-1163 "SREGSET.spad" 1962592 1962609 1964534 1964561) (-1162 "SRDCMPK.spad" 1961153 1961173 1962582 1962587) (-1161 "SRAGG.spad" 1956296 1956305 1961121 1961148) (-1160 "SRAGG.spad" 1951459 1951470 1956286 1956291) (-1159 "SQMATRIX.spad" 1949038 1949056 1949954 1950041) (-1158 "SPLTREE.spad" 1943590 1943603 1948474 1948501) (-1157 "SPLNODE.spad" 1940178 1940191 1943580 1943585) (-1156 "SPFCAT.spad" 1938987 1938996 1940168 1940173) (-1155 "SPECOUT.spad" 1937539 1937548 1938977 1938982) (-1154 "SPADXPT.spad" 1929134 1929143 1937529 1937534) (-1153 "spad-parser.spad" 1928599 1928608 1929124 1929129) (-1152 "SPADAST.spad" 1928300 1928309 1928589 1928594) (-1151 "SPACEC.spad" 1912499 1912510 1928290 1928295) (-1150 "SPACE3.spad" 1912275 1912286 1912489 1912494) (-1149 "SORTPAK.spad" 1911824 1911837 1912231 1912236) (-1148 "SOLVETRA.spad" 1909587 1909598 1911814 1911819) (-1147 "SOLVESER.spad" 1908115 1908126 1909577 1909582) (-1146 "SOLVERAD.spad" 1904141 1904152 1908105 1908110) (-1145 "SOLVEFOR.spad" 1902603 1902621 1904131 1904136) (-1144 "SNTSCAT.spad" 1902203 1902220 1902571 1902598) (-1143 "SMTS.spad" 1900475 1900501 1901768 1901865) (-1142 "SMP.spad" 1897950 1897970 1898340 1898467) (-1141 "SMITH.spad" 1896795 1896820 1897940 1897945) (-1140 "SMATCAT.spad" 1894905 1894935 1896739 1896790) (-1139 "SMATCAT.spad" 1892947 1892979 1894783 1894788) (-1138 "SKAGG.spad" 1891910 1891921 1892915 1892942) (-1137 "SINT.spad" 1890850 1890859 1891776 1891905) (-1136 "SIMPAN.spad" 1890578 1890587 1890840 1890845) (-1135 "SIG.spad" 1889908 1889917 1890568 1890573) (-1134 "SIGNRF.spad" 1889026 1889037 1889898 1889903) (-1133 "SIGNEF.spad" 1888305 1888322 1889016 1889021) (-1132 "SIGAST.spad" 1887690 1887699 1888295 1888300) (-1131 "SHP.spad" 1885618 1885633 1887646 1887651) (-1130 "SHDP.spad" 1873821 1873848 1874330 1874429) (-1129 "SGROUP.spad" 1873429 1873438 1873811 1873816) (-1128 "SGROUP.spad" 1873035 1873046 1873419 1873424) (-1127 "SGCF.spad" 1866174 1866183 1873025 1873030) (-1126 "SFRTCAT.spad" 1865104 1865121 1866142 1866169) (-1125 "SFRGCD.spad" 1864167 1864187 1865094 1865099) (-1124 "SFQCMPK.spad" 1858804 1858824 1864157 1864162) (-1123 "SFORT.spad" 1858243 1858257 1858794 1858799) (-1122 "SEXOF.spad" 1858086 1858126 1858233 1858238) (-1121 "SEX.spad" 1857978 1857987 1858076 1858081) (-1120 "SEXCAT.spad" 1855759 1855799 1857968 1857973) (-1119 "SET.spad" 1854083 1854094 1855180 1855219) (-1118 "SETMN.spad" 1852533 1852550 1854073 1854078) (-1117 "SETCAT.spad" 1851855 1851864 1852523 1852528) (-1116 "SETCAT.spad" 1851175 1851186 1851845 1851850) (-1115 "SETAGG.spad" 1847724 1847735 1851155 1851170) (-1114 "SETAGG.spad" 1844281 1844294 1847714 1847719) (-1113 "SEQAST.spad" 1843984 1843993 1844271 1844276) (-1112 "SEGXCAT.spad" 1843140 1843153 1843974 1843979) (-1111 "SEG.spad" 1842953 1842964 1843059 1843064) (-1110 "SEGCAT.spad" 1841878 1841889 1842943 1842948) (-1109 "SEGBIND.spad" 1841636 1841647 1841825 1841830) (-1108 "SEGBIND2.spad" 1841334 1841347 1841626 1841631) (-1107 "SEGAST.spad" 1841048 1841057 1841324 1841329) (-1106 "SEG2.spad" 1840483 1840496 1841004 1841009) (-1105 "SDVAR.spad" 1839759 1839770 1840473 1840478) (-1104 "SDPOL.spad" 1837092 1837103 1837383 1837510) (-1103 "SCPKG.spad" 1835181 1835192 1837082 1837087) (-1102 "SCOPE.spad" 1834334 1834343 1835171 1835176) (-1101 "SCACHE.spad" 1833030 1833041 1834324 1834329) (-1100 "SASTCAT.spad" 1832939 1832948 1833020 1833025) (-1099 "SAOS.spad" 1832811 1832820 1832929 1832934) (-1098 "SAERFFC.spad" 1832524 1832544 1832801 1832806) (-1097 "SAE.spad" 1829994 1830010 1830605 1830740) (-1096 "SAEFACT.spad" 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(-1040 "REALSOLV.spad" 1695544 1695553 1696394 1696399) (-1039 "REAL.spad" 1695416 1695425 1695534 1695539) (-1038 "REAL0Q.spad" 1692714 1692729 1695406 1695411) (-1037 "REAL0.spad" 1689558 1689573 1692704 1692709) (-1036 "RDUCEAST.spad" 1689279 1689288 1689548 1689553) (-1035 "RDIV.spad" 1688934 1688959 1689269 1689274) (-1034 "RDIST.spad" 1688501 1688512 1688924 1688929) (-1033 "RDETRS.spad" 1687365 1687383 1688491 1688496) (-1032 "RDETR.spad" 1685504 1685522 1687355 1687360) (-1031 "RDEEFS.spad" 1684603 1684620 1685494 1685499) (-1030 "RDEEF.spad" 1683613 1683630 1684593 1684598) (-1029 "RCFIELD.spad" 1680799 1680808 1683515 1683608) (-1028 "RCFIELD.spad" 1678071 1678082 1680789 1680794) (-1027 "RCAGG.spad" 1675999 1676010 1678061 1678066) (-1026 "RCAGG.spad" 1673854 1673867 1675918 1675923) (-1025 "RATRET.spad" 1673214 1673225 1673844 1673849) (-1024 "RATFACT.spad" 1672906 1672918 1673204 1673209) (-1023 "RANDSRC.spad" 1672225 1672234 1672896 1672901) (-1022 "RADUTIL.spad" 1671981 1671990 1672215 1672220) (-1021 "RADIX.spad" 1668805 1668819 1670351 1670444) (-1020 "RADFF.spad" 1666544 1666581 1666663 1666819) (-1019 "RADCAT.spad" 1666139 1666148 1666534 1666539) (-1018 "RADCAT.spad" 1665732 1665743 1666129 1666134) (-1017 "QUEUE.spad" 1665080 1665091 1665339 1665366) (-1016 "QUAT.spad" 1663568 1663579 1663911 1663976) (-1015 "QUATCT2.spad" 1663188 1663207 1663558 1663563) (-1014 "QUATCAT.spad" 1661358 1661369 1663118 1663183) (-1013 "QUATCAT.spad" 1659279 1659292 1661041 1661046) (-1012 "QUAGG.spad" 1658106 1658117 1659247 1659274) (-1011 "QQUTAST.spad" 1657874 1657883 1658096 1658101) (-1010 "QFORM.spad" 1657492 1657507 1657864 1657869) (-1009 "QFCAT.spad" 1656194 1656205 1657394 1657487) (-1008 "QFCAT.spad" 1654487 1654500 1655689 1655694) (-1007 "QFCAT2.spad" 1654179 1654196 1654477 1654482) (-1006 "QEQUAT.spad" 1653737 1653746 1654169 1654174) (-1005 "QCMPACK.spad" 1648483 1648503 1653727 1653732) (-1004 "QALGSET.spad" 1644561 1644594 1648397 1648402) (-1003 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1587628 1587655) (-984 "PROPLOG.spad" 1586667 1586675 1587085 1587090) (-983 "PROPFUN2.spad" 1586290 1586303 1586657 1586662) (-982 "PROPFUN1.spad" 1585688 1585699 1586280 1586285) (-981 "PROPFRML.spad" 1584256 1584267 1585678 1585683) (-980 "PROPERTY.spad" 1583744 1583752 1584246 1584251) (-979 "PRODUCT.spad" 1581426 1581438 1581710 1581765) (-978 "PR.spad" 1579818 1579830 1580517 1580644) (-977 "PRINT.spad" 1579570 1579578 1579808 1579813) (-976 "PRIMES.spad" 1577823 1577833 1579560 1579565) (-975 "PRIMELT.spad" 1575904 1575918 1577813 1577818) (-974 "PRIMCAT.spad" 1575531 1575539 1575894 1575899) (-973 "PRIMARR.spad" 1574536 1574546 1574714 1574741) (-972 "PRIMARR2.spad" 1573303 1573315 1574526 1574531) (-971 "PREASSOC.spad" 1572685 1572697 1573293 1573298) (-970 "PPCURVE.spad" 1571822 1571830 1572675 1572680) (-969 "PORTNUM.spad" 1571597 1571605 1571812 1571817) (-968 "POLYROOT.spad" 1570446 1570468 1571553 1571558) (-967 "POLY.spad" 1567781 1567791 1568296 1568423) (-966 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1538802 1538807) (-947 "PMFS.spad" 1537969 1537987 1538382 1538387) (-946 "PMDOWN.spad" 1537259 1537273 1537959 1537964) (-945 "PMASS.spad" 1536269 1536277 1537249 1537254) (-944 "PMASSFS.spad" 1535236 1535252 1536259 1536264) (-943 "PLOTTOOL.spad" 1535016 1535024 1535226 1535231) (-942 "PLOT.spad" 1529939 1529947 1535006 1535011) (-941 "PLOT3D.spad" 1526403 1526411 1529929 1529934) (-940 "PLOT1.spad" 1525560 1525570 1526393 1526398) (-939 "PLEQN.spad" 1512850 1512877 1525550 1525555) (-938 "PINTERP.spad" 1512472 1512491 1512840 1512845) (-937 "PINTERPA.spad" 1512256 1512272 1512462 1512467) (-936 "PI.spad" 1511865 1511873 1512230 1512251) (-935 "PID.spad" 1510835 1510843 1511791 1511860) (-934 "PICOERCE.spad" 1510492 1510502 1510825 1510830) (-933 "PGROEB.spad" 1509093 1509107 1510482 1510487) (-932 "PGE.spad" 1500710 1500718 1509083 1509088) (-931 "PGCD.spad" 1499600 1499617 1500700 1500705) (-930 "PFRPAC.spad" 1498749 1498759 1499590 1499595) (-929 "PFR.spad" 1495412 1495422 1498651 1498744) (-928 "PFOTOOLS.spad" 1494670 1494686 1495402 1495407) (-927 "PFOQ.spad" 1494040 1494058 1494660 1494665) (-926 "PFO.spad" 1493459 1493486 1494030 1494035) (-925 "PF.spad" 1493033 1493045 1493264 1493357) (-924 "PFECAT.spad" 1490715 1490723 1492959 1493028) (-923 "PFECAT.spad" 1488425 1488435 1490671 1490676) (-922 "PFBRU.spad" 1486313 1486325 1488415 1488420) (-921 "PFBR.spad" 1483873 1483896 1486303 1486308) (-920 "PERM.spad" 1479680 1479690 1483703 1483718) (-919 "PERMGRP.spad" 1474450 1474460 1479670 1479675) (-918 "PERMCAT.spad" 1473111 1473121 1474430 1474445) (-917 "PERMAN.spad" 1471643 1471657 1473101 1473106) (-916 "PENDTREE.spad" 1470984 1470994 1471272 1471277) (-915 "PDSPC.spad" 1469797 1469807 1470974 1470979) (-914 "PDSPC.spad" 1468608 1468620 1469787 1469792) (-913 "PDRING.spad" 1468450 1468460 1468588 1468603) (-912 "PDEPROB.spad" 1467465 1467473 1468440 1468445) (-911 "PDEPACK.spad" 1461505 1461513 1467455 1467460) (-910 "PDECOMP.spad" 1460975 1460992 1461495 1461500) (-909 "PDECAT.spad" 1459331 1459339 1460965 1460970) (-908 "PDDOM.spad" 1458769 1458782 1459321 1459326) (-907 "PDDOM.spad" 1458205 1458220 1458759 1458764) (-906 "PCOMP.spad" 1458058 1458071 1458195 1458200) (-905 "PBWLB.spad" 1456646 1456663 1458048 1458053) (-904 "PATTERN.spad" 1451185 1451195 1456636 1456641) (-903 "PATTERN2.spad" 1450923 1450935 1451175 1451180) (-902 "PATTERN1.spad" 1449259 1449275 1450913 1450918) (-901 "PATRES.spad" 1446834 1446846 1449249 1449254) (-900 "PATRES2.spad" 1446506 1446520 1446824 1446829) (-899 "PATMATCH.spad" 1444703 1444734 1446214 1446219) (-898 "PATMAB.spad" 1444132 1444142 1444693 1444698) (-897 "PATLRES.spad" 1443218 1443232 1444122 1444127) (-896 "PATAB.spad" 1442982 1442992 1443208 1443213) (-895 "PARTPERM.spad" 1440990 1440998 1442972 1442977) (-894 "PARSURF.spad" 1440424 1440452 1440980 1440985) (-893 "PARSU2.spad" 1440221 1440237 1440414 1440419) (-892 "script-parser.spad" 1439741 1439749 1440211 1440216) (-891 "PARSCURV.spad" 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1388236) (-853 "ORDCOMP2.spad" 1386418 1386430 1387115 1387120) (-852 "OPTPROB.spad" 1385056 1385064 1386408 1386413) (-851 "OPTPACK.spad" 1377465 1377473 1385046 1385051) (-850 "OPTCAT.spad" 1375144 1375152 1377455 1377460) (-849 "OPSIG.spad" 1374798 1374806 1375134 1375139) (-848 "OPQUERY.spad" 1374347 1374355 1374788 1374793) (-847 "OP.spad" 1374089 1374099 1374169 1374236) (-846 "OPERCAT.spad" 1373555 1373565 1374079 1374084) (-845 "OPERCAT.spad" 1373019 1373031 1373545 1373550) (-844 "ONECOMP.spad" 1371764 1371774 1372566 1372595) (-843 "ONECOMP2.spad" 1371188 1371200 1371754 1371759) (-842 "OMSERVER.spad" 1370194 1370202 1371178 1371183) (-841 "OMSAGG.spad" 1369982 1369992 1370150 1370189) (-840 "OMPKG.spad" 1368598 1368606 1369972 1369977) (-839 "OM.spad" 1367571 1367579 1368588 1368593) (-838 "OMLO.spad" 1366996 1367008 1367457 1367496) (-837 "OMEXPR.spad" 1366830 1366840 1366986 1366991) (-836 "OMERR.spad" 1366375 1366383 1366820 1366825) (-835 "OMERRK.spad" 1365409 1365417 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T) (($) . T)) ((((-117 |#1|)) . T) (((-418 (-575))) . T) (($) . T)) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) @@ -111,14 +111,14 @@ ((((-418 (-575))) . T) (($) . T) (((-575)) . T)) ((($) . T) (((-575)) . T) (((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) . T)) (((|#2|) . T) (((-575)) . T) ((|#6|) . T)) -((((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) . T) (($) -3765 (|has| |#2| (-174)) (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924)))) +((((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) . T) (($) -3763 (|has| |#2| (-174)) (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924)))) ((($) . T)) (((|#2|) . T)) ((($) . T)) (((|#1|) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) (((-575)) . T) (($) . T)) ((((-575)) . T) (($) . T) ((|#1|) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) -(((#0=(-418 (-575)) #0#) |has| |#1| (-38 (-418 (-575)))) ((|#1| |#1|) . 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T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) -(-3765 (|has| |#1| (-861)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-861)) (|has| |#1| (-1117))) (|has| |#1| (-1117)) -(-3765 (|has| |#1| (-861)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-861)) (|has| |#1| (-1117))) (|has| |#1| (-1117)) -(-3765 (|has| |#1| (-861)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-861)) (|has| |#1| (-1117))) (|has| |#1| (-859)) (((|#1| |#1|) . T)) ((($) . T) (((-418 (-575))) . T)) @@ -165,7 +165,7 @@ (|has| |#3| (-804)) (|has| |#3| (-804)) (((|#1| |#2|) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((((-1199)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-373)) (|has| |#2| (-318 |#2|))) (((-1194) |#2|) -12 (|has| |#1| (-373)) (|has| |#2| (-525 (-1194) |#2|)))) @@ -190,29 +190,29 @@ ((((-1176) |#1|) . T)) ((((-1252 (-575)) $) . T) (((-575) (-130)) . T)) (((|#1|) . T)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) (((|#3| (-782)) . T)) (|has| |#1| (-148)) (|has| |#1| (-146)) ((($) . T) (((-418 (-575))) . T)) ((($) . T)) ((($) . T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((((-418 (-575))) . T) (($) . T)) ((($) . T)) ((($) . T)) (|has| |#1| (-1117)) ((((-418 (-575))) . T) (((-575)) . T)) ((((-575)) . T) ((|#1|) . T) (((-418 (-575))) |has| |#1| (-1055 (-418 (-575))))) -((((-575)) . T) (((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-1055 (-418 (-575))))) ((|#1|) . T) (($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#2|) . T)) +((((-575)) . 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T)) -((($) -3765 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) ((|#1|) |has| |#1| (-174))) +((($) -3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-418 (-575))) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) ((|#1|) |has| |#1| (-174))) ((((-575)) . T)) ((((-575)) . T)) ((((-418 (-575))) . T) (($) . T)) @@ -223,7 +223,7 @@ (((|#1|) . T)) (|has| |#2| (-373)) ((((-1252 (-575)) $) . T) (((-575) |#1|) . T)) -((($) -3765 (|has| (-418 |#2|) (-238)) (|has| (-418 |#2|) (-237)))) +((($) -3763 (|has| (-418 |#2|) (-238)) (|has| (-418 |#2|) (-237)))) ((($) . T) (((-575)) . T) (((-418 (-575))) . T)) (((|#1| |#2|) . T)) ((((-873)) . T)) @@ -236,13 +236,13 @@ ((((-873)) . T)) ((((-873)) . T)) (((|#1| |#1|) . T)) -(((#0=(-418 (-575)) #0#) |has| |#1| (-38 (-418 (-575)))) ((|#1| |#1|) . 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T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) -(((|#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066))) (($) |has| |#2| (-1066)) (((-575)) -12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066)))) +((((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) . T) (($) -3763 (|has| |#1| (-174)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924)))) +((($) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) +(((|#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066))) (($) |has| |#2| (-1066)) (((-575)) -12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066)))) ((((-873)) . T)) ((((-873)) . T)) ((((-873)) . T)) @@ -253,10 +253,10 @@ ((((-171 (-227))) |has| |#1| (-1039)) (((-171 (-389))) |has| |#1| (-1039)) (((-547)) |has| |#1| (-625 (-547))) (((-1190 |#1|)) . 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T)) (-12 (|has| |#4| (-238)) (|has| |#4| (-1066))) (-12 (|has| |#3| (-238)) (|has| |#3| (-1066))) -((($) -3765 (|has| |#2| (-238)) (|has| |#2| (-237)))) +((($) -3763 (|has| |#2| (-238)) (|has| |#2| (-237)))) (|has| |#4| (-1066)) (|has| |#3| (-1066)) ((((-873)) . T) (((-1199)) . T)) @@ -278,42 +278,42 @@ (((|#2|) . T) (((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) (((|#1|) . T) (((-2 (|:| -4169 (-1176)) (|:| -3179 |#1|))) . 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T)) -((((-2 (|:| -4317 |#1|) (|:| -2398 |#2|))) . T) (((-873)) . T)) +((((-2 (|:| -4317 |#1|) (|:| -1658 |#2|))) . T) (((-873)) . T)) ((((-547)) |has| |#1| (-625 (-547))) (((-904 (-389))) |has| |#1| (-625 (-904 (-389)))) (((-904 (-575))) |has| |#1| (-625 (-904 (-575))))) -(((|#4|) -3765 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-1066)))) -(((|#3|) -3765 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-1066)))) -((((-2 (|:| -4317 |#1|) (|:| -2398 |#2|))) . T)) +(((|#4|) -3763 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-1066)))) +(((|#3|) -3763 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-1066)))) +((((-2 (|:| -4317 |#1|) (|:| -1658 |#2|))) . T)) ((((-873)) . T)) ((((-873)) . T)) ((((-547)) . T) (((-575)) . T) (((-904 (-575))) . T) (((-389)) . T) (((-227)) . T)) @@ -321,7 +321,7 @@ (((|#1|) . T) (((-575)) |has| |#1| (-1055 (-575))) (((-418 (-575))) |has| |#1| (-1055 (-418 (-575))))) ((($) . T) (((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) . 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T) ((#1=(-418 (-575)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -941,14 +942,14 @@ ((($) . T) (((-575)) . T) (((-418 (-575))) . T)) (|has| |#2| (-378)) (((#0=(-575) #0#) . T) ((#1=(-418 (-575)) #1#) . T) (($ $) . T)) -(-3765 (|has| |#1| (-861)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-861)) (|has| |#1| (-1117))) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) ((((-575)) . T) (((-418 (-575))) . T) (($) . T)) -((($) -3765 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) ((|#1|) |has| |#1| (-174))) +((($) -3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-418 (-575))) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) ((|#1|) |has| |#1| (-174))) (((|#1| |#2|) . 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T)) ((((-1192 |#1| |#2| |#3|) $) -12 (|has| (-1192 |#1| |#2| |#3|) (-295 (-1192 |#1| |#2| |#3|) (-1192 |#1| |#2| |#3|))) (|has| |#1| (-373))) (($ $) . T) (((-575) |#1|) . T)) ((($ $) . T) (((-418 (-575)) |#1|) . T)) @@ -969,14 +970,14 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-575)) . T) (($) . T)) -((($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) +((($) -3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) ((($) . T) (((-575)) . T) ((|#2|) . T)) ((((-575)) . T) (($) . T) ((|#2|) . T) (((-418 (-575))) |has| |#2| (-38 (-418 (-575))))) ((((-418 (-575))) . T) (((-575)) . T)) ((((-575) (-145)) . T)) ((((-145)) . T)) (((|#1|) . 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T)) (((|#1| (-418 (-575))) . T)) @@ -1170,9 +1171,9 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) -((($ (-1194)) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194))))) +((($ (-1281 |#2|)) . T) (($ (-1194)) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194))))) ((((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) -((((-575)) -3765 (-12 (|has| |#2| (-1055 (-575))) (|has| |#2| (-1117))) (|has| |#2| (-1066))) ((|#2|) |has| |#2| (-1117)) (((-418 (-575))) -12 (|has| |#2| (-1055 (-418 (-575)))) (|has| |#2| (-1117)))) +((((-575)) -3763 (-12 (|has| |#2| (-1055 (-575))) (|has| |#2| (-1117))) (|has| |#2| (-1066))) ((|#2|) |has| |#2| (-1117)) (((-418 (-575))) -12 (|has| |#2| (-1055 (-418 (-575)))) (|has| |#2| (-1117)))) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-575)) . T) (($) . T) (((-418 (-575))) . T)) @@ -1188,7 +1189,7 @@ (((|#1|) . T)) ((($) . T) ((|#2|) . T) (((-575)) |has| |#2| (-650 (-575)))) ((((-1194) (-52)) . T)) -((((-1194)) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) +((((-1194)) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-875 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-839)) @@ -1196,10 +1197,10 @@ ((($) . T) (((-575)) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) . T)) ((((-575)) . T) (($) . T) ((|#1|) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) (|has| (-1111 |#1|) (-1117)) -(((|#2| |#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) -(((|#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)))) +(((|#2| |#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) +(((|#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)))) ((((-575) (-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) +(((|#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) ((((-575)) . T)) ((((-1199)) . T)) ((((-782)) . T)) @@ -1217,32 +1218,32 @@ ((((-117 |#1|)) . T)) (((|#1|) . T)) ((((-418 (-575))) . T) (($) . T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-567))) ((($) . T) (((-418 (-575))) . T)) ((((-1199)) . T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-567))) ((((-575)) . 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T)) (((|#1|) |has| |#1| (-318 |#1|))) @@ -1309,12 +1310,12 @@ (|has| |#1| (-378)) ((((-1194) $) |has| |#1| (-525 (-1194) $)) (($ $) |has| |#1| (-318 $)) ((|#1| |#1|) |has| |#1| (-318 |#1|)) (((-1194) |#1|) |has| |#1| (-525 (-1194) |#1|))) ((((-1194)) |has| |#1| (-913 (-1194)))) -(-3765 (-12 (|has| |#1| (-238)) (|has| |#1| (-373))) (|has| |#1| (-359))) +(-3763 (-12 (|has| |#1| (-238)) (|has| |#1| (-373))) (|has| |#1| (-359))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-399) |#1|) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-359))) (|has| |#1| (-1117)) (((|#2|) . T) (((-873)) . T)) ((((-873)) . T)) @@ -1322,8 +1323,8 @@ ((((-925 |#1|)) . T)) ((((-873)) . T) (((-1199)) . T)) ((((-1199)) . T)) -((((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) |has| |#2| (-174)) (($) -3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924)))) -((((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) |has| |#1| (-174)) (($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924)))) +((((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) |has| |#2| (-174)) (($) -3763 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924)))) +((((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) |has| |#1| (-174)) (($) -3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-575)) . T) (($) . T) (((-418 (-575))) . T)) @@ -1332,7 +1333,7 @@ (((|#1|) . T) (((-418 (-575))) . T) (($) . T) (((-575)) . T)) (((|#1| |#1|) . T)) (((#0=(-881 |#1|)) |has| #0# (-318 #0#))) -((((-575)) . T) (($) -3765 (|has| |#1| (-373)) (|has| |#1| (-359))) (((-418 (-575))) -3765 (|has| |#1| (-373)) (|has| |#1| (-359)) (|has| |#1| (-1055 (-418 (-575))))) ((|#1|) . T)) +((((-575)) . T) (($) -3763 (|has| |#1| (-373)) (|has| |#1| (-359))) (((-418 (-575))) -3763 (|has| |#1| (-373)) (|has| |#1| (-359)) (|has| |#1| (-1055 (-418 (-575))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-804)) (|has| |#2| (-804)) @@ -1355,14 +1356,14 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-418 (-575)) #0#) . T)) (|has| |#1| (-373)) ((((-575)) . T) (((-418 (-575))) . T) (($) . T)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) (((|#1|) . T) (($) . T) (((-418 (-575))) . T)) ((((-873)) . T)) ((((-873)) . T)) (((|#1|) . T) (($) . T) (((-418 (-575))) . T)) (((|#1|) . T) (($) . T) (((-418 (-575))) . T)) (((|#1|) . T)) -((($ $) . T) ((#0=(-418 (-575)) #0#) -3765 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1| |#1|) . T)) +((($ $) . T) ((#0=(-418 (-575)) #0#) -3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1| |#1|) . T)) ((((-873)) . T)) (((|#1|) . T)) ((((-547)) |has| |#3| (-625 (-547)))) @@ -1370,25 +1371,25 @@ (((|#1| |#2|) . T)) (|has| |#1| (-859)) (|has| |#1| (-859)) -((($) . T) (((-418 (-575))) -3765 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1|) . T)) +((($) . T) (((-418 (-575))) -3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1|) . T)) ((((-575) |#3|) . T)) (((|#2|) . T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-567))) ((($) . T)) (((#0=(-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) #0#) |has| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (-318 (-2 (|:| -4169 (-1194)) (|:| -3179 (-52)))))) -((((-1194)) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194)))) (((-1099)) . T)) +((((-1194)) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194)))) (((-1099)) . T)) ((($) . T)) ((($) . 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T)) @@ -1403,11 +1404,11 @@ (|has| |#1| (-373)) (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-859)) -((($) -3765 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359)) (|has| |#1| (-567))) (((-418 (-575))) -3765 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1|) . T)) +((($) -3763 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359)) (|has| |#1| (-567))) (((-418 (-575))) -3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1|) . T)) (|has| |#1| (-373)) (((|#1|) . T) (($) . T)) (|has| |#1| (-859)) -((($) . T) (((-418 (-575))) -3765 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1|) . T)) +((($) . T) (((-418 (-575))) -3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((|#1|) . T)) ((((-1194)) |has| |#1| (-913 (-1194)))) (|has| |#1| (-859)) ((((-517)) . T)) @@ -1435,9 +1436,9 @@ (((|#1|) |has| |#1| (-174))) (|has| |#2| (-428 |#1|)) (|has| |#2| (-428 |#1|)) -((($) -3765 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-575)) . 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T)) ((((-547)) |has| |#1| (-625 (-547))) (((-904 (-389))) |has| |#1| (-625 (-904 (-389)))) (((-904 (-575))) |has| |#1| (-625 (-904 (-575))))) @@ -1446,11 +1447,11 @@ (((|#2|) . T) (((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) ((((-517)) . T)) ((((-517)) . T)) -((((-1194)) -3765 (-12 (|has| |#4| (-913 (-1194))) (|has| |#4| (-1066))) (-12 (|has| |#4| (-915 (-1194))) (|has| |#4| (-1066))))) -((((-1194)) -3765 (-12 (|has| |#3| (-913 (-1194))) (|has| |#3| (-1066))) (-12 (|has| |#3| (-915 (-1194))) (|has| |#3| (-1066))))) +((((-1194)) -3763 (-12 (|has| |#4| (-913 (-1194))) (|has| |#4| (-1066))) (-12 (|has| |#4| (-915 (-1194))) (|has| |#4| (-1066))))) +((((-1194)) -3763 (-12 (|has| |#3| (-913 (-1194))) (|has| |#3| (-1066))) (-12 (|has| |#3| (-915 (-1194))) (|has| |#3| (-1066))))) (|has| |#1| (-567)) (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-3763 (|has| |#1| (-238)) (|has| |#1| (-237))) ((((-881 |#1|)) . T) (((-418 (-575))) . T) (($) . T)) (|has| |#1| (-378)) (|has| |#1| (-378)) @@ -1459,7 +1460,7 @@ ((((-1176) |#1|) . T)) (|has| |#1| (-1169)) ((((-973 |#1|)) . T)) -(((#0=(-418 (-575)) #0#) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($ $) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((|#1| |#1|) . T)) +(((#0=(-418 (-575)) #0#) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($ $) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((|#1| |#1|) . T)) ((((-418 (-575))) |has| |#1| (-1055 (-575))) (((-575)) |has| |#1| (-1055 (-575))) (((-1194)) |has| |#1| (-1055 (-1194))) ((|#1|) . T)) ((($) . T)) ((($) . T)) @@ -1467,7 +1468,7 @@ ((((-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) (((-575)) |has| |#1| (-1055 (-575))) ((|#1|) . T)) ((($) . T) (((-575)) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) . 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T)) -(-3765 (|has| |#1| (-861)) (|has| |#1| (-1117))) -(((|#2| |#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) +(-3763 (|has| |#1| (-861)) (|has| |#1| (-1117))) +(((|#2| |#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) (((|#2|) . T) (((-575)) . T)) ((((-873)) . T)) ((((-873)) . T)) @@ -1541,9 +1542,9 @@ ((((-418 (-575))) . T) (($) . T)) ((((-873)) . T)) ((((-547)) |has| |#1| (-625 (-547)))) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) ((($) . T) (((-418 (-575))) . T)) -(((|#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) +(((|#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066)))) (|has| $ (-148)) ((((-418 |#2|)) . T)) ((((-418 (-575))) |has| #0=(-418 |#2|) (-1055 (-418 (-575)))) (((-575)) |has| #0# (-1055 (-575))) ((#0#) . T)) @@ -1553,11 +1554,11 @@ (|has| |#2| (-148)) (|has| |#1| (-148)) (|has| |#1| (-146)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) (|has| |#1| (-148)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) (|has| |#1| (-148)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) (|has| |#1| (-148)) (((|#1|) . T)) (|has| |#2| (-238)) @@ -1593,7 +1594,7 @@ ((((-873)) . T)) ((((-873)) . T)) ((((-1016 |#1|)) . T) ((|#1|) . T)) -((((-1194)) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194)))) (((-829 (-1194))) . T)) +((((-1194)) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194)))) (((-829 (-1194))) . T)) ((((-873)) . T)) ((((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) ((((-418 (-575))) . T) (((-418 |#1|)) . T) ((|#1|) . T) (($) . T)) @@ -1605,7 +1606,7 @@ (((|#2|) . T)) ((((-575)) . T) (($) . T) (((-418 (-575))) . T)) ((((-2 (|:| -4169 (-1176)) (|:| -3179 |#1|))) . T)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) ((((-575) |#2|) . T)) (((|#1|) . T) (((-418 (-575))) . T) (((-575)) . T) (($) . T)) ((($) . T) (((-575)) . T) (((-418 (-575))) . T)) @@ -1616,7 +1617,7 @@ ((((-873)) . T)) (((|#4|) -12 (|has| |#4| (-318 |#4|)) (|has| |#4| (-1117)))) (((|#3|) -12 (|has| |#3| (-318 |#3|)) (|has| |#3| (-1117)))) -(-3765 (|has| |#1| (-15 * (|#1| (-575) |#1|))) (-12 (|has| |#1| (-373)) (|has| |#2| (-238))) (-12 (|has| |#1| (-373)) (|has| |#2| (-237)))) +(-3763 (|has| |#1| (-15 * (|#1| (-575) |#1|))) (-12 (|has| |#1| (-373)) (|has| |#2| (-238))) (-12 (|has| |#1| (-373)) (|has| |#2| (-237)))) (|has| |#1| (-38 (-418 (-575)))) (((|#2| |#2|) -12 (|has| |#2| (-318 |#2|)) (|has| |#2| (-1117))) ((#0=(-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) #0#) |has| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (-318 (-2 (|:| -4169 |#1|) (|:| -3179 |#2|))))) (((|#2| |#2|) . T)) @@ -1628,21 +1629,21 @@ ((((-1277 |#1| |#2| |#3|)) |has| |#1| (-373))) (|has| |#1| (-1117)) (((|#1|) |has| |#1| (-174))) -((((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) |has| |#1| (-174)) (($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924)))) -((($) -3765 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) +((((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) |has| |#1| (-174)) (($) -3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924)))) +((($) -3763 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) ((((-1176) (-52)) . T)) (((|#1|) . T)) -((((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) . 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T)) -((((-575)) -3765 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066))) ((|#2|) -3765 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-737)) (|has| |#2| (-1066))) (($) |has| |#2| (-1066))) +((((-575)) -3763 (|has| |#2| (-21)) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-1066))) ((|#2|) -3763 (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-737)) (|has| |#2| (-1066))) (($) |has| |#2| (-1066))) ((((-575) |#3|) . T)) ((((-575) (-145)) . T)) ((((-145)) . T)) @@ -1657,7 +1658,7 @@ ((((-575)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (((|#1|) . T)) -((($ (-1194)) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) +((($ (-1194)) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) (((|#2|) . T) (((-575)) |has| |#2| (-650 (-575)))) ((((-145)) . T)) ((((-873)) . T)) @@ -1668,25 +1669,25 @@ (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (((|#1| |#2|) . T)) -(-3765 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-3763 (|has| |#2| (-238)) (|has| |#2| (-237))) ((((-1252 (-575)) $) . T) (((-575) (-145)) . T)) (((#0=(-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) #0#) |has| (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)) (-318 (-2 (|:| -4169 |#1|) (|:| -3179 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-318 |#2|)) (|has| |#2| (-1117)))) -((($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) +((($) -3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) (|has| |#1| (-861)) (((|#2| (-782) (-1099)) . T)) (((|#1| |#2|) . 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T)) -(-3765 (|has| |#1| (-148)) (-12 (|has| |#1| (-373)) (|has| |#2| (-148)))) -(-3765 (|has| |#1| (-146)) (-12 (|has| |#1| (-373)) (|has| |#2| (-146)))) +(-3763 (|has| |#1| (-148)) (-12 (|has| |#1| (-373)) (|has| |#2| (-148)))) +(-3763 (|has| |#1| (-146)) (-12 (|has| |#1| (-373)) (|has| |#2| (-146)))) (((|#4|) . T)) (|has| |#1| (-146)) ((((-1176) |#1|) . T)) @@ -1701,24 +1702,24 @@ (((|#3|) . T)) ((((-1277 |#1| |#2| |#3|)) |has| |#1| (-373))) ((($) . T) (((-575)) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) . T)) -((((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (((-1192 |#1| |#2| |#3|)) |has| |#1| (-373)) (((-575)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (((-575)) . T) (($) . T)) +((((-418 (-575))) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (((-1192 |#1| |#2| |#3|)) |has| |#1| (-373)) (((-575)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . 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T)) -(((|#4|) -3765 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-737)))) -(((|#3|) -3765 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-737)))) +(((|#4|) -3763 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-737)))) +(((|#3|) -3763 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-737)))) (|has| |#2| (-373)) (((|#1|) |has| |#1| (-174))) -(((|#4|) -3765 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-737)) (|has| |#4| (-1066)))) -(((|#3|) -3765 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-737)) (|has| |#3| (-1066)))) +(((|#4|) -3763 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-737)) (|has| |#4| (-1066)))) +(((|#3|) -3763 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-737)) (|has| |#3| (-1066)))) (((|#2|) |has| |#2| (-1066))) (((|#2|) |has| |#2| (-1066))) ((((-1176) |#1|) . T)) @@ -1730,7 +1731,7 @@ ((((-399) (-1176)) . T)) ((($ (-1194)) . T)) ((($) |has| |#1| (-567)) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) -((((-873)) -3765 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-624 (-873))) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-378)) (|has| |#2| (-737)) (|has| |#2| (-804)) (|has| |#2| (-861)) (|has| |#2| (-1066)) (|has| |#2| (-1117))) (((-1285 |#2|)) . T)) +((((-873)) -3763 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-132)) (|has| |#2| (-624 (-873))) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-378)) (|has| |#2| (-737)) (|has| |#2| (-804)) (|has| |#2| (-861)) (|has| |#2| (-1066)) (|has| |#2| (-1117))) (((-1285 |#2|)) . T)) (((#0=(-52)) . T) (((-2 (|:| -4169 (-1176)) (|:| -3179 #0#))) . T)) (((|#1|) . T)) ((((-873)) . T)) @@ -1740,7 +1741,7 @@ ((((-575)) . T)) (|has| |#2| (-148)) (|has| |#1| (-484)) -(-3765 (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066))) +(-3763 (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066))) (|has| |#1| (-373)) ((((-873)) . T)) (|has| |#1| (-38 (-418 (-575)))) @@ -1751,8 +1752,8 @@ (|has| |#1| (-859)) ((((-873)) . T)) (((|#2|) . T)) -((((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($) -3765 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-1277 |#1| |#2| |#3|)) |has| |#1| (-373)) ((|#1|) |has| |#1| (-174))) -(((|#1|) |has| |#1| (-174)) (((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($) -3765 (|has| |#1| (-373)) (|has| |#1| (-567)))) +((((-418 (-575))) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($) -3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (((-1277 |#1| |#2| |#3|)) |has| |#1| (-373)) ((|#1|) |has| |#1| (-174))) +(((|#1|) |has| |#1| (-174)) (((-418 (-575))) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($) -3763 (|has| |#1| (-373)) (|has| |#1| (-567)))) ((($) |has| |#1| (-567)) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) (((|#2|) . T) (((-575)) . T) (((-830 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1762,7 +1763,7 @@ ((((-873)) . T)) ((((-873)) . T)) (|has| |#1| (-1117)) -(((|#2| (-493 (-2871 |#1|) (-782)) (-875 |#1|)) . T)) +(((|#2| (-493 (-2869 |#1|) (-782)) (-875 |#1|)) . T)) ((((-418 (-575))) . #0=(|has| |#2| (-373))) (($) . #0#)) (((|#1| (-542 (-1194)) (-1194)) . T)) (((|#1|) . T)) @@ -1793,8 +1794,8 @@ ((((-418 (-575)) |#1|) . T) (($ $) . T)) (((|#1| (-575)) . T)) ((((-925 |#1|)) . T)) -(((|#1|) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-1066))) (($) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)))) -((((-1194)) -3765 (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))))) +(((|#1|) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-1066))) (($) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)))) +((((-1194)) -3763 (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))))) (((|#1|) . T) (((-575)) |has| |#1| (-1055 (-575))) (((-418 (-575))) |has| |#1| (-1055 (-418 (-575))))) (|has| |#1| (-861)) (|has| |#1| (-861)) @@ -1814,15 +1815,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-318 |#4|)) (|has| |#4| (-1117)))) (((|#1|) |has| |#1| (-174))) (((|#4| |#4|) -12 (|has| |#4| (-318 |#4|)) (|has| |#4| (-1117)))) -(((|#3|) -3765 (|has| |#3| (-174)) (|has| |#3| (-373)))) -((($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) -(-3765 (|has| |#2| (-373)) (|has| |#2| (-463)) (|has| |#2| (-924))) -((($) -3765 (|has| |#1| (-174)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) . 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T)) @@ -1831,7 +1832,7 @@ (|has| |#1| (-831)) (|has| |#1| (-831)) (((|#1|) . T)) -(-3765 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359))) (|has| |#1| (-859)) (|has| |#1| (-859)) (|has| |#1| (-859)) @@ -1840,7 +1841,7 @@ ((((-575)) . T) (($) . T) (((-418 (-575))) . T)) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-359))) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) ((((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) @@ -1871,14 +1872,14 @@ (((|#1| (-782) (-1099)) . T)) (((|#3|) . T)) ((((-145)) . T)) -((((-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) (((-575)) -3765 (|has| |#1| (-859)) (|has| |#1| (-1055 (-575)))) ((|#1|) . T)) +((((-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) (((-575)) -3763 (|has| |#1| (-859)) (|has| |#1| (-1055 (-575)))) ((|#1|) . T)) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) @@ -2297,9 +2298,9 @@ ((((-710)) . T)) ((((-710)) . T)) (((|#2|) |has| |#2| (-174))) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-3763 (|has| |#1| (-238)) (|has| |#1| (-237))) ((((-575)) . T) ((|#2|) . T) (((-418 (-575))) |has| |#2| (-1055 (-418 (-575))))) -((((-112)) |has| |#1| (-1117)) (((-873)) -3765 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)) (|has| |#1| (-1129)) (|has| |#1| (-1117)))) +((((-112)) |has| |#1| (-1117)) (((-873)) -3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)) (|has| |#1| (-1129)) (|has| |#1| (-1117)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-575)) . T) (((-418 (-575))) . T)) @@ -2311,13 +2312,13 @@ ((((-575)) . T) (($) . T) (((-418 (-575))) . 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T)) @@ -2326,8 +2327,8 @@ (((|#1|) |has| |#1| (-174))) ((((-418 (-967 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) -(-3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) +(-3763 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) +(-3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1066))) @@ -2345,8 +2346,8 @@ (|has| |#1| (-378)) (|has| |#1| (-378)) (|has| |#1| (-373)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-484)) (|has| |#1| (-567)) (|has| |#1| (-1066)) (|has| |#1| (-1129))) -((($) -3765 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-359)))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-484)) (|has| |#1| (-567)) (|has| |#1| (-1066)) (|has| |#1| (-1129))) +((($) -3763 (|has| |#1| (-238)) (|has| |#1| (-237)) (|has| |#1| (-359)))) ((((-117 |#1|)) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-359)) @@ -2357,7 +2358,7 @@ (|has| |#1| (-38 (-418 (-575)))) (((|#2|) . T) (((-873)) . T)) (((|#2|) . T) (((-873)) . T)) -((($ (-1194)) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) +((($ (-1194)) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) @@ -2379,7 +2380,7 @@ (((|#3|) . T)) ((((-117 |#1|)) . T)) (|has| |#1| (-378)) -(-3765 (-12 (|has| (-1277 |#1| |#2| |#3|) (-238)) (|has| |#1| (-373))) (-12 (|has| (-1277 |#1| |#2| |#3|) (-237)) (|has| |#1| (-373))) (|has| |#1| (-15 * (|#1| (-575) |#1|)))) +(-3763 (-12 (|has| (-1277 |#1| |#2| |#3|) (-238)) (|has| |#1| (-373))) (-12 (|has| (-1277 |#1| |#2| |#3|) (-237)) (|has| |#1| (-373))) (|has| |#1| (-15 * (|#1| (-575) |#1|)))) (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-861)) (|has| |#1| (-15 * (|#1| (-782) |#1|))) @@ -2400,15 +2401,15 @@ ((((-873)) . 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T)) @@ -2617,7 +2618,7 @@ ((((-575)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-575)) . T)) (((|#2|) . T)) -((((-1194)) -3765 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) +((((-1194)) -3763 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-373))) ((((-418 |#2|)) . T)) @@ -2629,7 +2630,7 @@ ((((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) ((((-575)) . T) (($) . T) (((-418 (-575))) . T)) ((((-1194) |#1|) |has| |#1| (-525 (-1194) |#1|)) ((|#1| |#1|) |has| |#1| (-318 |#1|))) -(((|#1|) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)))) +(((|#1|) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)))) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) ((((-575)) . T) (((-418 (-575))) . T) (($) . T)) (((|#1|) . T) (((-418 (-575))) . T) (($) . T)) @@ -2639,14 +2640,14 @@ (((|#1|) . T) (($) . T) (((-418 (-575))) . T)) (((|#1|) . T) (($) . T) (((-418 (-575))) . 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T)) (((|#2|) |has| |#2| (-174))) @@ -2655,7 +2656,7 @@ ((((-1194)) |has| |#1| (-913 (-1194))) (((-1099)) . T)) ((((-1194)) |has| |#1| (-913 (-1194))) (((-1105 (-1194))) . T)) (((|#2|) -12 (|has| |#2| (-318 |#2|)) (|has| |#2| (-1117)))) -((($ (-1194)) -3765 (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))))) +((($ (-1194)) -3763 (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))))) ((((-418 (-575))) . T) (((-575)) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (|has| |#1| (-38 (-418 (-575)))) @@ -2664,13 +2665,13 @@ (|has| |#1| (-146)) (|has| |#1| (-148)) ((($ $) . T)) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)) (|has| |#1| (-1129)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)) (|has| |#1| (-1129)) (|has| |#1| (-1117))) (|has| |#1| (-567)) (((|#2|) . T)) ((((-575)) . T)) ((((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) (((|#1|) . T)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-567)) (|has| |#1| (-1066))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-174)) (|has| |#1| (-567)) (|has| |#1| (-1066))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-592 |#1|)) . T)) ((($) . T)) @@ -2690,7 +2691,7 @@ (((|#1|) . T)) (((|#3|) . T) (((-575)) . T)) ((((-1270 |#2| |#3| |#4|)) . T) (((-575)) . T) (((-1271 |#1| |#2| |#3| |#4|)) . 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T)) ((((-418 (-575))) |has| |#2| (-1055 (-418 (-575)))) (((-575)) |has| |#2| (-1055 (-575))) ((|#2|) . T) (((-875 |#1|)) . T)) ((($) . T) (((-117 |#1|)) . T) (((-418 (-575))) . T)) ((((-1142 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-575)) |has| |#1| (-1055 (-575))) (((-418 (-575))) |has| |#1| (-1055 (-418 (-575))))) @@ -2703,24 +2704,24 @@ (((|#1| |#2|) . T)) ((((-1194) |#1|) . T)) (((|#4|) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((((-1194) (-52)) . T)) ((((-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) (((-575)) |has| |#1| (-1055 (-575))) ((|#1|) . T)) ((((-1270 |#2| |#3| |#4|) (-328 |#2| |#3| |#4|)) . T)) ((((-873)) . 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T)) +((((-418 (-575))) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) (($) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((|#1|) . T)) (|has| |#1| (-373)) -((($) |has| |#1| (-859)) (((-575)) -3765 (|has| |#1| (-21)) (|has| |#1| (-859)))) -((($) -3765 (-12 (|has| (-1277 |#1| |#2| |#3|) (-238)) (|has| |#1| (-373))) (-12 (|has| (-1277 |#1| |#2| |#3|) (-237)) (|has| |#1| (-373))) (|has| |#1| (-15 * (|#1| (-575) |#1|))))) +((($) |has| |#1| (-859)) (((-575)) -3763 (|has| |#1| (-21)) (|has| |#1| (-859)))) +((($) -3763 (-12 (|has| (-1277 |#1| |#2| |#3|) (-238)) (|has| |#1| (-373))) (-12 (|has| (-1277 |#1| |#2| |#3|) (-237)) (|has| |#1| (-373))) (|has| |#1| (-15 * (|#1| (-575) |#1|))))) ((($) |has| |#1| (-15 * (|#1| (-418 (-575)) |#1|)))) ((($) |has| |#1| (-15 * (|#1| (-782) |#1|)))) (|has| |#1| (-146)) @@ -2735,18 +2736,18 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-318 |#2|)) (|has| |#2| (-1117)))) (((|#2| |#3|) . T)) -(-3765 (|has| |#2| (-373)) (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) +(-3763 (|has| |#2| (-373)) (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) (((|#1| (-542 |#2|)) . T)) (((|#1| (-782)) . T)) (((|#1| (-542 (-1105 (-1194)))) . T)) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (|has| |#2| (-924)) -(-3765 (|has| |#2| (-804)) (|has| |#2| (-861))) +(-3763 (|has| |#2| (-804)) (|has| |#2| (-861))) ((((-873)) . 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T)) -(-3765 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359)) (|has| |#1| (-567))) (|has| |#1| (-373)) (|has| |#1| (-373)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1270 |#2| |#3| |#4|)) . T) (((-418 (-575))) |has| #0# (-38 (-418 (-575))))) ((((-1192 |#1| |#2| |#3|)) |has| |#1| (-373))) -(-3765 (-12 (|has| |#1| (-316)) (|has| |#1| (-924))) (|has| |#1| (-373)) (|has| |#1| (-359))) -(-3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066))) +(-3763 (-12 (|has| |#1| (-316)) (|has| |#1| (-924))) (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066))) ((((-575)) |has| |#1| (-650 (-575))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-873)) . T)) @@ -2798,7 +2799,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1194)) -3765 (-12 (|has| |#1| (-373)) (|has| |#1| (-913 (-1194)))) (-12 (|has| |#1| (-373)) (|has| |#1| (-915 (-1194)))))) +((($ (-1194)) -3763 (-12 (|has| |#1| (-373)) (|has| |#1| (-913 (-1194)))) (-12 (|has| |#1| (-373)) (|has| |#1| (-915 (-1194)))))) ((((-873)) . T)) (((|#1| (-542 (-1194))) . T)) ((($ $) . T)) @@ -2808,12 +2809,12 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-318 |#4|)) (|has| |#4| (-1117)))) (((|#2|) . T)) -(((|#2|) -3765 (|has| |#2| (-6 (-4462 "*"))) (|has| |#2| (-174)))) -(-3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) -(-3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) +(((|#2|) -3763 (|has| |#2| (-6 (-4462 "*"))) (|has| |#2| (-174)))) +(-3763 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) +(-3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) (|has| |#2| (-924)) (|has| |#1| (-924)) -((($) -3765 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066))))) +((($) -3763 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066))))) (((|#2|) |has| |#2| (-174))) ((((-2 (|:| -4169 |#1|) (|:| -3179 |#2|))) . T)) ((((-1277 |#1| |#2| |#3|)) |has| |#1| (-373))) @@ -2830,7 +2831,7 @@ ((($) . T) (((-575)) . T)) (((|#1| (-418 (-575))) . T)) (((|#1|) . T)) -(-3765 (|has| |#1| (-299)) (|has| |#1| (-373))) +(-3763 (|has| |#1| (-299)) (|has| |#1| (-373))) ((((-145)) . T)) ((((-575)) |has| #0=(-418 |#2|) (-650 (-575))) ((#0#) . T) (((-418 (-575))) . T) (($) . T)) (|has| |#1| (-859)) @@ -2864,7 +2865,7 @@ ((((-2 (|:| -4169 (-1176)) (|:| -3179 |#1|))) . T)) ((((-873)) . T)) ((((-547)) |has| |#1| (-625 (-547)))) -((($) -3765 (-12 (|has| (-1192 |#1| |#2| |#3|) (-238)) (|has| |#1| (-373))) (-12 (|has| (-1192 |#1| |#2| |#3|) (-237)) (|has| |#1| (-373))) (|has| |#1| (-15 * (|#1| (-575) |#1|))))) +((($) -3763 (-12 (|has| (-1192 |#1| |#2| |#3|) (-238)) (|has| |#1| (-373))) (-12 (|has| (-1192 |#1| |#2| |#3|) (-237)) (|has| |#1| (-373))) (|has| |#1| (-15 * (|#1| (-575) |#1|))))) ((($) |has| |#1| (-15 * (|#1| (-418 (-575)) |#1|)))) ((((-873)) . T)) (((|#2|) |has| |#2| (-373))) @@ -2878,13 +2879,13 @@ (|has| |#4| (-1066)) (|has| |#3| (-1066)) ((((-1194) (-52)) . 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T)) (|has| |#1| (-924)) @@ -2893,7 +2894,7 @@ (((|#1|) . T)) ((((-873)) . T)) ((((-575)) . T)) -((($ (-1194)) -3765 (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))))) +((($ (-1194)) -3763 (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))))) (((#0=(-418 (-575)) #0#) . T) (($ $) . T)) ((((-418 (-575))) . T) (($) . T)) (((|#1| (-418 (-575)) (-1099)) . T)) @@ -2902,12 +2903,12 @@ (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) (|has| |#1| (-831)) (((#0=(-925 |#1|) #0#) . T) (($ $) . T) ((#1=(-418 (-575)) #1#) . T)) ((((-418 |#2|)) . T)) (|has| |#1| (-859)) -((((-1221 |#1|)) . T) (((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-1221 |#1|)) . T) (((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) (((|#1| |#1|) . T) ((#0=(-418 (-575)) #0#) . T) ((#1=(-575) #1#) . T) (($ $) . T)) ((((-925 |#1|)) . T) (($) . T) (((-418 (-575))) . T)) (((|#2|) |has| |#2| (-1066)) (((-575)) -12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066)))) @@ -2924,9 +2925,9 @@ (((|#2|) |has| |#2| (-174))) (((|#1|) . T)) (((|#2|) . T)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) ((((-2 (|:| -4169 (-1194)) (|:| -3179 (-52)))) . T)) ((((-575) |#3|) . T)) (((#0=(-52)) . T) (((-2 (|:| -4169 (-1194)) (|:| -3179 #0#))) . T)) @@ -2936,23 +2937,23 @@ (((|#1|) . T)) (((#0=(-1271 |#1| |#2| |#3| |#4|) $) |has| #0# (-295 #0# #0#))) (|has| |#1| (-373)) -(-3765 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066)))) -(((|#1|) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-1066))) (($) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066))) (((-575)) -3765 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)))) +(-3763 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066)))) +(((|#1|) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-1066))) (($) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066))) (((-575)) -3763 (|has| |#1| (-21)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)))) (((#0=(-1099) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-359))) (((#0=(-418 (-575)) #0#) . T) ((#1=(-710) #1#) . T) (($ $) . T)) ((((-325 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-418 (-575))) |has| |#1| (-373))) ((((-873)) . T)) (|has| |#1| (-1117)) (((|#1|) . T)) -(((|#1|) -3765 (|has| |#2| (-377 |#1|)) (|has| |#2| (-428 |#1|)))) -(((|#1|) -3765 (|has| |#2| (-377 |#1|)) (|has| |#2| (-428 |#1|)))) +(((|#1|) -3763 (|has| |#2| (-377 |#1|)) (|has| |#2| (-428 |#1|)))) +(((|#1|) -3763 (|has| |#2| (-377 |#1|)) (|has| |#2| (-428 |#1|)))) (((|#2|) . T)) ((((-418 (-575))) . T) (((-710)) . T) (($) . T)) ((((-590)) . T)) (((|#3| |#3|) . T)) -((($ (-1194)) -3765 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) +((($ (-1194)) -3763 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) (|has| |#2| (-238)) ((((-875 |#1|)) . T)) ((((-1194)) |has| |#1| (-913 (-1194))) ((|#3|) . T)) @@ -2971,10 +2972,10 @@ (|has| |#1| (-1117)) (((|#2|) . T)) (((|#1|) . T)) -((($) -3765 (|has| |#1| (-238)) (|has| |#1| (-237)))) +((($) -3763 (|has| |#1| (-238)) (|has| |#1| (-237)))) ((((-575)) . T)) (((|#2|) . T) (((-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((|#1|) . T) (($) . T) (((-575)) . T)) -(-3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) +(-3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) (((|#2|) . T) (((-575)) |has| |#2| (-650 (-575)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3030,14 +3031,14 @@ (|has| |#1| (-373)) ((((-925 |#1|)) . T)) ((($) . T) (((-575)) . T) ((|#1|) . T) (((-418 (-575))) . T)) -((($) -3765 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) -((($) |has| |#1| (-859)) (((-575)) -3765 (|has| |#1| (-21)) (|has| |#1| (-859)))) +((($) -3763 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) |has| |#1| (-174)) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) +((($) |has| |#1| (-859)) (((-575)) -3763 (|has| |#1| (-21)) (|has| |#1| (-859)))) ((($ $) . T) ((#0=(-418 (-575)) #0#) . T)) -(-3765 (|has| |#1| (-378)) (|has| |#1| (-861))) +(-3763 (|has| |#1| (-378)) (|has| |#1| (-861))) (((|#1|) . T)) ((((-782)) . T)) ((((-873)) . T)) -(-3765 (-12 (|has| |#3| (-238)) (|has| |#3| (-1066))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1066)))) +(-3763 (-12 (|has| |#3| (-238)) (|has| |#3| (-1066))) (-12 (|has| |#3| (-237)) (|has| |#3| (-1066)))) ((((-1194)) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194))))) ((((-418 |#2|) |#3|) . T)) ((($) . T) (((-418 (-575))) . T)) @@ -3045,17 +3046,17 @@ ((((-575)) . T) (($) . T)) ((((-575)) . T) (($) . T)) ((((-782) |#1|) . T)) -(((|#2| (-245 (-2871 |#1|) (-782))) . T)) +(((|#2| (-245 (-2869 |#1|) (-782))) . T)) (((|#1| (-542 |#3|)) . T)) ((((-418 (-575))) . T)) -(-3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) +(-3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((((-1176)) . T) (((-873)) . T)) (((#0=(-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) #0#) |has| (-2 (|:| -4169 (-1194)) (|:| -3179 (-52))) (-318 (-2 (|:| -4169 (-1194)) (|:| -3179 (-52)))))) ((((-1176)) . T)) (|has| |#1| (-924)) (|has| |#2| (-373)) (((|#1|) . T) (($) . T) (((-575)) . T)) -(-3765 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-804)) (|has| |#2| (-1066))) +(-3763 (|has| |#2| (-21)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-804)) (|has| |#2| (-1066))) ((((-171 (-389))) . T) (((-227)) . T) (((-389)) . T)) ((((-873)) . T)) (((|#1|) . T)) @@ -3072,11 +3073,11 @@ (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) -(-3765 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359))) (|has| |#1| (-38 (-418 (-575)))) (-12 (|has| |#1| (-556)) (|has| |#1| (-839))) ((((-873)) . T)) -((((-1194)) -3765 (-12 (|has| |#1| (-15 * (|#1| (-575) |#1|))) (|has| |#1| (-913 (-1194)))) (-12 (|has| |#1| (-373)) (|has| |#2| (-913 (-1194)))))) +((((-1194)) -3763 (-12 (|has| |#1| (-15 * (|#1| (-575) |#1|))) (|has| |#1| (-913 (-1194)))) (-12 (|has| |#1| (-373)) (|has| |#2| (-913 (-1194)))))) (|has| |#1| (-373)) ((((-1194)) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194))))) (|has| |#1| (-373)) @@ -3089,7 +3090,7 @@ ((((-575) |#1|) . T)) ((((-1194)) |has| |#1| (-913 (-1194)))) (((|#1|) . T)) -(-3765 (-12 (|has| |#1| (-238)) (|has| |#1| (-373))) (-12 (|has| |#1| (-237)) (|has| |#1| (-373))) (|has| |#1| (-359))) +(-3763 (-12 (|has| |#1| (-238)) (|has| |#1| (-373))) (-12 (|has| |#1| (-237)) (|has| |#1| (-373))) (|has| |#1| (-359))) (((|#2|) |has| |#1| (-373))) (((|#2|) |has| |#1| (-373))) ((((-575)) . T) (($) . T)) @@ -3125,11 +3126,11 @@ (((|#1| |#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (((|#2|) |has| |#1| (-373))) ((((-389)) -12 (|has| |#1| (-373)) (|has| |#2| (-898 (-389)))) (((-575)) -12 (|has| |#1| (-373)) (|has| |#2| (-898 (-575))))) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (|has| |#1| (-373)) (((|#1|) . T)) ((($) . T) (((-575)) . T) ((|#2|) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (((|#3|) . T)) ((((-1176)) . T) (((-517)) . T) (((-227)) . T) (((-575)) . T)) (((|#1|) . T)) @@ -3137,7 +3138,7 @@ (|has| |#1| (-567)) (((|#4| |#4|) -12 (|has| |#4| (-318 |#4|)) (|has| |#4| (-1117)))) ((((-418 |#2|)) . T) (((-418 (-575))) . T) (($) . T) (((-575)) . T)) -(-3765 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-804)) (|has| |#2| (-1066))) +(-3763 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-132)) (|has| |#2| (-174)) (|has| |#2| (-373)) (|has| |#2| (-804)) (|has| |#2| (-1066))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1066)) @@ -3147,13 +3148,13 @@ (|has| |#1| (-38 (-418 (-575)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-418 (-575)))) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) ((($) . T)) ((((-1176) |#1|) . T)) (|has| |#1| (-148)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) (|has| |#1| (-148)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-378))) ((($) . T)) (|has| |#1| (-148)) ((((-592 |#1|)) . T)) @@ -3168,7 +3169,7 @@ ((((-418 (-575))) |has| |#2| (-1055 (-575))) (((-575)) |has| |#2| (-1055 (-575))) (((-1194)) |has| |#2| (-1055 (-1194))) ((|#2|) . T)) (((#0=(-418 |#2|) #0#) . T) ((#1=(-418 (-575)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-3765 (|has| |#1| (-146)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-146)) (|has| |#1| (-359))) (|has| |#1| (-148)) ((((-873)) . T)) ((($) . T)) @@ -3188,7 +3189,7 @@ ((((-418 |#2|)) . T)) ((((-873)) . T)) (((|#1|) . T)) -((((-1194)) -3765 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) +((((-1194)) -3763 (|has| |#1| (-913 (-1194))) (|has| |#1| (-915 (-1194))))) (|has| |#1| (-1117)) (|has| |#1| (-802)) (|has| |#1| (-802)) @@ -3196,7 +3197,7 @@ ((((-925 |#1|)) . T) (((-418 (-575))) . T) (($) . T) (((-575)) . T)) ((((-873)) . T)) ((((-547)) |has| |#1| (-625 (-547)))) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-861)) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-861)) (|has| |#1| (-1117)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3205,7 +3206,7 @@ ((((-1271 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-418 (-575))) . T)) (((|#1|) |has| |#1| (-174)) (($) |has| |#1| (-567)) (((-418 (-575))) |has| |#1| (-567))) ((((-873)) . T)) -(-3765 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066)))) +(-3763 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066)))) ((((-873)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -3218,10 +3219,10 @@ ((((-873)) . T)) (((|#2|) . T)) ((((-575)) . T)) -((((-1194)) -3765 (|has| (-418 |#2|) (-913 (-1194))) (|has| (-418 |#2|) (-915 (-1194))))) +((((-1194)) -3763 (|has| (-418 |#2|) (-913 (-1194))) (|has| (-418 |#2|) (-915 (-1194))))) ((((-873)) . T)) ((((-575)) . T)) -(-3765 (|has| |#2| (-804)) (|has| |#2| (-861))) +(-3763 (|has| |#2| (-804)) (|has| |#2| (-861))) ((((-171 (-389))) . T) (((-227)) . T) (((-389)) . T)) ((((-873)) . T)) ((((-873)) . T)) @@ -3233,10 +3234,10 @@ (((|#1|) . T) (($) . T) (((-418 (-575))) . T)) (|has| |#1| (-373)) (|has| |#1| (-373)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) ((((-575) $) . T) (((-655 (-575)) $) . T)) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)) (|has| |#1| (-1129)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-484)) (|has| |#1| (-737)) (|has| |#1| (-913 (-1194))) (|has| |#1| (-1066)) (|has| |#1| (-1129)) (|has| |#1| (-1117))) (|has| |#1| (-1169)) ((((-925 |#1|)) . T) (((-418 (-575))) . T) (($) . T)) ((($) . T)) @@ -3246,20 +3247,20 @@ (((#0=(-117 |#1|) $) |has| #0# (-295 #0# #0#))) (((|#1|) |has| |#1| (-174))) ((((-325 |#1|)) . T) (((-575)) . T)) -(-3765 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-3763 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) ((((-873)) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-873)) . T)) -((((-1194)) -3765 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) +((((-1194)) -3763 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) (((|#1|) |has| |#1| (-318 |#1|))) ((((-575) |#1|) . T) (((-1252 (-575)) $) . T)) (((|#1| |#2|) . T)) ((((-1194) |#1|) . T)) -(((|#1|) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)))) +(((|#1|) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)))) (((|#1|) . T)) ((($ (-1194)) . T)) -(((|#1|) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-1066)))) +(((|#1|) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-1066)))) ((((-575)) . T) (((-418 (-575))) . T)) (((|#1|) . T)) (|has| |#1| (-567)) @@ -3269,15 +3270,15 @@ ((((-418 |#2|)) . T) (((-418 (-575))) . T) (($) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (|has| |#1| (-373)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-567))) (|has| |#1| (-373)) (|has| |#1| (-567)) ((($) . T)) (|has| |#1| (-1117)) ((((-791 |#1| (-875 |#2|))) |has| (-791 |#1| (-875 |#2|)) (-318 (-791 |#1| (-875 |#2|))))) -(-3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) +(-3763 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3287,7 +3288,7 @@ (|has| |#1| (-238)) (((|#1| (-542 (-1105 (-1194)))) . T)) (|has| |#2| (-373)) -((($) -3765 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066))))) +((($) -3763 (-12 (|has| |#2| (-238)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-237)) (|has| |#2| (-1066))))) ((((-592 |#1|)) . T) (((-418 (-575))) . T) (($) . T) (((-575)) . T)) ((((-575)) . T) (((-418 (-575))) . T) (($) . T)) ((((-2 (|:| -4169 (-1176)) (|:| -3179 (-52)))) . T)) @@ -3296,7 +3297,7 @@ (((|#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) ((((-873)) . T)) ((((-873)) . T)) -(-3765 (|has| |#3| (-804)) (|has| |#3| (-861))) +(-3763 (|has| |#3| (-804)) (|has| |#3| (-861))) ((((-873)) . T)) ((((-1137)) . T) (((-873)) . T)) ((((-547)) . T) (((-873)) . T)) @@ -3307,12 +3308,12 @@ ((((-575)) . T)) (((|#3|) . T)) ((((-873)) . T)) -(-3765 (|has| |#1| (-316)) (|has| |#1| (-373)) (|has| |#1| (-359))) -((((-575)) . T) (((-418 (-575))) -3765 (|has| |#2| (-38 (-418 (-575)))) (|has| |#2| (-1055 (-418 (-575))))) ((|#2|) . T) (($) -3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) (((-875 |#1|)) . T)) -((((-1142 |#1| |#2|)) . T) ((|#2|) . T) (($) -3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((|#1|) . T) (((-418 (-575))) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-1055 (-418 (-575))))) (((-575)) . T)) -((((-1190 |#1|)) . T) (((-575)) . 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T) (((-575)) |has| |#1| (-1055 (-575))) (((-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) (((-1194)) . T)) ((($) . T)) @@ -3755,12 +3756,12 @@ (((#0=(-1271 |#1| |#2| |#3| |#4|)) |has| #0# (-318 #0#))) ((($) . T)) (((|#1|) . T)) -((($ $) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((#0=(-418 (-575)) #0#) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) ((|#2| |#2|) |has| |#1| (-373)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -3765 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((#0=(-418 (-575)) #0#) -3765 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373)))) +((($ $) -3763 (|has| |#1| (-174)) (|has| |#1| (-373)) (|has| |#1| (-567))) ((#0=(-418 (-575)) #0#) -3763 (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-373))) ((|#2| |#2|) |has| |#1| (-373)) ((|#1| |#1|) . T)) +(((|#1| |#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-418 (-575)) #0#) . T) (($ $) . T)) (((|#2|) . T) (((-418 (-575))) . T) (($) . T)) @@ -3831,7 +3832,7 @@ ((((-873)) . T)) ((((-873)) . T)) ((((-873)) . T)) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-237))) +(-3763 (|has| |#1| (-238)) (|has| |#1| (-237))) (((|#1|) . T) (((-873)) . T) (((-1199)) . T)) ((((-1199)) . T)) ((((-873)) . T)) @@ -3841,21 +3842,21 @@ (((|#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (((|#1| (-542 (-875 |#2|)) (-875 |#2|) (-791 |#1| (-875 |#2|))) . T)) (((|#1| |#2| (-245 |#1| |#2|) (-245 |#1| |#2|)) . T)) -((((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) |has| |#2| (-174)) (($) -3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924)))) +((((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) |has| |#2| (-174)) (($) -3763 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-418 (-575))) |has| |#2| (-38 (-418 (-575)))) ((|#2|) . 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T)) (|has| |#2| (-1066)) ((((-1194)) -12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066)))) -(-3765 (-12 (|has| |#1| (-484)) (|has| |#2| (-484))) (-12 (|has| |#1| (-737)) (|has| |#2| (-737)))) +(-3763 (-12 (|has| |#1| (-484)) (|has| |#2| (-484))) (-12 (|has| |#1| (-737)) (|has| |#2| (-737)))) (|has| |#1| (-146)) (|has| |#1| (-148)) (|has| |#1| (-373)) @@ -3952,7 +3953,7 @@ (((|#1| |#2|) . T)) ((((-575)) . T) ((|#2|) |has| |#2| (-174))) ((((-115)) . T) ((|#1|) . T) (((-575)) . T)) -(-3765 (|has| |#1| (-359)) (|has| |#1| (-378))) +(-3763 (|has| |#1| (-359)) (|has| |#1| (-378))) (((|#1| |#2|) . T)) ((((-227)) . T)) ((((-418 (-575))) . T) (($) . T) (((-575)) . T)) @@ -3961,11 +3962,11 @@ ((($) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((|#1|) . T) (((-575)) |has| |#1| (-650 (-575)))) ((($) . T) (((-575)) |has| |#1| (-650 (-575))) ((|#1|) . T) (((-418 (-575))) |has| |#1| (-38 (-418 (-575))))) (((|#2|) |has| |#2| (-1117)) (((-575)) -12 (|has| |#2| (-1055 (-575))) (|has| |#2| (-1117))) (((-418 (-575))) -12 (|has| |#2| (-1055 (-418 (-575)))) (|has| |#2| (-1117)))) -(-3765 (|has| |#2| (-238)) (|has| |#2| (-237))) +(-3763 (|has| |#2| (-238)) (|has| |#2| (-237))) (((|#1|) . T)) (((|#1|) . T)) ((((-547)) |has| |#1| (-625 (-547)))) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-861)) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-861)) (|has| |#1| (-1117)))) ((((-575) $) . T) (((-655 (-575)) $) . T)) ((($) . T) (((-418 (-575))) . T)) (|has| |#1| (-924)) @@ -3977,14 +3978,14 @@ (((|#1| |#1|) |has| |#1| (-174))) (((|#1|) . T) (((-575)) . T)) ((((-1199)) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-567))) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-859))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-567))) +(-3763 (|has| |#1| (-21)) (|has| |#1| (-859))) (((|#2|) . T)) -(-3765 (|has| |#1| (-21)) (|has| |#1| (-859))) +(-3763 (|has| |#1| (-21)) (|has| |#1| (-859))) (((|#1|) |has| |#1| (-174))) (((|#1|) . T)) (((|#1|) . T)) -((((-873)) -3765 (-12 (|has| |#1| (-624 (-873))) (|has| |#2| (-624 (-873)))) (-12 (|has| |#1| (-1117)) (|has| |#2| (-1117))))) +((((-873)) -3763 (-12 (|has| |#1| (-624 (-873))) (|has| |#2| (-624 (-873)))) (-12 (|has| |#1| (-1117)) (|has| |#2| (-1117))))) ((((-418 |#2|) |#3|) . T)) ((((-418 (-575))) . T) (($) . T)) (|has| |#1| (-38 (-418 (-575)))) @@ -4008,7 +4009,7 @@ ((((-1199)) . T)) ((((-575)) . T)) (((|#2|) . T)) -((((-1194)) -3765 (-12 (|has| (-1192 |#1| |#2| |#3|) (-913 (-1194))) (|has| |#1| (-373))) (-12 (|has| |#1| (-15 * (|#1| (-575) |#1|))) (|has| |#1| (-913 (-1194)))))) +((((-1194)) -3763 (-12 (|has| (-1192 |#1| |#2| |#3|) (-913 (-1194))) (|has| |#1| (-373))) (-12 (|has| |#1| (-15 * (|#1| (-575) |#1|))) (|has| |#1| (-913 (-1194)))))) ((((-1194)) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194))))) ((((-1194)) -12 (|has| |#1| (-15 * (|#1| (-782) |#1|))) (|has| |#1| (-913 (-1194))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4036,7 +4037,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575)))) -((((-1194)) -3765 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) +((((-1194)) -3763 (|has| |#2| (-913 (-1194))) (|has| |#2| (-915 (-1194))))) ((((-873)) . T)) (((|#2|) . T)) ((((-873)) . T)) @@ -4046,15 +4047,15 @@ ((((-1192 |#1| |#2| |#3|)) . T)) ((((-1192 |#1| |#2| |#3|)) . T) (((-1185 |#1| |#2| |#3|)) . T)) ((((-873)) . T)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) ((((-575) |#1|) . T)) ((((-1192 |#1| |#2| |#3|)) |has| |#1| (-373))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-373)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -3765 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-1066))) (($) |has| |#4| (-1066)) (((-575)) -12 (|has| |#4| (-650 (-575))) (|has| |#4| (-1066)))) -(((|#2|) . T) ((|#3|) -3765 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-1066))) (($) |has| |#3| (-1066)) (((-575)) -12 (|has| |#3| (-650 (-575))) (|has| |#3| (-1066)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -3763 (|has| |#4| (-174)) (|has| |#4| (-373)) (|has| |#4| (-1066))) (($) |has| |#4| (-1066)) (((-575)) -12 (|has| |#4| (-650 (-575))) (|has| |#4| (-1066)))) +(((|#2|) . T) ((|#3|) -3763 (|has| |#3| (-174)) (|has| |#3| (-373)) (|has| |#3| (-1066))) (($) |has| |#3| (-1066)) (((-575)) -12 (|has| |#3| (-650 (-575))) (|has| |#3| (-1066)))) (((|#1|) . T)) (((|#1|) . T)) ((((-117 |#1|)) . T)) @@ -4068,7 +4069,7 @@ ((((-189)) . T) (((-873)) . T)) ((((-873)) . T)) (((|#1|) . T)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) ((((-130)) . T) (((-873)) . T)) ((((-575) |#1|) . T) (((-1252 (-575)) $) . T)) ((((-130)) . T)) @@ -4077,9 +4078,9 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-373)) (|has| |#2| (-295 |#2| |#2|))) (($ $) . T) (((-575) |#1|) . T)) ((($ $) . T) (((-418 (-575)) |#1|) . T)) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-924))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-463)) (|has| |#1| (-924))) ((($ (-1194)) |has| |#1| (-1066))) -(-3765 (|has| |#1| (-861)) (|has| |#1| (-1117))) +(-3763 (|has| |#1| (-861)) (|has| |#1| (-1117))) ((((-873)) . T)) ((((-873)) . T)) ((((-873)) . T)) @@ -4099,8 +4100,8 @@ ((((-1199)) . T)) ((((-873)) . T) (((-1199)) . T)) ((((-873)) . T) (((-1199)) . T)) -(-3765 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) -(-3765 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) +(-3763 (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) +(-3763 (|has| |#1| (-463)) (|has| |#1| (-567)) (|has| |#1| (-924))) ((($) . T)) (((|#2| (-542 (-875 |#1|))) . T)) ((((-1199)) . T)) @@ -4115,7 +4116,7 @@ ((((-1199)) . T)) ((((-873)) . T) (((-1199)) . T)) ((((-1199)) . T)) -((((-873)) -3765 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) +((((-873)) -3763 (|has| |#1| (-624 (-873))) (|has| |#1| (-1117)))) (((|#1|) . T)) (((|#2| (-782)) . T)) (((|#1| |#2|) . T)) @@ -4133,14 +4134,14 @@ ((((-575)) . T) (($) . T)) (((|#2| $) |has| |#2| (-295 |#2| |#2|))) (((|#1| (-655 |#1|)) |has| |#1| (-859))) -(-3765 (|has| |#1| (-238)) (|has| |#1| (-359))) -(-3765 (|has| |#1| (-373)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-238)) (|has| |#1| (-359))) +(-3763 (|has| |#1| (-373)) (|has| |#1| (-359))) ((((-1281 |#1|)) . T) (((-575)) . T) ((|#2|) . T) (((-418 (-575))) |has| |#2| (-1055 (-418 (-575))))) (|has| |#1| (-1117)) (((|#1|) . T)) -((((-1281 |#1|)) . T) (((-575)) . T) (($) -3765 (|has| |#2| (-373)) (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) (((-1099)) . T) ((|#2|) . T) (((-418 (-575))) -3765 (|has| |#2| (-38 (-418 (-575)))) (|has| |#2| (-1055 (-418 (-575)))))) +((((-1281 |#1|)) . T) (((-575)) . T) (($) -3763 (|has| |#2| (-373)) (|has| |#2| (-463)) (|has| |#2| (-567)) (|has| |#2| (-924))) (((-1099)) . T) ((|#2|) . T) (((-418 (-575))) -3763 (|has| |#2| (-38 (-418 (-575)))) (|has| |#2| (-1055 (-418 (-575)))))) ((((-418 (-575))) . T) (($) . T)) -((((-1016 |#1|)) . T) ((|#1|) . T) (((-575)) -3765 (|has| (-1016 |#1|) (-1055 (-575))) (|has| |#1| (-1055 (-575)))) (((-418 (-575))) -3765 (|has| (-1016 |#1|) (-1055 (-418 (-575)))) (|has| |#1| (-1055 (-418 (-575)))))) +((((-1016 |#1|)) . T) ((|#1|) . T) (((-575)) -3763 (|has| (-1016 |#1|) (-1055 (-575))) (|has| |#1| (-1055 (-575)))) (((-418 (-575))) -3763 (|has| (-1016 |#1|) (-1055 (-418 (-575)))) (|has| |#1| (-1055 (-418 (-575)))))) ((((-925 |#1|)) . T) (((-418 (-575))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (((|#1| |#1|) -12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) @@ -4159,10 +4160,10 @@ (((|#1|) . 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((-1207 . -615) 192650) ((-561 . -1211) 192629) ((-346 . -1117) T) ((-328 . -373) 192608) ((-418 . -148) 192587) ((-418 . -146) 192566) ((-979 . -1129) 192465) ((-245 . -913) 192397) ((-826 . -1129) 192375) ((-665 . -863) 192359) ((-490 . -615) 192338) ((-561 . -107) 192288) ((-1021 . -387) 192270) ((-1021 . -348) 192252) ((-1194 . -624) 192234) ((-97 . -1117) T) ((-979 . -23) 192045) ((-488 . -21) T) ((-488 . -25) T) ((-826 . -23) 191897) ((-1194 . -625) 191819) ((-59 . -19) 191803) ((-1190 . -737) T) ((-1142 . -737) T) ((-1104 . -1117) T) ((-527 . -19) 191787) ((-507 . -19) 191771) ((-59 . -615) 191748) ((-1020 . -237) 191685) ((-916 . -102) 191663) ((-865 . -737) T) ((-793 . -1117) T) ((-527 . -615) 191640) ((-507 . -615) 191617) ((-791 . -1117) T) ((-791 . -1082) 191584) ((-472 . -1117) T) ((-465 . -1117) T) ((-597 . -728) 191559) ((-660 . -1117) T) ((-1277 . -47) 191536) ((-1271 . -102) T) ((-1270 . -47) 191506) ((-1249 . -47) 191483) ((-1229 . -174) 191434) ((-1191 . -316) 191413) ((-1185 . -316) 191392) ((-1113 . -627) 191373) ((-1107 . -627) 191354) ((-1097 . -567) 191305) ((-1097 . -1239) 191256) ((-1021 . -913) NIL) ((-1090 . -627) 191237) ((-681 . -132) T) ((-638 . -1129) T) ((-1083 . -627) 191218) ((-1053 . -627) 191199) ((-1036 . -627) 191180) ((-725 . -1073) 191150) ((-710 . -657) 191100) ((-283 . -1117) T) ((-85 . -452) T) ((-85 . -406) T) ((-723 . -908) 191003) ((-722 . -174) T) ((-50 . -1117) T) ((-606 . -47) 190980) ((-227 . -659) 190945) ((-592 . -1117) T) ((-529 . -1117) T) ((-498 . -831) T) ((-498 . -935) T) ((-369 . -1239) T) ((-363 . -1239) T) ((-355 . -1239) T) ((-328 . -1129) T) ((-325 . -1068) 190855) ((-322 . -1068) 190784) ((-108 . -1239) T) ((-637 . -627) 190765) ((-369 . -567) T) ((-219 . -935) T) ((-219 . -831) T) ((-325 . -651) 190675) ((-322 . -651) 190604) ((-363 . -567) T) ((-355 . -567) T) ((-494 . -627) 190585) ((-108 . -567) T) ((-669 . -728) 190555) ((-1185 . -1039) NIL) ((-220 . -627) 190536) ((-328 . -23) T) ((-67 . -1235) T) ((-1017 . -624) 190468) ((-705 . -271) 190450) ((-705 . -232) 190432) ((-725 . -111) 190397) ((-655 . -34) T) ((-250 . -500) 190381) ((-1314 . -1169) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-1307 . -132) T) ((-1119 . -1115) 190365) ((-173 . -1117) T) ((-1305 . -132) T) ((-1298 . -102) T) ((-1281 . -624) 190331) ((-1277 . -1235) T) ((-1270 . -1235) T) ((-967 . -924) 190310) ((-1270 . -1055) 190245) ((-1249 . -1235) T) ((-1249 . -898) NIL) ((-526 . -627) 190229) ((-1249 . -896) 190181) ((-1249 . -1055) 190147) ((-1229 . -525) 190114) ((-492 . -924) 190093) ((-1207 . -625) NIL) ((-1207 . -624) 190075) ((-1104 . -728) 189924) ((-1079 . -659) 189896) ((-967 . -659) 189785) ((-608 . -501) 189766) ((-596 . -501) 189747) ((-793 . -728) 189576) ((-608 . -624) 189542) ((-596 . -624) 189508) ((-547 . -624) 189490) ((-547 . -625) 189471) ((-791 . -728) 189320) ((-1094 . -102) T) ((-391 . -25) T) ((-634 . -657) 189292) ((-391 . -21) T) ((-492 . -659) 189181) ((-472 . -728) 189152) ((-465 . -728) 189001) ((-1004 . -102) T) ((-1159 . -1140) 188946) ((-1063 . -1228) 188875) ((-916 . -318) 188813) ((-748 . -102) T) ((-118 . -657) 188743) ((-616 . -627) 188725) ((-887 . -93) T) ((-725 . -627) 188679) ((-542 . -25) T) ((-692 . -93) T) ((-687 . -93) T) ((-675 . -624) 188661) ((-656 . -501) 188642) ((-142 . -102) T) ((-44 . -132) T) ((-656 . -624) 188595) ((-606 . -1235) T) ((-353 . -1075) T) ((-298 . -1129) T) ((-489 . -93) T) ((-418 . -237) 188546) ((-365 . -624) 188528) ((-362 . -624) 188510) ((-354 . -624) 188492) ((-272 . -625) 188240) ((-272 . -624) 188222) ((-252 . -624) 188204) ((-252 . -625) 188065) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1158 . -624) 188047) ((-1137 . -651) 188034) ((-1137 . -1068) 188021) ((-830 . -737) T) ((-830 . -868) T) ((-613 . -297) 187998) ((-592 . -728) 187963) ((-490 . -625) NIL) ((-490 . -624) 187945) ((-529 . -728) 187890) ((-325 . -102) T) ((-322 . -102) T) ((-298 . -23) T) ((-153 . -132) T) ((-925 . -624) 187872) ((-925 . -625) 187854) ((-397 . -737) T) ((-883 . -1073) 187806) ((-883 . -111) 187744) ((-725 . -1066) T) ((-723 . -1261) 187728) ((-705 . -359) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-530 . -624) 187660) ((-389 . -806) T) ((-225 . -1117) T) ((-169 . -1235) T) ((-389 . -803) T) ((-227 . -805) T) ((-227 . -802) T) ((-59 . -625) 187621) ((-59 . -624) 187533) ((-227 . -737) T) ((-527 . -625) 187494) ((-527 . -624) 187406) ((-508 . -624) 187338) ((-507 . -625) 187299) ((-507 . -624) 187211) ((-1097 . -373) 187162) ((-40 . -422) 187139) ((-77 . -1235) T) ((-882 . -924) NIL) ((-369 . -338) 187123) ((-369 . -373) T) ((-363 . -338) 187107) ((-363 . -373) T) ((-355 . -338) 187091) ((-355 . -373) T) ((-325 . -293) 187070) ((-108 . -373) T) ((-70 . -1235) T) ((-1249 . -348) 187022) ((-882 . -659) 186967) ((-1249 . -387) 186919) ((-979 . -132) 186774) ((-826 . -132) 186645) ((-973 . -662) 186629) ((-1104 . -174) 186540) ((-973 . -383) 186524) ((-1079 . -805) T) ((-1079 . -802) T) ((-883 . -627) 186422) ((-793 . -174) 186313) ((-791 . -174) 186224) ((-827 . -47) 186186) ((-1079 . -737) T) ((-336 . -500) 186170) ((-967 . -737) T) ((-1298 . -318) 186108) ((-1277 . -913) 186021) ((-465 . -174) 185932) ((-250 . -295) 185884) ((-1270 . -913) 185790) ((-1269 . -1073) 185625) ((-1249 . -913) 185458) ((-492 . -737) T) ((-1248 . -1073) 185266) ((-1229 . -299) 185245) ((-1204 . -1235) T) ((-1201 . -378) T) ((-1200 . -378) T) ((-1163 . -152) 185229) ((-1137 . -102) T) ((-1135 . -1117) T) ((-1097 . -23) T) ((-1097 . -1129) T) ((-1092 . -102) T) ((-1074 . -624) 185196) ((-1020 . -420) 185168) ((-942 . -970) T) ((-748 . -318) 185106) ((-75 . -1235) T) ((-675 . -392) 185078) ((-171 . -924) 185031) ((-30 . -970) T) ((-112 . -855) T) ((-1 . -624) 185013) ((-1016 . -908) 184934) ((-129 . -662) 184916) ((-50 . -631) 184900) ((-705 . -657) 184835) ((-606 . -913) 184748) ((-449 . -102) T) ((-129 . -383) 184730) ((-142 . -318) NIL) ((-883 . -1066) T) ((-844 . -861) 184709) ((-81 . -1235) T) ((-722 . -299) T) ((-40 . -1075) T) ((-592 . -174) T) ((-529 . -174) T) ((-522 . -624) 184691) ((-171 . -659) 184565) ((-518 . -624) 184547) ((-361 . -148) 184529) ((-361 . -146) T) ((-369 . -1129) T) ((-363 . -1129) T) ((-355 . -1129) T) ((-1021 . -316) T) ((-929 . -316) T) ((-883 . -248) T) ((-108 . -1129) T) ((-883 . -238) 184508) ((-1269 . -111) 184329) ((-1248 . -111) 184118) ((-250 . -1273) 184102) ((-575 . -859) T) ((-369 . -23) T) ((-364 . -359) T) ((-325 . -318) 184089) ((-322 . -318) 184030) ((-363 . -23) T) ((-328 . -132) T) ((-355 . -23) T) ((-1021 . -1039) T) ((-31 . -627) 184011) ((-108 . -23) T) ((-665 . -1068) 183995) ((-250 . -615) 183972) ((-342 . -1117) T) ((-665 . -651) 183942) ((-1271 . -38) 183834) ((-1258 . -924) 183813) ((-112 . -1117) T) ((-827 . -1235) T) ((-1052 . -102) T) ((-1258 . -659) 183702) ((-882 . -805) NIL) ((-866 . -659) 183676) ((-882 . -802) NIL) ((-827 . -898) NIL) ((-882 . -737) T) ((-1104 . -525) 183549) ((-793 . -525) 183496) ((-791 . -525) 183448) ((-582 . -659) 183435) ((-827 . -1055) 183263) ((-465 . -525) 183206) ((-399 . -400) T) ((-1269 . -627) 183019) ((-1248 . -627) 182767) ((-60 . -1235) T) ((-632 . -861) 182746) ((-511 . -672) T) ((-1163 . -993) 182715) ((-1041 . -657) 182652) ((-1020 . -463) T) ((-710 . -859) T) ((-521 . -803) T) ((-485 . -1073) 182487) ((-511 . -113) T) ((-353 . -1117) T) ((-322 . -1169) NIL) ((-298 . -132) T) ((-405 . -1117) T) ((-881 . -1075) T) ((-705 . -380) 182454) ((-364 . -657) 182384) ((-225 . -631) 182361) ((-336 . -295) 182313) ((-485 . -111) 182134) ((-1269 . -1066) T) ((-1248 . -1066) T) ((-827 . -387) 182118) ((-171 . -737) T) ((-665 . -102) T) ((-1269 . -248) 182097) ((-1269 . -238) 182049) ((-1248 . -238) 181954) ((-1248 . -248) 181933) ((-1020 . -413) NIL) ((-681 . -650) 181881) ((-325 . -38) 181791) ((-322 . -38) 181720) ((-69 . -624) 181702) ((-328 . -504) 181668) ((-48 . -657) 181618) ((-1207 . -297) 181597) ((-1243 . -861) T) ((-1130 . -1129) 181575) ((-83 . -1235) T) ((-61 . -624) 181557) ((-490 . -297) 181536) ((-1300 . -1055) 181513) ((-1182 . -1117) T) ((-1130 . -23) 181365) ((-827 . -913) 181301) ((-1258 . -737) T) ((-1119 . -1235) T) ((-485 . -627) 181127) ((-361 . -237) T) ((-1104 . -299) 181058) ((-981 . -1117) T) ((-905 . -102) T) ((-793 . -299) 180969) ((-336 . -19) 180953) ((-59 . -297) 180930) ((-791 . -299) 180861) ((-866 . -737) T) ((-118 . -859) NIL) ((-527 . -297) 180838) ((-336 . -615) 180815) ((-507 . -297) 180792) ((-465 . -299) 180723) ((-1052 . -318) 180574) ((-887 . -501) 180555) ((-887 . -624) 180521) ((-692 . -501) 180502) ((-582 . -737) T) ((-687 . -501) 180483) ((-692 . -624) 180433) ((-687 . -624) 180399) ((-673 . -624) 180381) ((-489 . -501) 180362) ((-489 . -624) 180328) ((-250 . -625) 180289) ((-250 . -501) 180266) ((-139 . -501) 180247) ((-138 . -501) 180228) ((-134 . -501) 180209) ((-250 . -624) 180101) ((-215 . -102) T) ((-139 . -624) 180067) ((-138 . -624) 180033) ((-134 . -624) 179999) ((-1164 . -34) T) ((-958 . -1235) T) ((-353 . -728) 179944) ((-681 . -25) T) ((-681 . -21) T) ((-1194 . -627) 179925) ((-485 . -1066) T) ((-646 . -428) 179890) ((-618 . -428) 179855) ((-1137 . -1169) T) ((-723 . -1068) 179678) ((-592 . -299) T) ((-529 . -299) T) ((-1270 . -316) 179657) ((-485 . -238) 179609) ((-485 . -248) 179588) ((-1249 . -316) 179567) ((-723 . -651) 179396) ((-1249 . -1039) NIL) ((-1097 . -132) T) ((-883 . -806) 179375) ((-145 . -102) T) ((-40 . -1117) T) ((-883 . -803) 179354) ((-655 . -1027) 179338) ((-591 . -1075) T) ((-575 . -1075) T) ((-506 . -1075) T) ((-418 . -463) T) ((-369 . -132) T) ((-325 . -411) 179322) ((-322 . -411) 179283) ((-363 . -132) T) ((-355 . -132) T) ((-1199 . -1117) T) ((-1137 . -38) 179270) ((-1111 . -624) 179237) ((-108 . -132) T) ((-969 . -1117) T) ((-936 . -1117) T) ((-782 . -1117) T) ((-683 . -1117) T) ((-712 . -148) T) ((-117 . -148) T) ((-1307 . -21) T) ((-1307 . -25) T) ((-1305 . -21) T) ((-1305 . -25) T) ((-675 . -1073) 179221) ((-542 . -861) T) ((-511 . -861) T) ((-365 . -1073) 179173) ((-362 . -1073) 179125) ((-354 . -1073) 179077) ((-257 . -1235) T) ((-256 . -1235) T) ((-272 . -1073) 178920) ((-252 . -1073) 178763) ((-675 . -111) 178742) ((-828 . -1239) 178721) ((-558 . -855) T) ((-325 . -915) 178687) ((-365 . -111) 178625) ((-362 . -111) 178563) ((-354 . -111) 178501) ((-272 . -111) 178330) ((-252 . -111) 178159) ((-322 . -915) NIL) ((-634 . -422) 178143) ((-44 . -21) T) ((-44 . -25) T) ((-826 . -650) 178049) ((-828 . -567) 178028) ((-257 . -1055) 177855) ((-256 . -1055) 177682) ((-127 . -120) 177666) ((-925 . -1073) 177631) ((-723 . -102) T) ((-710 . -1075) T) ((-608 . -627) 177612) ((-596 . -627) 177593) ((-547 . -629) 177496) ((-353 . -174) T) ((-88 . -624) 177478) ((-153 . -21) T) ((-153 . -25) T) ((-925 . -111) 177434) ((-40 . -728) 177379) ((-881 . -1117) T) ((-675 . -627) 177356) ((-656 . -627) 177337) ((-365 . -627) 177274) ((-362 . -627) 177211) ((-558 . -1117) T) ((-354 . -627) 177148) ((-336 . -625) 177109) ((-336 . -624) 177021) ((-272 . -627) 176774) ((-252 . -627) 176559) ((-1248 . -803) 176512) ((-1248 . -806) 176465) ((-257 . -387) 176434) ((-256 . -387) 176403) ((-665 . -38) 176373) ((-619 . -34) T) ((-493 . -1129) 176351) ((-486 . -34) T) ((-1130 . -132) 176222) ((-979 . -25) 176033) ((-925 . -627) 175983) ((-885 . -624) 175965) ((-979 . -21) 175920) ((-826 . -25) 175753) ((-826 . -21) 175664) ((-1241 . -378) T) ((-634 . -1075) T) ((-1196 . -567) 175643) ((-1190 . -47) 175620) ((-365 . -1066) T) ((-362 . -1066) T) ((-493 . -23) 175472) ((-354 . -1066) T) ((-272 . -1066) T) ((-252 . -1066) T) ((-1142 . -47) 175444) ((-118 . -1075) T) ((-1051 . -659) 175418) ((-973 . -34) T) ((-365 . -238) 175397) ((-365 . -248) T) ((-362 . -238) 175376) ((-362 . -248) T) ((-354 . -238) 175355) ((-354 . -248) T) ((-272 . -335) 175327) ((-252 . -335) 175284) ((-272 . -238) 175263) ((-1174 . -152) 175247) ((-257 . -913) 175179) ((-256 . -913) 175111) ((-1159 . -908) 175032) ((-1099 . -861) T) ((-425 . -1129) T) ((-1071 . -23) T) ((-1041 . -859) T) ((-925 . -1066) T) ((-331 . -659) 175014) ((-712 . -237) T) ((-681 . -234) 174959) ((-1229 . -1019) 174925) ((-1191 . -935) 174904) ((-1185 . -935) 174883) ((-1185 . -831) NIL) ((-1016 . -1068) 174779) ((-982 . -1235) T) ((-925 . -248) T) ((-828 . -373) 174758) ((-395 . -23) T) ((-128 . -1117) 174736) ((-122 . -1117) 174714) ((-925 . -238) T) ((-129 . -34) T) ((-389 . -659) 174679) ((-1016 . -651) 174627) ((-881 . -728) 174614) ((-1314 . -657) 174586) ((-1063 . -152) 174551) ((-1010 . -1235) T) ((-40 . -174) T) ((-705 . -422) 174533) ((-723 . -318) 174520) ((-847 . -659) 174480) ((-838 . -659) 174454) ((-328 . -25) T) ((-328 . -21) T) ((-669 . -295) 174433) ((-591 . -1117) T) ((-575 . -1117) T) ((-506 . -1117) T) ((-250 . -297) 174410) ((-1190 . -1235) T) ((-1142 . -1235) T) ((-322 . -271) 174371) ((-322 . -232) 174332) ((-1190 . -898) NIL) ((-55 . -1117) T) ((-1142 . -898) 174191) ((-130 . -861) T) ((-1190 . -1055) 174071) ((-1142 . -1055) 173954) ((-185 . -624) 173936) ((-865 . -1055) 173832) ((-793 . -295) 173759) ((-828 . -1129) T) ((-1051 . -737) T) ((-1063 . -993) 173688) ((-613 . -662) 173672) ((-1020 . -908) 173579) ((-1016 . -102) T) ((-828 . -23) T) ((-723 . -1169) 173557) ((-705 . -1075) T) ((-613 . -383) 173541) ((-361 . -463) T) ((-353 . -299) T) ((-1286 . -1117) T) ((-253 . -1117) T) ((-410 . -102) T) ((-298 . -21) T) ((-298 . -25) T) ((-371 . -737) T) ((-721 . -1117) T) ((-710 . -1117) T) ((-371 . -484) T) ((-1229 . -624) 173523) ((-1190 . -387) 173507) ((-1142 . -387) 173491) ((-1041 . -422) 173453) ((-142 . -231) 173435) ((-389 . -805) T) ((-389 . -802) T) ((-881 . -174) T) ((-389 . -737) T) ((-722 . -624) 173417) ((-723 . -38) 173246) ((-1285 . -1283) 173230) ((-361 . -413) T) ((-1285 . -1117) 173180) ((-1208 . -1117) T) ((-591 . -728) 173167) ((-575 . -728) 173154) ((-506 . -728) 173119) ((-1271 . -657) 173009) ((-325 . -640) 172988) ((-847 . -737) T) ((-838 . -737) T) ((-655 . -1235) T) ((-1097 . -650) 172936) ((-1190 . -913) 172879) ((-1142 . -913) 172863) ((-826 . -234) 172754) ((-673 . -1073) 172738) ((-108 . -650) 172720) ((-493 . -132) 172591) ((-1196 . -1129) T) ((-967 . -47) 172560) ((-634 . -1117) T) ((-673 . -111) 172539) ((-502 . -624) 172505) ((-336 . -297) 172482) ((-492 . -47) 172439) ((-1196 . -23) T) ((-118 . -1117) T) ((-103 . -102) 172417) ((-1297 . -1129) T) ((-559 . -861) T) ((-227 . -1235) T) ((-1071 . -132) T) ((-1041 . -1075) T) ((-1297 . -23) T) ((-830 . -1055) 172401) ((-1215 . -624) 172383) ((-1020 . -735) 172355) ((-1137 . -839) T) ((-710 . -728) 172320) ((-597 . -624) 172302) ((-397 . -1055) 172286) ((-364 . -1075) T) ((-395 . -132) T) ((-333 . -1055) 172270) ((-1122 . -1117) T) ((-1097 . -21) T) ((-1097 . -25) T) ((-227 . -898) 172252) ((-1021 . -935) T) ((-91 . -34) T) ((-1021 . -831) T) ((-929 . -935) T) ((-1016 . -318) 172217) ((-887 . -627) 172198) ((-498 . -1239) T) ((-725 . -659) 172158) ((-692 . -627) 172139) ((-687 . -627) 172120) ((-219 . -1239) T) ((-418 . -908) 172041) ((-227 . -1055) 172001) ((-40 . -299) T) ((-498 . -567) T) ((-489 . -627) 171982) ((-369 . -25) T) ((-325 . -657) 171637) ((-322 . -657) 171551) ((-369 . -21) T) ((-363 . -25) T) ((-363 . -21) T) ((-219 . -567) T) ((-355 . -25) T) ((-355 . -21) T) ((-328 . -234) 171497) ((-250 . -627) 171474) ((-139 . -627) 171455) ((-138 . -627) 171436) ((-134 . -627) 171417) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1075) T) ((-591 . -174) T) ((-575 . -174) T) ((-506 . -174) T) ((-1079 . -1235) T) ((-967 . -1235) T) ((-669 . -624) 171399) ((-492 . -1235) T) ((-748 . -747) 171383) ((-346 . -624) 171365) ((-68 . -393) T) ((-68 . -406) T) ((-1119 . -107) 171349) ((-1079 . -898) 171331) ((-967 . -898) 171256) ((-664 . -1129) T) ((-634 . -728) 171243) ((-492 . -898) NIL) ((-1163 . -102) T) ((-1111 . -629) 171227) ((-1079 . -1055) 171209) ((-97 . -624) 171191) ((-488 . -148) T) ((-967 . -1055) 171071) ((-118 . -728) 171016) ((-723 . -915) 170923) ((-664 . -23) T) ((-492 . -1055) 170799) ((-1104 . -625) NIL) ((-1104 . -624) 170781) ((-793 . -625) NIL) ((-793 . -624) 170742) ((-791 . -625) 170376) ((-791 . -624) 170290) ((-1130 . -650) 170196) ((-472 . -624) 170178) ((-465 . -624) 170160) ((-465 . -625) 170021) ((-1052 . -231) 169967) ((-883 . -924) 169946) ((-127 . -34) T) ((-828 . -132) T) ((-660 . -624) 169928) ((-589 . -102) T) ((-365 . -1304) 169912) ((-362 . -1304) 169896) ((-354 . -1304) 169880) ((-128 . -525) 169813) ((-122 . -525) 169746) ((-522 . -803) T) ((-522 . -806) T) ((-521 . -805) T) ((-103 . -318) 169684) ((-224 . -102) 169662) ((-710 . -174) T) ((-705 . -1117) T) ((-883 . -659) 169578) ((-65 . -394) T) ((-283 . -624) 169560) ((-65 . -406) T) ((-967 . -387) 169544) ((-881 . -299) T) ((-50 . -624) 169526) ((-1016 . -38) 169474) ((-1137 . -657) 169446) ((-592 . -624) 169428) ((-492 . -387) 169412) ((-592 . -625) 169394) ((-529 . -624) 169376) ((-925 . -1304) 169363) ((-882 . -1235) T) ((-712 . -463) T) ((-506 . -525) 169329) ((-498 . -373) T) ((-365 . -378) 169308) ((-362 . -378) 169287) ((-354 . -378) 169266) ((-725 . -737) T) ((-219 . -373) T) ((-117 . -463) T) ((-1308 . -1299) 169250) ((-882 . -896) 169227) ((-882 . -898) NIL) ((-979 . -861) 169126) ((-826 . -861) 169077) ((-1242 . -102) T) ((-665 . -667) 169061) ((-1221 . -34) T) ((-173 . -624) 169043) ((-1130 . -25) 168876) ((-1130 . -21) 168787) ((-882 . -1055) 168764) ((-967 . -913) 168745) ((-1258 . -47) 168722) ((-925 . -378) T) ((-59 . -662) 168706) ((-527 . -662) 168690) ((-492 . -913) 168667) ((-71 . -452) T) ((-71 . -406) T) ((-507 . -662) 168651) ((-59 . -383) 168635) ((-634 . -174) T) ((-527 . -383) 168619) ((-507 . -383) 168603) ((-838 . -719) 168587) ((-1190 . -316) 168566) ((-1196 . -132) T) ((-1159 . -1068) 168550) ((-118 . -174) T) ((-1159 . -651) 168482) ((-1163 . -318) 168420) ((-171 . -1235) T) ((-1297 . -132) T) ((-877 . -1068) 168390) ((-646 . -755) 168374) ((-618 . -755) 168358) ((-1270 . -935) 168337) ((-1249 . -935) 168316) ((-1249 . -831) NIL) ((-877 . -651) 168286) ((-705 . -728) 168236) ((-1248 . -924) 168189) ((-1041 . -1117) T) ((-882 . -387) 168166) ((-882 . -348) 168143) ((-920 . -1129) T) ((-171 . -896) 168127) ((-171 . -898) 168052) ((-1285 . -525) 167985) ((-1269 . -659) 167882) ((-1097 . -234) 167755) ((-498 . -1129) T) ((-364 . -1117) T) ((-219 . -1129) T) ((-76 . -452) T) ((-76 . -406) T) ((-171 . -1055) 167651) ((-303 . -908) 167608) ((-328 . -861) T) ((-1248 . -659) 167416) ((-883 . -805) 167395) ((-883 . -802) 167374) ((-883 . -737) T) ((-498 . -23) T) ((-369 . -234) 167347) ((-363 . -234) 167320) ((-355 . -234) 167293) ((-225 . -624) 167275) ((-176 . -463) T) ((-224 . -318) 167213) ((-86 . -452) T) ((-86 . -406) T) ((-108 . -234) 167200) ((-219 . -23) T) ((-1309 . -1302) 167179) ((-688 . -1055) 167163) ((-591 . -299) T) ((-575 . -299) T) ((-506 . -299) T) ((-137 . -481) 167118) ((-1258 . -1235) T) ((-665 . -657) 167077) ((-48 . -1117) T) ((-723 . -271) 167061) ((-723 . -232) 167045) ((-882 . -913) NIL) ((-1258 . -898) NIL) ((-901 . -102) T) ((-897 . -102) T) ((-399 . -1117) T) ((-171 . -387) 167029) ((-171 . -348) 167013) ((-1258 . -1055) 166893) ((-866 . -1055) 166789) ((-1159 . -102) T) ((-1016 . -915) 166712) ((-673 . -803) 166691) ((-664 . -132) T) ((-673 . -806) 166670) ((-118 . -525) 166578) ((-582 . -1055) 166560) ((-303 . -1292) 166530) ((-877 . -102) T) ((-978 . -567) 166509) ((-1229 . -1073) 166392) ((-1020 . -1068) 166337) ((-493 . -650) 166243) ((-919 . -1117) T) ((-1041 . -728) 166180) ((-722 . -1073) 166145) ((-1020 . -651) 166090) ((-628 . -102) T) ((-613 . -34) T) ((-1164 . -1235) T) ((-1229 . -111) 165959) ((-485 . -659) 165856) ((-364 . -728) 165801) ((-171 . -913) 165760) ((-710 . -299) T) ((-705 . -174) T) ((-722 . -111) 165716) ((-1314 . -1075) T) ((-1258 . -387) 165700) ((-429 . -1239) 165678) ((-1135 . -624) 165660) ((-322 . -859) NIL) ((-429 . -567) T) ((-227 . -316) T) ((-1248 . -802) 165613) ((-1248 . -805) 165566) ((-1269 . -737) T) ((-1248 . -737) T) ((-48 . -728) 165531) ((-227 . -1039) T) ((-1271 . -422) 165497) ((-361 . -1292) 165474) ((-1258 . -913) 165417) ((-729 . -737) T) ((-342 . -624) 165399) ((-1229 . -627) 165281) ((-1130 . -234) 165172) ((-112 . -624) 165154) ((-112 . -625) 165136) ((-729 . -484) T) ((-722 . -627) 165086) ((-1308 . -1068) 165070) ((-493 . -25) 164903) ((-128 . -500) 164887) ((-122 . -500) 164871) ((-493 . -21) 164782) ((-1308 . -651) 164752) ((-634 . -299) T) ((-597 . -1073) 164727) ((-448 . -1117) T) ((-1079 . -316) T) ((-118 . -299) T) ((-1121 . -102) T) ((-1020 . -102) T) ((-597 . -111) 164695) ((-1159 . -318) 164633) ((-1229 . -1066) T) ((-1079 . -1039) T) ((-66 . -1235) T) ((-1071 . -25) T) ((-1071 . -21) T) ((-722 . -1066) T) ((-395 . -21) T) ((-395 . -25) T) ((-705 . -525) NIL) ((-1041 . -174) T) ((-722 . -248) T) ((-1079 . -556) T) ((-723 . -657) 164543) ((-517 . -102) T) ((-513 . -102) T) ((-364 . -174) T) ((-353 . -624) 164525) ((-418 . -1068) 164477) ((-405 . -624) 164459) ((-1137 . -859) T) ((-485 . -737) T) ((-904 . -1055) 164427) ((-418 . -651) 164379) ((-108 . -861) T) ((-669 . -1073) 164363) ((-498 . -132) T) ((-1271 . -1075) T) ((-219 . -132) T) ((-1174 . -102) 164341) ((-99 . -1117) T) ((-250 . -677) 164325) ((-250 . -662) 164309) ((-669 . -111) 164288) ((-597 . -627) 164272) ((-325 . -422) 164256) ((-250 . -383) 164240) ((-1177 . -240) 164187) ((-1016 . -271) 164171) ((-1016 . -232) 164155) ((-74 . -1235) T) ((-48 . -174) T) ((-712 . -398) T) ((-712 . -144) T) ((-1308 . -102) T) ((-1215 . -627) 164137) ((-1105 . -1235) T) ((-1104 . -1073) 163980) ((-1093 . -1235) T) ((-272 . -924) 163959) ((-252 . -924) 163938) ((-793 . -1073) 163761) ((-791 . -1073) 163604) ((-619 . -1235) T) ((-1182 . -624) 163586) ((-1104 . -111) 163415) ((-1063 . -102) T) ((-486 . -1235) T) ((-472 . -1073) 163386) ((-465 . -1073) 163229) ((-675 . -659) 163213) ((-882 . -316) T) ((-793 . -111) 163022) ((-791 . -111) 162851) ((-365 . -659) 162803) ((-362 . -659) 162755) ((-354 . -659) 162707) ((-272 . -659) 162596) ((-252 . -659) 162485) ((-1176 . -861) T) ((-1105 . -1055) 162469) ((-472 . -111) 162430) ((-465 . -111) 162259) ((-1093 . -1055) 162236) ((-1017 . -34) T) ((-981 . -624) 162218) ((-973 . -1235) T) ((-127 . -1027) 162202) ((-978 . -1129) T) ((-882 . -1039) NIL) ((-746 . -1129) T) ((-726 . -1129) T) ((-669 . -627) 162120) ((-1285 . -500) 162104) ((-1159 . -38) 162064) ((-978 . -23) T) ((-925 . -659) 162029) ((-876 . -1117) T) ((-854 . -102) T) ((-828 . -21) T) ((-646 . -1068) 162013) ((-618 . -1068) 161997) ((-828 . -25) T) ((-746 . -23) T) ((-726 . -23) T) ((-646 . -651) 161981) ((-110 . -672) T) ((-618 . -651) 161965) ((-592 . -1073) 161930) ((-529 . -1073) 161875) ((-229 . -57) 161833) ((-464 . -23) T) ((-418 . -102) T) ((-269 . -102) T) ((-110 . -113) T) ((-705 . -299) T) ((-877 . -38) 161803) ((-592 . -111) 161759) ((-529 . -111) 161688) ((-1104 . -627) 161424) ((-429 . -1129) T) ((-325 . -1075) 161314) ((-322 . -1075) T) ((-129 . -1235) T) ((-793 . -627) 161062) ((-791 . -627) 160828) ((-669 . -1066) T) ((-1314 . -1117) T) ((-465 . -627) 160613) ((-171 . -316) 160544) ((-429 . -23) T) ((-40 . -624) 160526) ((-40 . -625) 160510) ((-108 . -1009) 160492) ((-117 . -880) 160476) ((-660 . -627) 160460) ((-48 . -525) 160426) ((-1221 . -1027) 160410) ((-1199 . -624) 160377) ((-1207 . -34) T) ((-969 . -624) 160343) ((-936 . -624) 160325) ((-1130 . -861) 160276) ((-782 . -624) 160258) ((-683 . -624) 160240) ((-1174 . -318) 160178) ((-490 . -34) T) ((-1109 . -1235) T) ((-488 . -463) T) ((-1158 . -34) T) ((-1104 . -1066) T) ((-50 . -627) 160147) ((-793 . -1066) T) ((-791 . -1066) T) ((-658 . -240) 160131) ((-643 . -240) 160077) ((-592 . -627) 160027) ((-529 . -627) 159957) ((-493 . -234) 159848) ((-1258 . -316) 159827) ((-1104 . -335) 159788) ((-465 . -1066) T) ((-1196 . -21) T) ((-1104 . -238) 159767) ((-793 . -335) 159744) ((-793 . -238) T) ((-791 . -335) 159716) ((-742 . -1239) 159695) ((-336 . -662) 159679) ((-1196 . -25) T) ((-59 . -34) T) ((-530 . -34) T) ((-527 . -34) T) ((-465 . -335) 159658) ((-336 . -383) 159642) ((-508 . -34) T) ((-507 . -34) T) ((-1020 . -1169) NIL) ((-742 . -567) 159573) ((-646 . -102) T) ((-618 . -102) T) ((-365 . -737) T) ((-362 . -737) T) ((-354 . -737) T) ((-272 . -737) T) ((-252 . -737) T) ((-389 . -1235) T) ((-1063 . -318) 159481) ((-1297 . -21) T) ((-916 . -1117) 159459) ((-829 . -234) 159446) ((-50 . -1066) T) ((-1297 . -25) T) ((-1192 . -567) 159425) ((-1191 . -1239) 159404) ((-1191 . -567) 159355) ((-1185 . -1239) 159334) ((-1185 . -567) 159285) ((-592 . -1066) T) ((-529 . -1066) T) ((-1041 . -299) T) ((-371 . -1055) 159269) ((-331 . -1055) 159253) ((-1020 . -38) 159198) ((-389 . -898) 159180) ((-1016 . -657) 159103) ((-847 . -1235) T) ((-838 . -1235) 159082) ((-810 . -1129) T) ((-925 . -737) T) ((-592 . -248) T) ((-592 . -238) T) ((-529 . -238) T) ((-529 . -248) T) ((-1143 . -567) 159061) ((-364 . -299) T) ((-658 . -706) 159045) ((-389 . -1055) 159005) ((-303 . -1068) 158926) ((-349 . -908) 158905) ((-1137 . -1075) T) ((-103 . -126) 158889) ((-303 . -651) 158831) ((-810 . -23) T) ((-1307 . -1302) 158807) ((-1305 . -1302) 158786) ((-1285 . -295) 158738) ((-418 . -318) 158703) ((-1271 . -1117) T) ((-1159 . -915) 158626) ((-881 . -624) 158608) ((-847 . -1055) 158577) ((-205 . -798) T) ((-204 . -798) T) ((-203 . -798) T) ((-202 . -798) T) ((-201 . -798) T) ((-200 . -798) T) ((-199 . -798) T) ((-198 . -798) T) ((-197 . -798) T) ((-196 . -798) T) ((-558 . -624) 158559) ((-506 . -1019) T) ((-282 . -850) T) ((-281 . -850) T) ((-280 . -850) T) ((-279 . -850) T) ((-48 . -299) T) ((-278 . -850) T) ((-277 . -850) T) ((-276 . -850) T) ((-195 . -798) T) ((-623 . -861) T) ((-665 . -422) 158543) ((-681 . -237) 158494) ((-225 . -627) 158456) ((-110 . -861) T) ((-664 . -21) T) ((-664 . -25) T) ((-1308 . -38) 158426) ((-118 . -295) 158377) ((-1285 . -19) 158361) ((-1285 . -615) 158338) ((-1298 . -1117) T) ((-361 . -1068) 158283) ((-1094 . -1117) T) ((-1004 . -1117) T) ((-978 . -132) T) ((-828 . -234) 158270) ((-748 . -1117) T) ((-361 . -651) 158215) ((-746 . -132) T) ((-726 . -132) T) ((-522 . -804) T) ((-522 . -805) T) ((-464 . -132) T) ((-418 . -1169) 158193) ((-225 . -1066) T) ((-303 . -102) 157975) ((-142 . -1117) T) ((-710 . -1019) T) ((-1122 . -295) 157931) ((-91 . -1235) T) ((-128 . -624) 157863) ((-122 . -624) 157795) ((-1314 . -174) T) ((-1191 . -373) 157774) ((-1185 . -373) 157753) ((-325 . -1117) T) ((-429 . -132) T) ((-322 . -1117) T) ((-418 . -38) 157705) ((-1150 . -102) T) ((-1271 . -728) 157597) ((-665 . -1075) T) ((-1152 . -1280) T) ((-328 . -146) 157576) ((-328 . -148) 157555) ((-140 . -1117) T) ((-137 . -1117) T) ((-115 . -1117) T) ((-869 . -102) T) ((-591 . -624) 157537) ((-575 . -625) 157436) ((-575 . -624) 157418) ((-506 . -624) 157400) ((-506 . -625) 157345) ((-496 . -23) T) ((-493 . -861) 157296) ((-498 . -650) 157278) ((-980 . -624) 157260) ((-1020 . -915) 157169) ((-219 . -650) 157151) ((-227 . -415) T) ((-673 . -659) 157135) ((-55 . -624) 157117) ((-1190 . -935) 157096) ((-742 . -1129) T) ((-361 . -102) T) ((-1234 . -1100) T) ((-1137 . -855) T) ((-829 . -861) T) ((-742 . -23) T) ((-353 . -1073) 157041) ((-1176 . -1175) T) ((-1164 . -107) 157025) ((-1192 . -1129) T) ((-1191 . -1129) T) ((-526 . -1055) 157009) ((-1185 . -1129) T) ((-1143 . -1129) T) ((-353 . -111) 156938) ((-1021 . -1239) T) ((-127 . -1235) T) ((-929 . -1239) T) ((-1286 . -624) 156920) ((-705 . -295) NIL) ((-725 . -1235) T) ((-1192 . -23) T) ((-1191 . -23) T) ((-1185 . -23) T) ((-1159 . -271) 156904) ((-1159 . -232) 156888) ((-1021 . -567) T) ((-1143 . -23) T) ((-929 . -567) T) ((-1092 . -1117) T) ((-253 . -624) 156870) ((-826 . -237) 156767) ((-810 . -132) T) ((-721 . -624) 156749) ((-325 . -728) 156659) ((-322 . -728) 156588) ((-710 . -624) 156570) ((-710 . -625) 156515) ((-418 . -411) 156499) ((-449 . -1117) T) ((-498 . -25) T) ((-498 . -21) T) ((-1137 . -1117) T) ((-219 . -25) T) ((-219 . -21) T) ((-723 . -422) 156483) ((-725 . -1055) 156452) ((-1285 . -624) 156364) ((-1285 . -625) 156325) ((-1271 . -174) T) ((-1208 . -624) 156307) ((-250 . -34) T) ((-353 . -627) 156237) ((-405 . -627) 156219) ((-941 . -991) T) ((-1221 . -1235) T) ((-673 . -802) 156198) ((-673 . -805) 156177) ((-409 . -406) T) ((-534 . -102) 156155) ((-1052 . -1117) T) ((-418 . -915) 156078) ((-224 . -1012) 156062) ((-515 . -102) T) ((-634 . -624) 156044) ((-45 . -861) NIL) ((-634 . -625) 156021) ((-1052 . -621) 155996) ((-916 . -525) 155929) ((-328 . -237) 155881) ((-353 . -1066) T) ((-118 . -625) NIL) ((-118 . -624) 155863) ((-883 . -1235) T) ((-681 . -428) 155847) ((-681 . -1140) 155792) ((-511 . -152) 155774) ((-353 . -238) T) ((-353 . -248) T) ((-40 . -1073) 155719) ((-883 . -896) 155703) ((-883 . -898) 155628) ((-723 . -1075) T) ((-705 . -1019) NIL) ((-1269 . -47) 155598) ((-1248 . -47) 155575) ((-1158 . -1027) 155546) ((-1137 . -728) 155533) ((-3 . |UnionCategory|) T) ((-1122 . -624) 155515) ((-1097 . -148) 155494) ((-1097 . -146) 155445) ((-1021 . -373) T) ((-981 . -627) 155429) ((-227 . -935) T) ((-40 . -111) 155358) ((-883 . -1055) 155222) ((-1020 . -232) 155199) ((-1020 . -271) 155176) ((-712 . -1068) 155163) ((-929 . -373) T) ((-712 . -651) 155150) ((-328 . -1223) 155116) ((-389 . -316) T) ((-328 . -1220) 155082) ((-325 . -174) 155061) ((-322 . -174) T) ((-592 . -1304) 155048) ((-529 . -1304) 155025) ((-369 . -148) 155004) ((-117 . -1068) 154991) ((-369 . -146) 154942) ((-363 . -148) 154921) ((-363 . -146) 154872) ((-355 . -148) 154851) ((-619 . -1211) 154827) ((-117 . -651) 154814) ((-355 . -146) 154765) ((-328 . -35) 154731) ((-486 . -1211) 154710) ((0 . |EnumerationCategory|) T) ((-328 . -95) 154676) ((-389 . -1039) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -240) 154626) ((-665 . -1117) T) ((-619 . -107) 154573) ((-496 . -132) T) ((-486 . -107) 154523) ((-245 . -1129) 154501) ((-883 . -387) 154485) ((-883 . -348) 154469) ((-245 . -23) 154321) ((-40 . -627) 154251) ((-1079 . -935) T) ((-1079 . -831) T) ((-592 . -378) T) ((-529 . -378) T) ((-1298 . -525) 154184) ((-1277 . -567) 154163) ((-1270 . -1239) 154142) ((-361 . -1169) T) ((-336 . -34) T) ((-44 . -428) 154126) ((-1199 . -627) 154062) ((-884 . -1235) T) ((-401 . -755) 154046) ((-1270 . -567) 153997) ((-1269 . -1235) T) ((-1159 . -657) 153956) ((-742 . -132) T) ((-683 . -627) 153940) ((-1249 . -1239) 153919) ((-1249 . -567) 153870) ((-1248 . -1235) T) ((-1248 . -898) 153743) ((-1248 . -896) 153713) ((-1192 . -132) T) ((-320 . -1100) T) ((-1191 . -132) T) ((-748 . -525) 153646) ((-1185 . -132) T) ((-1143 . -132) T) ((-905 . -1117) T) ((-145 . -855) T) ((-1041 . -1019) T) ((-702 . -624) 153628) ((-1021 . -23) T) ((-534 . -318) 153566) ((-1021 . -1129) T) ((-142 . -525) NIL) ((-877 . -657) 153511) ((-1020 . -359) NIL) ((-988 . -23) T) ((-929 . -1129) T) ((-361 . -38) 153476) ((-929 . -23) T) ((-883 . -913) 153435) ((-82 . -624) 153417) ((-40 . -1066) T) ((-881 . -1073) 153404) ((-881 . -111) 153389) ((-712 . -102) T) ((-705 . -624) 153371) ((-613 . -1235) T) 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. -102) T) ((-1277 . -132) T) ((-1270 . -132) T) ((-1249 . -132) T) ((-1192 . -25) T) ((-1159 . -422) 146459) ((-646 . -377) 146391) ((-618 . -377) 146323) ((-1174 . -1166) 146307) ((-103 . -1117) 146285) ((-1192 . -21) T) ((-1191 . -21) T) ((-876 . -624) 146267) ((-1016 . -728) 146215) ((-225 . -659) 146182) ((-705 . -111) 146116) ((-50 . -737) T) ((-1191 . -25) T) ((-361 . -359) T) ((-1185 . -21) T) ((-1097 . -463) 146067) ((-1185 . -25) T) ((-723 . -525) 146014) ((-592 . -737) T) ((-529 . -737) T) ((-1143 . -21) T) ((-1143 . -25) T) ((-607 . -132) T) ((-606 . -132) T) ((-303 . -657) 145749) ((-493 . -237) 145646) ((-369 . -463) T) ((-363 . -463) T) ((-355 . -463) T) ((-485 . -316) 145625) ((-1243 . -102) T) ((-322 . -295) 145560) ((-108 . -463) T) ((-79 . -452) T) ((-79 . -406) T) ((-488 . -102) T) ((-702 . -627) 145544) ((-1314 . -624) 145526) ((-1314 . -625) 145508) ((-1097 . -413) 145487) ((-1052 . -500) 145418) ((-137 . -295) 145395) ((-575 . -806) T) ((-575 . -803) T) ((-1080 . 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. -624) 140847) ((-130 . -102) T) ((-52 . -102) T) ((-1249 . -650) 140799) ((-490 . -107) 140749) ((-1010 . -23) T) ((-1309 . -38) 140719) ((-1190 . -1129) T) ((-1142 . -1129) T) ((-1079 . -1239) T) ((-245 . -234) 140610) ((-320 . -102) T) ((-865 . -1129) T) ((-967 . -1239) 140589) ((-492 . -1239) 140568) ((-1079 . -567) T) ((-967 . -567) 140499) ((-1190 . -23) T) ((-1168 . -1100) T) ((-1142 . -23) T) ((-865 . -23) T) ((-492 . -567) 140430) ((-1159 . -728) 140362) ((-681 . -1068) 140346) ((-1163 . -525) 140279) ((-681 . -651) 140263) ((-1052 . -625) NIL) ((-1052 . -624) 140245) ((-96 . -1100) T) ((-1314 . -1073) 140232) ((-877 . -728) 140202) ((-1314 . -111) 140187) ((-1229 . -47) 140156) ((-1185 . -861) NIL) ((-257 . -132) T) ((-256 . -132) T) ((-1121 . -1117) T) ((-1020 . -1117) T) ((-62 . -624) 140138) ((-1097 . -908) 140007) ((-1041 . -803) T) ((-1041 . -806) T) ((-1277 . -25) T) ((-1277 . -21) T) ((-1270 . -21) T) ((-1270 . -25) T) ((-881 . -659) 139994) ((-1249 . -21) T) ((-1249 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-1068) 132016) ((-1020 . -299) T) ((-705 . -659) 131966) ((-257 . -25) T) ((-361 . -1117) T) ((-257 . -21) T) ((-256 . -25) T) ((-256 . -21) T) ((-153 . -38) 131950) ((-2 . -102) T) ((-925 . -935) T) ((-1097 . -651) 131818) ((-493 . -1292) 131788) ((-1137 . -1066) T) ((-722 . -316) T) ((-369 . -1068) 131740) ((-363 . -1068) 131692) ((-355 . -1068) 131644) ((-369 . -651) 131596) ((-225 . -1055) 131573) ((-363 . -651) 131525) ((-108 . -1068) 131475) ((-355 . -651) 131427) ((-303 . -728) 131369) ((-712 . -1075) T) ((-498 . -463) T) ((-418 . -525) 131281) ((-108 . -651) 131231) ((-219 . -463) T) ((-1137 . -238) T) ((-304 . -152) 131181) ((-1016 . -625) 131142) ((-1016 . -624) 131124) ((-1006 . -624) 131106) ((-117 . -1075) T) ((-665 . -1073) 131090) ((-227 . -504) T) ((-410 . -624) 131072) ((-410 . -625) 131049) ((-1071 . -1292) 131019) ((-665 . -111) 130998) ((-681 . -915) 130921) ((-1159 . -500) 130905) ((-1309 . -657) 130864) ((-391 . -657) 130833) ((-63 . -452) T) ((-63 . -406) T) 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129587) ((-1130 . -651) 129509) ((-1184 . -102) T) ((-1011 . -102) T) ((-1010 . -21) T) ((-128 . -1027) 129493) ((-122 . -1027) 129477) ((-1010 . -25) T) ((-916 . -120) 129461) ((-1176 . -102) T) ((-1258 . -132) T) ((-1190 . -25) T) ((-353 . -1235) T) ((-1190 . -21) T) ((-866 . -132) T) ((-1142 . -25) T) ((-1142 . -21) T) ((-865 . -25) T) ((-865 . -21) T) ((-793 . -316) 129440) ((-1177 . -318) 129235) ((-1174 . -500) 129219) ((-1167 . -152) 129169) ((-658 . -102) 129147) ((-643 . -102) T) ((-1163 . -624) 129109) ((-582 . -132) T) ((-632 . -859) 129088) ((-1163 . -625) 129049) ((-1041 . -802) T) ((-1041 . -805) T) ((-1041 . -737) T) ((-826 . -915) 128918) ((-723 . -1073) 128741) ((-495 . -318) 128679) ((-464 . -428) 128649) ((-361 . -174) T) ((-298 . -38) 128636) ((-257 . -234) 128527) ((-256 . -234) 128418) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-278 . -102) T) ((-277 . -102) T) ((-353 . -1055) 128395) ((-276 . -102) T) ((-214 . -102) T) ((-213 . 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125839) ((-492 . -650) 125787) ((-40 . -1055) 125675) ((-723 . -238) T) ((-712 . -728) 125662) ((-349 . -1117) T) ((-176 . -1117) T) ((-340 . -861) T) ((-429 . -463) 125612) ((-389 . -23) T) ((-369 . -38) 125577) ((-363 . -38) 125542) ((-355 . -38) 125507) ((-80 . -452) T) ((-80 . -406) T) ((-227 . -25) T) ((-227 . -21) T) ((-847 . -1129) T) ((-108 . -38) 125457) ((-838 . -1129) T) ((-785 . -1117) T) ((-117 . -728) 125444) ((-683 . -1055) 125428) ((-623 . -102) T) ((-847 . -23) T) ((-838 . -23) T) ((-1174 . -295) 125380) ((-1130 . -318) 125318) ((-493 . -1068) 125219) ((-1119 . -240) 125203) ((-64 . -407) T) ((-64 . -406) T) ((-1168 . -102) T) ((-110 . -102) T) ((-493 . -651) 125125) ((-40 . -387) 125102) ((-96 . -102) T) ((-664 . -863) 125086) ((-1190 . -234) 125073) ((-1152 . -1100) T) ((-1079 . -21) T) ((-1079 . -25) T) ((-1071 . -1068) 125057) ((-826 . -271) 125026) ((-826 . -232) 124995) ((-967 . -25) T) ((-967 . -21) T) ((-1071 . -651) 124937) ((-632 . -1075) T) ((-1137 . -378) 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. -463) 121057) ((-1308 . -624) 121039) ((-1297 . -1068) 121009) ((-1071 . -318) 120947) ((-682 . -1100) T) ((-617 . -1100) T) ((-401 . -1117) T) ((-582 . -25) T) ((-582 . -21) T) ((-182 . -1100) T) ((-162 . -1100) T) ((-157 . -1100) T) ((-155 . -1100) T) ((-1297 . -651) 120917) ((-632 . -1117) T) ((-710 . -898) 120899) ((-1285 . -1235) T) ((-229 . -318) 120837) ((-145 . -378) T) ((-1063 . -625) 120779) ((-1063 . -624) 120722) ((-322 . -924) NIL) ((-1243 . -855) T) ((-1130 . -915) 120591) ((-710 . -1055) 120536) ((-722 . -935) T) ((-485 . -1239) 120515) ((-1191 . -463) 120494) ((-1185 . -463) 120473) ((-339 . -102) T) ((-883 . -1129) T) ((-328 . -657) 120355) ((-325 . -659) 120084) ((-322 . -659) 120013) ((-485 . -567) 119964) ((-349 . -525) 119930) ((-561 . -152) 119880) ((-40 . -316) T) ((-854 . -624) 119862) ((-712 . -299) T) ((-883 . -23) T) ((-389 . -504) T) ((-1097 . -271) 119832) ((-1097 . -232) 119802) ((-523 . -102) T) ((-418 . -625) 119609) ((-418 . -624) 119591) ((-269 . 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-1220) 118426) ((-1270 . -1220) 118392) ((-526 . -132) T) ((-1270 . -1223) 118358) ((-1249 . -1220) 118324) ((-1249 . -1223) 118290) ((-1277 . -95) 118256) ((-1270 . -95) 118222) ((-429 . -908) 118143) ((-646 . -624) 118112) ((-618 . -624) 118081) ((-227 . -861) T) ((-1270 . -35) 118047) ((-1269 . -1129) T) ((-1249 . -95) 118013) ((-1137 . -659) 117985) ((-1249 . -35) 117951) ((-1248 . -1129) T) ((-604 . -152) 117933) ((-1097 . -359) 117912) ((-176 . -299) T) ((-118 . -387) 117889) ((-118 . -348) 117866) ((-171 . -234) 117791) ((-881 . -316) T) ((-322 . -805) NIL) ((-322 . -802) NIL) ((-325 . -737) 117640) ((-322 . -737) T) ((-485 . -373) 117619) ((-369 . -359) 117598) ((-363 . -359) 117577) ((-355 . -359) 117556) ((-325 . -484) 117535) ((-1269 . -23) T) ((-1248 . -23) T) ((-729 . -1129) T) ((-725 . -132) T) ((-664 . -102) T) ((-488 . -728) 117500) ((-45 . -291) 117450) ((-105 . -1117) T) ((-68 . -624) 117432) ((-987 . -102) T) ((-875 . -102) T) ((-634 . -913) 117391) ((-1309 . -1117) 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-1068) 116410) ((-485 . -1129) T) ((-529 . -935) T) ((-493 . -915) 116279) ((-65 . -624) 116261) ((-219 . -1068) 116211) ((-498 . -651) 116161) ((-369 . -657) 116098) ((-363 . -657) 116035) ((-355 . -657) 115972) ((-643 . -231) 115918) ((-219 . -651) 115868) ((-108 . -657) 115818) ((-485 . -23) T) ((-1137 . -805) T) ((-883 . -132) T) ((-1137 . -802) T) ((-1300 . -1302) 115797) ((-1137 . -737) T) ((-665 . -659) 115771) ((-303 . -624) 115512) ((-1159 . -627) 115430) ((-1052 . -34) T) ((-827 . -237) 115381) ((-591 . -316) T) ((-575 . -316) T) ((-506 . -316) T) ((-1309 . -728) 115351) ((-705 . -387) 115333) ((-705 . -348) 115315) ((-488 . -174) T) ((-391 . -728) 115285) ((-877 . -627) 115220) ((-882 . -861) NIL) ((-575 . -1039) T) ((-506 . -1039) T) ((-1150 . -624) 115202) ((-1130 . -243) 115181) ((-216 . -102) T) ((-1167 . -102) T) ((-71 . -624) 115163) ((-1159 . -1066) T) ((-1196 . -38) 115060) ((-869 . -624) 115042) ((-575 . -556) T) ((-681 . -1075) T) ((-742 . -964) 114995) ((-364 . 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-908) 110412) ((-135 . -624) 110394) ((-117 . -624) 110376) ((-158 . -25) T) ((-1307 . -1117) T) ((-883 . -650) 110324) ((-1305 . -1117) T) ((-978 . -102) T) ((-746 . -102) T) ((-726 . -102) T) ((-464 . -102) T) ((-827 . -463) 110275) ((-44 . -1117) T) ((-1105 . -861) T) ((-1080 . -318) 110126) ((-675 . -132) T) ((-1071 . -657) 110095) ((-681 . -728) 110079) ((-298 . -1075) T) ((-365 . -132) T) ((-362 . -132) T) ((-354 . -132) T) ((-272 . -132) T) ((-252 . -132) T) ((-395 . -657) 110048) ((-429 . -102) T) ((-153 . -1117) T) ((-45 . -231) 109998) ((-1021 . -908) NIL) ((-810 . -1068) 109982) ((-973 . -861) 109961) ((-1016 . -659) 109863) ((-810 . -651) 109847) ((-245 . -1292) 109817) ((-1041 . -316) T) ((-303 . -1073) 109738) ((-925 . -132) T) ((-40 . -935) T) ((-498 . -411) 109720) ((-364 . -316) T) ((-219 . -411) 109702) ((-1097 . -422) 109686) ((-303 . -111) 109602) ((-1201 . -861) T) ((-1200 . -861) T) ((-883 . -25) T) ((-883 . -21) T) ((-1271 . -47) 109546) ((-349 . -624) 109528) 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-1075) T) ((-363 . -1075) T) ((-355 . -1075) T) ((-303 . -1066) 108279) ((-1249 . -990) 108248) ((-389 . -861) T) ((-108 . -1075) T) ((-1016 . -737) T) ((-881 . -935) T) ((-854 . -806) 108227) ((-854 . -803) 108206) ((-429 . -318) 108145) ((-479 . -102) T) ((-606 . -990) 108114) ((-328 . -1117) T) ((-418 . -806) 108093) ((-418 . -803) 108072) ((-511 . -500) 108054) ((-1271 . -1055) 108020) ((-1269 . -21) T) ((-1269 . -25) T) ((-1248 . -21) T) ((-1248 . -25) T) ((-826 . -728) 107962) ((-361 . -627) 107892) ((-710 . -415) T) ((-1298 . -1235) T) ((-1130 . -422) 107861) ((-617 . -102) T) ((-1094 . -1235) T) ((-1020 . -378) NIL) ((-682 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1196 . -657) 107771) ((-748 . -1235) T) ((-742 . -1068) 107614) ((-44 . -772) T) ((-742 . -651) 107463) ((-604 . -102) T) ((-664 . -667) 107447) ((-77 . -407) T) ((-77 . -406) T) ((-142 . -1235) T) ((-882 . -148) T) ((-882 . -146) NIL) ((-1297 . -657) 107392) ((-1277 . -908) 107303) ((-1234 . -93) T) ((-361 . -1066) T) ((-227 . -237) T) ((-70 . -393) T) ((-70 . -406) T) ((-1183 . -102) T) ((-681 . -525) 107236) ((-1270 . -908) 107140) ((-1249 . -908) 106899) ((-700 . -318) 106837) ((-978 . -38) 106734) ((-1198 . -624) 106716) ((-746 . -38) 106686) ((-561 . -318) 106490) ((-1192 . -1068) 106373) ((-325 . -1235) T) ((-361 . -238) T) ((-361 . -248) T) ((-322 . -1235) T) ((-298 . -1117) T) ((-1191 . -1068) 106208) ((-1185 . -1068) 105998) ((-1143 . -1068) 105881) ((-1192 . -651) 105778) ((-1191 . -651) 105619) ((-722 . -1239) T) ((-1185 . -651) 105415) ((-1174 . -662) 105399) ((-1143 . -651) 105296) ((-1229 . -567) 105275) ((-830 . -396) 105259) ((-722 . -567) T) ((-606 . -908) 105170) ((-325 . -896) 105154) ((-325 . -898) 105079) ((-137 . -1235) T) ((-322 . -896) 105040) ((-322 . -898) NIL) ((-810 . -318) 105005) ((-328 . -728) 104846) ((-397 . -396) 104830) ((-333 . -332) 104807) ((-496 . -102) T) ((-485 . -25) T) ((-485 . -21) T) 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-102) T) ((-1185 . -102) T) ((-1177 . -1117) T) ((-1143 . -102) T) ((-224 . -34) T) ((-298 . -728) 103692) ((-1177 . -621) 103668) ((-604 . -318) NIL) ((-1277 . -1276) 103652) ((-495 . -1117) 103630) ((-1167 . -231) 103580) ((-401 . -624) 103562) ((-521 . -861) T) ((-1137 . -1235) T) ((-1277 . -1263) 103539) ((-1270 . -1268) 103500) ((-1270 . -1263) 103470) ((-1270 . -1266) 103454) ((-1249 . -1247) 103415) ((-1249 . -1263) 103392) ((-1249 . -1245) 103376) ((-632 . -624) 103358) ((-1192 . -293) 103324) ((-710 . -935) T) ((-1191 . -293) 103290) ((-1185 . -293) 103256) ((-1143 . -293) 103222) ((-1097 . -1117) T) ((-1078 . -1117) T) ((-48 . -311) T) ((-325 . -913) 103188) ((-322 . -913) NIL) ((-1078 . -1085) 103167) ((-1137 . -898) 103149) ((-810 . -38) 103133) ((-272 . -650) 103081) ((-252 . -650) 103029) ((-712 . -1073) 103016) ((-606 . -1263) 102993) ((-1137 . -1055) 102975) ((-328 . -174) 102906) ((-369 . -1117) T) ((-363 . -1117) T) ((-355 . -1117) T) ((-511 . -19) 102888) ((-1119 . -152) 102872) ((-882 . -237) NIL) ((-108 . -1117) T) ((-117 . -1073) 102859) ((-722 . -373) T) ((-511 . -615) 102834) ((-712 . -111) 102819) ((-1310 . -624) 102786) ((-1310 . -501) 102768) ((-1269 . -234) 102714) ((-1248 . -234) 102567) ((-447 . -102) T) ((-887 . -1280) T) ((-255 . -102) T) ((-45 . -1166) 102517) ((-117 . -111) 102502) ((-1287 . -624) 102484) ((-1258 . -237) T) ((-1243 . -624) 102466) ((-1241 . -861) T) ((-646 . -731) T) ((-618 . -731) T) ((-1229 . -1129) T) ((-1229 . -23) T) ((-1190 . -463) 102397) ((-1185 . -318) 102282) ((-1184 . -1117) T) ((-826 . -525) 102215) ((-1052 . -1235) T) ((-245 . -1068) 102116) ((-1176 . -1117) T) ((-1159 . -659) 102054) ((-958 . -152) 102038) ((-1143 . -318) 102025) ((-1142 . -463) 101976) ((-245 . -651) 101898) ((-1104 . -567) 101829) ((-1104 . -1239) 101808) ((-1097 . -728) 101676) ((-536 . -102) T) ((-531 . -102) 101626) ((-1021 . -1068) 101576) ((-1011 . -1117) T) ((-827 . -908) 101472) ((-793 . -1239) 101451) ((-791 . -1239) 101430) 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-621) 100388) ((-643 . -1117) T) ((-592 . -1239) T) ((-592 . -567) T) ((-529 . -1239) T) ((-529 . -567) T) ((-498 . -657) 100338) ((-485 . -234) 100284) ((-438 . -1068) 100268) ((-438 . -651) 100252) ((-369 . -728) 100204) ((-363 . -728) 100156) ((-349 . -1073) 100140) ((-355 . -728) 100092) ((-349 . -111) 100071) ((-176 . -1073) 100003) ((-219 . -657) 99953) ((-176 . -111) 99864) ((-108 . -728) 99814) ((-282 . -1117) T) ((-281 . -1117) T) ((-280 . -1117) T) ((-279 . -1117) T) ((-278 . -1117) T) ((-277 . -1117) T) ((-276 . -1117) T) ((-214 . -1117) T) ((-213 . -1117) T) ((-171 . -1223) 99792) ((-171 . -1220) 99770) ((-211 . -1117) T) ((-210 . -1117) T) ((-117 . -1066) T) ((-209 . -1117) T) ((-208 . -1117) T) ((-205 . -1117) T) ((-204 . -1117) T) ((-203 . -1117) T) ((-202 . -1117) T) ((-201 . -1117) T) ((-200 . -1117) T) ((-199 . -1117) T) ((-198 . -1117) T) ((-197 . -1117) T) ((-196 . -1117) T) ((-195 . -1117) T) ((-245 . -102) 99522) ((-171 . -35) 99500) ((-171 . -95) 99478) ((-665 . 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. -23) T) ((-171 . -420) 94732) ((-1157 . -1117) T) ((-1300 . -1299) 94716) ((-742 . -915) 94693) ((-712 . -806) T) ((-712 . -803) T) ((-1137 . -316) T) ((-389 . -148) T) ((-289 . -624) 94675) ((-288 . -624) 94657) ((-1248 . -1009) 94627) ((-48 . -935) T) ((-686 . -500) 94611) ((-257 . -1292) 94581) ((-256 . -1292) 94551) ((-1105 . -237) T) ((-1194 . -861) T) ((-1137 . -1039) T) ((-1063 . -34) T) ((-847 . -148) 94530) ((-847 . -146) 94509) ((-748 . -107) 94493) ((-623 . -133) T) ((-1196 . -1075) T) ((-493 . -1117) 94245) ((-1192 . -915) 94158) ((-1191 . -915) 94064) ((-1185 . -915) 93825) ((-882 . -463) T) ((-85 . -1235) T) ((-142 . -107) 93807) ((-1143 . -915) 93791) ((-723 . -387) 93775) ((-844 . -627) 93643) ((-1308 . -737) T) ((-1297 . -1075) T) ((-1277 . -102) T) ((-1137 . -556) T) ((-590 . -102) T) ((-130 . -501) 93625) ((-1270 . -102) T) ((-401 . -1073) 93609) ((-1190 . -964) 93578) ((-44 . -295) 93555) ((-130 . -624) 93522) ((-52 . -624) 93504) ((-1142 . -964) 93471) ((-664 . 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. -627) 33337) ((-723 . -650) 33285) ((-664 . -659) 33259) ((-1143 . -627) 33141) ((-304 . -34) T) ((-1137 . -113) T) ((-742 . -1066) T) ((-592 . -1292) 33128) ((-529 . -1292) 33105) ((-1258 . -1117) T) ((-1190 . -299) 33016) ((-1142 . -299) 32947) ((-1079 . -174) T) ((-298 . -1235) T) ((-866 . -1117) T) ((-967 . -174) 32858) ((-793 . -1261) 32842) ((-655 . -525) 32775) ((-77 . -624) 32757) ((-742 . -335) 32722) ((-1196 . -737) T) ((-582 . -1117) T) ((-492 . -174) 32633) ((-250 . -318) 32571) ((-1159 . -1129) T) ((-70 . -624) 32553) ((-1297 . -737) T) ((-1192 . -1066) T) ((-1191 . -1066) T) ((-336 . -102) 32503) ((-1185 . -1066) T) ((-1159 . -23) T) ((-1143 . -1066) T) ((-91 . -1138) 32487) ((-877 . -1129) T) ((-1192 . -238) 32446) ((-1191 . -248) 32425) ((-1191 . -238) 32377) ((-1185 . -238) 32264) ((-1185 . -248) 32243) ((-328 . -913) 32149) ((-877 . -23) T) ((-171 . -728) 31977) ((-418 . -1239) T) ((-1118 . -378) T) ((-1020 . -373) T) ((-881 . -463) T) ((-1041 . -148) T) ((-958 . 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. -525) 9752) ((-1142 . -627) 9544) ((-865 . -627) 9462) ((-219 . -1055) 9422) ((-245 . -34) T) ((-1017 . -1117) 9400) ((-591 . -1068) 9387) ((-575 . -1068) 9374) ((-506 . -1068) 9339) ((-1269 . -174) 9270) ((-1248 . -174) 9201) ((-591 . -651) 9188) ((-575 . -651) 9175) ((-506 . -651) 9140) ((-723 . -146) 9119) ((-723 . -148) 9098) ((-712 . -132) T) ((-137 . -476) 9075) ((-1164 . -624) 9007) ((-669 . -667) 8991) ((-129 . -295) 8941) ((-117 . -132) T) ((-488 . -1239) T) ((-619 . -615) 8917) ((-486 . -615) 8896) ((-346 . -345) 8865) ((-608 . -1117) T) ((-596 . -1117) T) ((-547 . -1117) T) ((-488 . -567) T) ((-1190 . -1066) T) ((-1142 . -1066) T) ((-865 . -1066) T) ((-245 . -805) 8844) ((-245 . -804) 8823) ((-1190 . -335) 8800) ((-245 . -737) 8778) ((-973 . -19) 8762) ((-498 . -387) 8744) ((-498 . -348) 8726) ((-1142 . -335) 8698) ((-364 . -1292) 8675) ((-219 . -387) 8657) ((-219 . -348) 8639) ((-973 . -615) 8616) ((-1190 . -238) T) ((-1281 . -1117) T) ((-675 . -1117) T) ((-656 . -1117) 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((-844 . -861) 184883) ((-81 . -1235) T) ((-722 . -299) T) ((-40 . -1075) T) ((-592 . -174) T) ((-529 . -174) T) ((-522 . -624) 184865) ((-171 . -659) 184739) ((-518 . -624) 184721) ((-361 . -148) 184703) ((-361 . -146) T) ((-369 . -1129) T) ((-363 . -1129) T) ((-355 . -1129) T) ((-1021 . -316) T) ((-929 . -316) T) ((-883 . -248) T) ((-108 . -1129) T) ((-883 . -238) 184682) ((-1269 . -111) 184503) ((-1248 . -111) 184292) ((-250 . -1273) 184276) ((-575 . -859) T) ((-369 . -23) T) ((-364 . -359) T) ((-325 . -318) 184263) ((-322 . -318) 184204) ((-363 . -23) T) ((-328 . -132) T) ((-355 . -23) T) ((-1021 . -1039) T) ((-31 . -627) 184185) ((-108 . -23) T) ((-665 . -1068) 184169) ((-250 . -615) 184146) ((-342 . -1117) T) ((-665 . -651) 184116) ((-1271 . -38) 184008) ((-1258 . -924) 183987) ((-112 . -1117) T) ((-827 . -1235) T) ((-1052 . -102) T) ((-1258 . -659) 183876) ((-882 . -805) NIL) ((-866 . -659) 183850) ((-882 . -802) NIL) ((-827 . -898) NIL) ((-882 . -737) T) ((-1104 . -525) 183723) ((-793 . -525) 183670) ((-791 . -525) 183622) ((-582 . -659) 183609) ((-827 . -1055) 183437) ((-465 . -525) 183380) ((-399 . -400) T) ((-1269 . -627) 183193) ((-1248 . -627) 182941) ((-60 . -1235) T) ((-632 . -861) 182920) ((-511 . -672) T) ((-1163 . -993) 182889) ((-1041 . -657) 182826) ((-1020 . -463) T) ((-710 . -859) T) ((-521 . -803) T) ((-485 . -1073) 182661) ((-511 . -113) T) ((-353 . -1117) T) ((-322 . -1169) NIL) ((-298 . -132) T) ((-405 . -1117) T) ((-881 . -1075) T) ((-705 . -380) 182628) ((-364 . -657) 182558) ((-225 . -631) 182535) ((-336 . -295) 182487) ((-485 . -111) 182308) ((-1269 . -1066) T) ((-1248 . -1066) T) ((-827 . -387) 182292) ((-171 . -737) T) ((-665 . -102) T) ((-1269 . -248) 182271) ((-1269 . -238) 182223) ((-1248 . -238) 182128) ((-1248 . -248) 182107) ((-1020 . -413) NIL) ((-681 . -650) 182055) ((-325 . -38) 181965) ((-322 . -38) 181894) ((-69 . -624) 181876) ((-328 . -504) 181842) ((-48 . -657) 181792) ((-1207 . -297) 181771) ((-1243 . -861) T) ((-1130 . -1129) 181749) ((-83 . -1235) T) ((-61 . -624) 181731) ((-490 . -297) 181710) ((-1300 . -1055) 181687) ((-1182 . -1117) T) ((-1130 . -23) 181539) ((-827 . -913) 181475) ((-1258 . -737) T) ((-1119 . -1235) T) ((-485 . -627) 181301) ((-361 . -237) T) ((-1104 . -299) 181232) ((-981 . -1117) T) ((-905 . -102) T) ((-793 . -299) 181143) ((-336 . -19) 181127) ((-59 . -297) 181104) ((-791 . -299) 181035) ((-866 . -737) T) ((-118 . -859) NIL) ((-527 . -297) 181012) ((-336 . -615) 180989) ((-507 . -297) 180966) ((-465 . -299) 180897) ((-1052 . -318) 180748) ((-887 . -501) 180729) ((-887 . -624) 180695) ((-692 . -501) 180676) ((-582 . -737) T) ((-687 . -501) 180657) ((-692 . -624) 180607) ((-687 . -624) 180573) ((-673 . -624) 180555) ((-489 . -501) 180536) ((-489 . -624) 180502) ((-250 . -625) 180463) ((-250 . -501) 180440) ((-139 . -501) 180421) ((-138 . -501) 180402) ((-134 . -501) 180383) ((-250 . -624) 180275) ((-215 . -102) T) ((-139 . -624) 180241) ((-138 . -624) 180207) ((-134 . -624) 180173) ((-1164 . -34) T) ((-958 . -1235) T) ((-353 . -728) 180118) ((-681 . -25) T) ((-681 . -21) T) ((-1194 . -627) 180099) ((-485 . -1066) T) ((-646 . -428) 180064) ((-618 . -428) 180029) ((-1137 . -1169) T) ((-723 . -1068) 179852) ((-592 . -299) T) ((-529 . -299) T) ((-1270 . -316) 179831) ((-485 . -238) 179783) ((-485 . -248) 179762) ((-1249 . -316) 179741) ((-723 . -651) 179570) ((-1249 . -1039) NIL) ((-1097 . -132) T) ((-883 . -806) 179549) ((-145 . -102) T) ((-40 . -1117) T) ((-883 . -803) 179528) ((-655 . -1027) 179512) ((-591 . -1075) T) ((-575 . -1075) T) ((-506 . -1075) T) ((-418 . -463) T) ((-369 . -132) T) ((-325 . -411) 179496) ((-322 . -411) 179457) ((-363 . -132) T) ((-355 . -132) T) ((-1199 . -1117) T) ((-1137 . -38) 179444) ((-1111 . -624) 179411) ((-108 . -132) T) ((-969 . -1117) T) ((-936 . -1117) T) ((-782 . -1117) T) ((-683 . -1117) T) ((-712 . -148) T) ((-117 . -148) T) ((-1307 . -21) T) ((-1307 . -25) T) ((-1305 . -21) T) ((-1305 . -25) T) ((-675 . -1073) 179395) ((-542 . -861) T) ((-511 . -861) T) ((-365 . -1073) 179347) ((-362 . -1073) 179299) ((-354 . -1073) 179251) ((-257 . -1235) T) ((-256 . -1235) T) ((-272 . -1073) 179094) ((-252 . -1073) 178937) ((-675 . -111) 178916) ((-828 . -1239) 178895) ((-558 . -855) T) ((-325 . -915) 178861) ((-365 . -111) 178799) ((-362 . -111) 178737) ((-354 . -111) 178675) ((-272 . -111) 178504) ((-252 . -111) 178333) ((-322 . -915) NIL) ((-634 . -422) 178317) ((-44 . -21) T) ((-44 . -25) T) ((-826 . -650) 178223) ((-828 . -567) 178202) ((-257 . -1055) 178029) ((-256 . -1055) 177856) ((-127 . -120) 177840) ((-925 . -1073) 177805) ((-723 . -102) T) ((-710 . -1075) T) ((-608 . -627) 177786) ((-596 . -627) 177767) ((-547 . -629) 177670) ((-353 . -174) T) ((-88 . -624) 177652) ((-153 . -21) T) ((-153 . -25) T) ((-925 . -111) 177608) ((-40 . -728) 177553) ((-881 . -1117) T) ((-675 . -627) 177530) ((-656 . -627) 177511) ((-365 . -627) 177448) ((-362 . -627) 177385) ((-558 . -1117) T) ((-354 . -627) 177322) ((-336 . -625) 177283) ((-336 . -624) 177195) ((-272 . -627) 176948) ((-252 . -627) 176733) ((-1248 . -803) 176686) ((-1248 . -806) 176639) ((-257 . -387) 176608) ((-256 . -387) 176577) ((-665 . -38) 176547) ((-619 . -34) T) ((-493 . -1129) 176525) ((-486 . -34) T) ((-1130 . -132) 176396) ((-979 . -25) 176207) ((-925 . -627) 176157) ((-885 . -624) 176139) ((-979 . -21) 176094) ((-826 . -25) 175927) ((-826 . -21) 175838) ((-1241 . -378) T) ((-634 . -1075) T) ((-1196 . -567) 175817) ((-1190 . -47) 175794) ((-365 . -1066) T) ((-362 . -1066) T) ((-493 . -23) 175646) ((-354 . -1066) T) ((-272 . -1066) T) ((-252 . -1066) T) ((-1142 . -47) 175618) ((-118 . -1075) T) ((-1051 . -659) 175592) ((-973 . -34) T) ((-365 . -238) 175571) ((-365 . -248) T) ((-362 . -238) 175550) ((-362 . -248) T) ((-354 . -238) 175529) ((-354 . -248) T) ((-272 . -335) 175501) ((-252 . -335) 175458) ((-272 . -238) 175437) ((-1174 . -152) 175421) ((-257 . -913) 175353) ((-256 . -913) 175285) ((-1159 . -908) 175206) ((-1099 . -861) T) ((-425 . -1129) T) ((-1071 . -23) T) ((-1041 . -859) T) ((-925 . -1066) T) ((-331 . -659) 175188) ((-712 . -237) T) ((-681 . -234) 175133) ((-1229 . -1019) 175099) ((-1191 . -935) 175078) ((-1185 . -935) 175057) ((-1185 . -831) NIL) ((-1016 . -1068) 174953) ((-982 . -1235) T) ((-925 . -248) T) ((-828 . -373) 174932) ((-395 . -23) T) ((-128 . -1117) 174910) ((-122 . -1117) 174888) ((-925 . -238) T) ((-129 . -34) T) ((-389 . -659) 174853) ((-1016 . -651) 174801) ((-881 . -728) 174788) ((-1314 . -657) 174760) ((-1063 . -152) 174725) ((-1010 . -1235) T) ((-40 . -174) T) ((-705 . -422) 174707) ((-723 . -318) 174694) ((-847 . -659) 174654) ((-838 . -659) 174628) ((-328 . -25) T) ((-328 . -21) T) ((-669 . -295) 174607) ((-591 . -1117) T) ((-575 . -1117) T) ((-506 . -1117) T) ((-250 . -297) 174584) ((-1190 . -1235) T) ((-1142 . -1235) T) ((-322 . -271) 174545) ((-322 . -232) 174506) ((-1190 . -898) NIL) ((-55 . -1117) T) ((-1142 . -898) 174365) ((-130 . -861) T) ((-1190 . -1055) 174245) ((-1142 . -1055) 174128) ((-185 . -624) 174110) ((-865 . -1055) 174006) ((-793 . -295) 173933) ((-828 . -1129) T) ((-1051 . -737) T) ((-1063 . -993) 173862) ((-613 . -662) 173846) ((-1020 . -908) 173753) ((-1016 . -102) T) ((-828 . -23) T) ((-723 . -1169) 173731) ((-705 . -1075) T) ((-613 . -383) 173715) ((-361 . -463) T) ((-353 . -299) T) ((-1286 . -1117) T) ((-253 . -1117) T) ((-410 . -102) T) ((-298 . -21) T) ((-298 . -25) T) ((-371 . -737) T) ((-721 . -1117) T) ((-710 . -1117) T) ((-371 . -484) T) ((-1229 . -624) 173697) ((-1190 . -387) 173681) ((-1142 . -387) 173665) ((-1041 . -422) 173627) ((-142 . -231) 173609) ((-389 . -805) T) ((-389 . -802) T) ((-881 . -174) T) ((-389 . -737) T) ((-722 . -624) 173591) ((-723 . -38) 173420) ((-1285 . -1283) 173404) ((-361 . -413) T) ((-1285 . -1117) 173354) ((-1208 . -1117) T) ((-591 . -728) 173341) ((-575 . -728) 173328) ((-506 . -728) 173293) ((-1271 . -657) 173183) ((-325 . -640) 173162) ((-847 . -737) T) ((-838 . -737) T) ((-655 . -1235) T) ((-1097 . -650) 173110) ((-1190 . -913) 173053) ((-1142 . -913) 173037) ((-826 . -234) 172928) ((-673 . -1073) 172912) ((-108 . -650) 172894) ((-493 . -132) 172765) ((-1196 . -1129) T) ((-967 . -47) 172734) ((-634 . -1117) T) ((-673 . -111) 172713) ((-502 . -624) 172679) ((-336 . -297) 172656) ((-492 . -47) 172613) ((-1196 . -23) T) ((-118 . -1117) T) ((-103 . -102) 172591) ((-1297 . -1129) T) ((-559 . -861) T) ((-227 . -1235) T) ((-1071 . -132) T) ((-1041 . -1075) T) ((-1297 . -23) T) ((-830 . -1055) 172575) ((-1215 . -624) 172557) ((-1020 . -735) 172529) ((-1137 . -839) T) ((-710 . -728) 172494) ((-597 . -624) 172476) ((-397 . -1055) 172460) ((-364 . -1075) T) ((-395 . -132) T) ((-333 . -1055) 172444) ((-1122 . -1117) T) ((-1097 . -21) T) ((-1097 . -25) T) ((-227 . -898) 172426) ((-1021 . -935) T) ((-91 . -34) T) ((-1021 . -831) T) ((-929 . -935) T) ((-1016 . -318) 172391) ((-887 . -627) 172372) ((-498 . -1239) T) ((-725 . -659) 172332) ((-692 . -627) 172313) ((-687 . -627) 172294) ((-219 . -1239) T) ((-418 . -908) 172215) ((-227 . -1055) 172175) ((-40 . -299) T) ((-498 . -567) T) ((-489 . -627) 172156) ((-369 . -25) T) ((-325 . -657) 171811) ((-322 . -657) 171725) ((-369 . -21) T) ((-363 . -25) T) ((-363 . -21) T) ((-219 . -567) T) ((-355 . -25) T) ((-355 . -21) T) ((-328 . -234) 171671) ((-250 . -627) 171648) ((-139 . -627) 171629) ((-138 . -627) 171610) ((-134 . -627) 171591) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1075) T) ((-591 . -174) T) ((-575 . -174) T) ((-506 . -174) T) ((-1079 . -1235) T) ((-967 . -1235) T) ((-669 . -624) 171573) ((-492 . -1235) T) ((-748 . -747) 171557) ((-346 . -624) 171539) ((-68 . -393) T) ((-68 . -406) T) ((-1119 . -107) 171523) ((-1079 . -898) 171505) ((-967 . -898) 171430) ((-664 . -1129) T) ((-634 . -728) 171417) ((-492 . -898) NIL) ((-1163 . -102) T) ((-1111 . -629) 171401) ((-1079 . -1055) 171383) ((-97 . -624) 171365) ((-488 . -148) T) ((-967 . -1055) 171245) ((-118 . -728) 171190) ((-723 . -915) 171097) ((-664 . -23) T) ((-492 . -1055) 170973) ((-1104 . -625) NIL) ((-1104 . -624) 170955) ((-793 . -625) NIL) ((-793 . -624) 170916) ((-791 . -625) 170550) ((-791 . -624) 170464) ((-1130 . -650) 170370) ((-472 . -624) 170352) ((-465 . -624) 170334) ((-465 . -625) 170195) ((-1052 . -231) 170141) ((-883 . -924) 170120) ((-127 . -34) T) ((-828 . -132) T) ((-660 . -624) 170102) ((-589 . -102) T) ((-365 . -1304) 170086) ((-362 . -1304) 170070) ((-354 . -1304) 170054) ((-128 . -525) 169987) ((-122 . -525) 169920) ((-522 . -803) T) ((-522 . -806) T) ((-521 . -805) T) ((-103 . -318) 169858) ((-224 . -102) 169836) ((-710 . -174) T) ((-705 . -1117) T) ((-883 . -659) 169752) ((-65 . -394) T) ((-283 . -624) 169734) ((-65 . -406) T) ((-967 . -387) 169718) ((-881 . -299) T) ((-50 . -624) 169700) ((-1016 . -38) 169648) ((-1137 . -657) 169620) ((-592 . -624) 169602) ((-492 . -387) 169586) ((-592 . -625) 169568) ((-529 . -624) 169550) ((-925 . -1304) 169537) ((-882 . -1235) T) ((-712 . -463) T) ((-506 . -525) 169503) ((-498 . -373) T) ((-365 . -378) 169482) ((-362 . -378) 169461) ((-354 . -378) 169440) ((-725 . -737) T) ((-219 . -373) T) ((-117 . -463) T) ((-1308 . -1299) 169424) ((-882 . -896) 169401) ((-882 . -898) NIL) ((-979 . -861) 169300) ((-826 . -861) 169251) ((-1242 . -102) T) ((-665 . -667) 169235) ((-1221 . -34) T) ((-173 . -624) 169217) ((-1130 . -25) 169050) ((-1130 . -21) 168961) ((-882 . -1055) 168938) ((-967 . -913) 168919) ((-1258 . -47) 168896) ((-925 . -378) T) ((-59 . -662) 168880) ((-527 . -662) 168864) ((-492 . -913) 168841) ((-71 . -452) T) ((-71 . -406) T) ((-507 . -662) 168825) ((-59 . -383) 168809) ((-634 . -174) T) ((-527 . -383) 168793) ((-507 . -383) 168777) ((-838 . -719) 168761) ((-1190 . -316) 168740) ((-1196 . -132) T) ((-1159 . -1068) 168724) ((-118 . -174) T) ((-1159 . -651) 168656) ((-1163 . -318) 168594) ((-171 . -1235) T) ((-1297 . -132) T) ((-877 . -1068) 168564) ((-646 . -755) 168548) ((-618 . -755) 168532) ((-1270 . -935) 168511) ((-1249 . -935) 168490) ((-1249 . -831) NIL) ((-877 . -651) 168460) ((-705 . -728) 168410) ((-1248 . -924) 168363) ((-1041 . -1117) T) ((-882 . -387) 168340) ((-882 . -348) 168317) ((-920 . -1129) T) ((-171 . -896) 168301) ((-171 . -898) 168226) ((-1285 . -525) 168159) ((-1269 . -659) 168056) ((-1097 . -234) 167929) ((-498 . -1129) T) ((-364 . -1117) T) ((-219 . -1129) T) ((-76 . -452) T) ((-76 . -406) T) ((-171 . -1055) 167825) ((-303 . -908) 167782) ((-328 . -861) T) ((-1248 . -659) 167590) ((-883 . -805) 167569) ((-883 . -802) 167548) ((-883 . -737) T) ((-498 . -23) T) ((-369 . -234) 167521) ((-363 . -234) 167494) ((-355 . -234) 167467) ((-225 . -624) 167449) ((-176 . -463) T) ((-224 . -318) 167387) ((-86 . -452) T) ((-86 . -406) T) ((-108 . -234) 167374) ((-219 . -23) T) ((-1309 . -1302) 167353) ((-688 . -1055) 167337) ((-591 . -299) T) ((-575 . -299) T) ((-506 . -299) T) ((-137 . -481) 167292) ((-1258 . -1235) T) ((-665 . -657) 167251) ((-48 . -1117) T) ((-723 . -271) 167235) ((-723 . -232) 167219) ((-882 . -913) NIL) ((-1258 . -898) NIL) ((-901 . -102) T) ((-897 . -102) T) ((-399 . -1117) T) ((-171 . -387) 167203) ((-171 . -348) 167187) ((-1258 . -1055) 167067) ((-866 . -1055) 166963) ((-1159 . -102) T) ((-1016 . -915) 166886) ((-673 . -803) 166865) ((-664 . -132) T) ((-673 . -806) 166844) ((-118 . -525) 166752) ((-582 . -1055) 166734) ((-303 . -1292) 166704) ((-877 . -102) T) ((-978 . -567) 166683) ((-1229 . -1073) 166566) ((-1020 . -1068) 166511) ((-493 . -650) 166417) ((-919 . -1117) T) ((-1041 . -728) 166354) ((-722 . -1073) 166319) ((-1020 . -651) 166264) ((-628 . -102) T) ((-613 . -34) T) ((-1164 . -1235) T) ((-1229 . -111) 166133) ((-485 . -659) 166030) ((-364 . -728) 165975) ((-171 . -913) 165934) ((-710 . -299) T) ((-705 . -174) T) ((-722 . -111) 165890) ((-1314 . -1075) T) ((-1258 . -387) 165874) ((-429 . -1239) 165852) ((-1135 . -624) 165834) ((-322 . -859) NIL) ((-429 . -567) T) ((-227 . -316) T) ((-1248 . -802) 165787) ((-1248 . -805) 165740) 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((-575 . -806) T) ((-575 . -803) T) ((-1080 . -240) 145515) ((-369 . -413) 145466) ((-363 . -413) 145417) ((-355 . -413) 145368) ((-1300 . -1129) T) ((-1309 . -1068) 145352) ((-391 . -1068) 145336) ((-1309 . -651) 145306) ((-829 . -237) T) ((-391 . -651) 145276) ((-705 . -627) 145211) ((-1300 . -23) T) ((-1287 . -102) T) ((-349 . -915) 145192) ((-177 . -624) 145174) ((-1159 . -1075) T) ((-558 . -378) T) ((-681 . -755) 145158) ((-1196 . -146) 145137) ((-1196 . -148) 145116) ((-1163 . -1117) T) ((-1163 . -1088) 145085) ((-69 . -1235) T) ((-1041 . -1073) 145022) ((-361 . -657) 144952) ((-877 . -1075) T) ((-245 . -650) 144858) ((-705 . -1066) T) ((-364 . -1073) 144803) ((-61 . -1235) T) ((-1041 . -111) 144719) ((-916 . -624) 144630) ((-705 . -248) T) ((-705 . -238) NIL) ((-854 . -859) 144609) ((-710 . -806) T) ((-710 . -803) T) ((-1020 . -422) 144586) ((-364 . -111) 144515) ((-389 . -935) T) ((-418 . -859) 144494) ((-723 . -299) 144405) ((-225 . -737) T) ((-1277 . -504) 144371) ((-1270 . -504) 144337) ((-1249 . -504) 144303) ((-589 . -1117) T) ((-325 . -1019) 144282) ((-224 . -1117) 144260) ((-1242 . -855) T) ((-328 . -990) 144222) ((-105 . -102) T) ((-48 . -1073) 144187) ((-1309 . -102) T) ((-391 . -102) T) ((-48 . -111) 144143) ((-826 . -908) 144010) ((-1021 . -650) 143992) ((-1271 . -624) 143974) ((-542 . -102) T) ((-511 . -102) T) ((-1150 . -1151) 143958) ((-153 . -1292) 143942) ((-250 . -1235) T) ((-1234 . -102) T) ((-1041 . -627) 143879) ((-828 . -237) T) ((-1190 . -1239) 143858) ((-364 . -627) 143788) ((-1142 . -1239) 143767) ((-245 . -25) 143600) ((-245 . -21) 143511) ((-128 . -120) 143495) ((-122 . -120) 143479) ((-44 . -755) 143463) ((-1190 . -567) 143374) ((-1142 . -567) 143305) ((-1242 . -1117) T) ((-1052 . -295) 143280) ((-1184 . -1100) T) ((-1011 . -1100) T) ((-827 . -132) T) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-365 . -316) T) ((-362 . -316) T) ((-354 . -316) T) ((-257 . -1129) 143258) ((-256 . -1129) 143236) ((-1041 . -1066) T) ((-1020 . -1075) T) ((-48 . -627) 143169) ((-353 . -659) 143114) ((-1298 . -624) 143076) ((-632 . -38) 143060) ((-1298 . -625) 143021) ((-1192 . -234) 142974) ((-1094 . -624) 142956) ((-1041 . -248) T) ((-364 . -1066) T) ((-826 . -1292) 142926) ((-257 . -23) T) ((-256 . -23) T) ((-1004 . -624) 142908) ((-1191 . -234) 142854) ((-1185 . -234) 142671) ((-748 . -625) 142632) ((-748 . -624) 142614) ((-1177 . -152) 142561) ((-810 . -861) 142540) ((-1021 . -25) T) ((-1016 . -525) 142452) ((-364 . -238) T) ((-364 . -248) T) ((-399 . -627) 142433) ((-925 . -316) T) ((-142 . -624) 142415) ((-142 . -625) 142374) ((-328 . -908) 142278) ((-1021 . -21) T) ((-988 . -25) T) ((-929 . -21) T) ((-929 . -25) T) ((-438 . -21) T) ((-438 . -25) T) ((-854 . -422) 142262) ((-48 . -1066) T) ((-1307 . -1299) 142246) ((-1305 . -1299) 142230) ((-1052 . -615) 142205) ((-325 . -625) 142066) ((-325 . -624) 142048) ((-322 . -625) NIL) ((-322 . -624) 142030) ((-48 . -248) T) ((-48 . -238) T) ((-665 . -295) 141991) ((-561 . -240) 141941) ((-140 . -624) 141908) ((-137 . -624) 141890) ((-115 . -624) 141872) ((-488 . -38) 141837) ((-1309 . -1306) 141816) ((-1300 . -132) T) ((-1308 . -1075) T) ((-1099 . -102) T) ((-88 . -1235) T) ((-511 . -318) NIL) ((-1017 . -107) 141800) ((-901 . -1117) T) ((-897 . -1117) T) ((-1285 . -662) 141784) ((-1285 . -383) 141768) ((-336 . -1235) T) ((-604 . -861) T) ((-1159 . -1117) T) ((-1159 . -1070) 141708) ((-103 . -525) 141641) ((-942 . -624) 141623) ((-353 . -737) T) ((-30 . -624) 141605) ((-877 . -1117) T) ((-854 . -1075) 141584) ((-40 . -659) 141491) ((-227 . -1239) T) ((-418 . -1075) T) ((-1176 . -152) 141473) ((-1016 . -299) 141424) ((-628 . -1117) T) ((-227 . -567) T) ((-328 . -1266) 141408) ((-328 . -1263) 141378) ((-712 . -657) 141350) ((-1207 . -1211) 141329) ((-1092 . -624) 141311) ((-1207 . -107) 141261) ((-658 . -152) 141245) ((-643 . -152) 141191) ((-117 . -657) 141163) ((-490 . -1211) 141142) ((-498 . -148) T) ((-498 . -146) NIL) ((-1137 . -625) 141057) ((-449 . -624) 141039) ((-219 . -148) T) ((-219 . -146) NIL) ((-1137 . -624) 141021) ((-130 . -102) T) ((-52 . -102) T) ((-1249 . -650) 140973) ((-490 . -107) 140923) ((-1010 . -23) T) ((-1309 . -38) 140893) ((-1190 . -1129) T) ((-1142 . -1129) T) ((-1079 . -1239) T) ((-245 . -234) 140784) ((-320 . -102) T) ((-865 . -1129) T) ((-967 . -1239) 140763) ((-492 . -1239) 140742) ((-1079 . -567) T) ((-967 . -567) 140673) ((-1190 . -23) T) ((-1168 . -1100) T) ((-1142 . -23) T) ((-865 . -23) T) ((-492 . -567) 140604) ((-1159 . -728) 140536) ((-681 . -1068) 140520) ((-1163 . -525) 140453) ((-681 . -651) 140437) ((-1052 . -625) NIL) ((-1052 . -624) 140419) ((-96 . -1100) T) ((-1314 . -1073) 140406) ((-877 . -728) 140376) ((-1314 . -111) 140361) ((-1229 . -47) 140330) ((-1185 . -861) NIL) ((-257 . -132) T) ((-256 . -132) T) ((-1121 . -1117) T) ((-1020 . -1117) T) ((-62 . -624) 140312) ((-1097 . -908) 140181) ((-1041 . -803) T) ((-1041 . -806) T) ((-1277 . -25) T) ((-1277 . -21) T) ((-1270 . -21) T) ((-1270 . -25) T) ((-881 . -659) 140168) ((-1249 . -21) T) ((-1249 . -25) T) ((-1044 . -152) 140152) ((-1021 . -234) 140139) ((-883 . -831) 140118) ((-883 . -935) T) ((-723 . -295) 140045) ((-607 . -21) T) ((-349 . -657) 140004) ((-108 . -908) NIL) ((-607 . -25) T) ((-606 . -21) T) ((-176 . -657) 139921) ((-40 . -737) T) ((-224 . -525) 139854) ((-606 . -25) T) ((-487 . -152) 139838) ((-474 . -152) 139822) ((-936 . -805) T) ((-936 . -737) T) ((-782 . -804) T) ((-782 . -805) T) ((-517 . -1117) T) ((-513 . -1117) T) ((-782 . -737) T) ((-227 . -373) T) ((-1307 . -1068) 139806) ((-1305 . -1068) 139790) ((-1307 . -651) 139760) ((-1174 . -1117) 139738) ((-882 . -1239) T) ((-1305 . -651) 139708) ((-665 . -624) 139690) ((-882 . -567) T) ((-705 . -378) NIL) ((-44 . -1068) 139674) ((-1314 . -627) 139656) ((-1308 . -1117) T) ((-681 . -102) T) ((-369 . -1292) 139640) ((-363 . -1292) 139624) ((-44 . -651) 139608) ((-355 . -1292) 139592) ((-559 . -102) T) ((-1229 . -1235) T) ((-531 . -861) 139571) ((-498 . -237) T) ((-219 . -237) T) ((-1063 . -1117) T) ((-828 . -463) 139550) ((-153 . -1068) 139534) ((-1063 . -1088) 139463) ((-1044 . -993) 139432) ((-830 . -1129) T) ((-1020 . -728) 139377) ((-153 . -651) 139361) ((-397 . -1129) T) ((-487 . -993) 139330) ((-474 . -993) 139299) ((-110 . -152) 139281) ((-73 . -624) 139263) ((-905 . -624) 139245) ((-1097 . -735) 139224) ((-1314 . -1066) T) ((-827 . -650) 139172) ((-303 . -1075) 139114) ((-171 . -1239) 139019) ((-227 . -1129) T) ((-333 . -23) T) ((-1185 . -1009) 138971) ((-854 . -1117) T) ((-1271 . -1073) 138876) ((-1143 . -751) 138855) ((-1269 . -935) 138834) ((-1248 . -935) 138813) ((-881 . -737) T) ((-171 . -567) 138724) ((-591 . -659) 138711) ((-575 . -659) 138683) ((-418 . -1117) T) ((-269 . -1117) T) ((-215 . -624) 138665) ((-506 . -659) 138615) ((-227 . -23) T) ((-1248 . -831) 138568) ((-1307 . -102) T) ((-364 . -1304) 138545) ((-1305 . -102) T) ((-1271 . -111) 138437) ((-1130 . -908) 138304) ((-826 . -1068) 138205) ((-826 . -651) 138127) ((-145 . -624) 138109) ((-1010 . -132) T) ((-44 . -102) T) ((-245 . -861) 138060) ((-1258 . -1239) 138039) ((-103 . -500) 138023) ((-1308 . -728) 137993) ((-1104 . -47) 137954) ((-1079 . -1129) T) ((-967 . -1129) T) ((-128 . -34) T) ((-122 . -34) T) ((-793 . -47) 137931) ((-791 . -47) 137903) ((-1258 . -567) 137814) ((-364 . -378) T) ((-492 . -1129) T) ((-1190 . -132) T) ((-1142 . -132) T) ((-465 . -47) 137793) ((-882 . -373) T) ((-865 . -132) T) ((-153 . -102) T) ((-1079 . -23) T) ((-967 . -23) T) ((-582 . -567) T) ((-827 . -25) T) ((-827 . -21) T) ((-1159 . -525) 137726) ((-603 . -1100) T) ((-597 . -1055) 137710) ((-1271 . -627) 137584) ((-492 . -23) T) ((-361 . -1075) T) ((-1229 . -913) 137565) ((-681 . -318) 137503) ((-1130 . -1292) 137473) ((-710 . -659) 137438) ((-1021 . -861) T) ((-1020 . -174) T) ((-978 . -146) 137417) ((-646 . -1117) T) ((-618 . -1117) T) ((-978 . -148) 137396) ((-746 . -148) 137375) ((-746 . -146) 137354) ((-669 . -1235) T) ((-988 . -861) T) ((-1277 . -234) 137307) ((-1270 . -234) 137253) ((-1249 . -234) 137070) ((-844 . -657) 136987) ((-485 . -935) 136966) ((-328 . -1068) 136801) ((-325 . -1073) 136711) ((-322 . -1073) 136640) ((-1016 . -295) 136598) ((-418 . -728) 136550) ((-328 . -651) 136391) ((-606 . -234) 136344) ((-712 . -859) T) ((-1271 . -1066) T) ((-325 . -111) 136240) ((-322 . -111) 136153) ((-979 . -102) T) ((-826 . -102) 135905) ((-723 . -625) NIL) ((-723 . -624) 135887) ((-1271 . -335) 135831) ((-669 . -1055) 135727) ((-1104 . -1235) T) ((-1052 . -297) 135702) ((-591 . -737) T) ((-575 . -805) T) ((-171 . -373) 135653) ((-575 . -802) T) ((-575 . -737) T) ((-506 . -737) T) ((-793 . -1235) T) ((-791 . -1235) T) ((-1163 . -500) 135637) ((-465 . -1235) T) ((-1104 . -898) NIL) ((-882 . -1129) T) ((-118 . -924) NIL) ((-1307 . -1306) 135613) ((-1305 . -1306) 135592) ((-793 . -898) NIL) ((-791 . -898) 135451) ((-1300 . -25) T) ((-1300 . -21) T) ((-1232 . -102) 135429) ((-1123 . -406) T) ((-634 . -659) 135416) ((-465 . -898) NIL) ((-686 . -102) 135394) ((-1104 . -1055) 135221) ((-882 . -23) T) ((-793 . -1055) 135080) ((-791 . -1055) 134937) ((-118 . -659) 134882) ((-465 . -1055) 134758) ((-325 . -627) 134322) ((-322 . -627) 134205) ((-401 . -657) 134174) ((-660 . -1055) 134158) ((-638 . -102) T) ((-592 . -1235) T) ((-529 . -1235) T) ((-224 . -500) 134142) ((-1285 . -34) T) ((-632 . -657) 134101) ((-298 . -1068) 134088) ((-137 . -627) 134072) ((-298 . -651) 134059) ((-646 . -728) 134043) ((-618 . -728) 134027) ((-681 . -38) 133987) ((-328 . -102) T) ((-85 . -624) 133969) ((-50 . -1055) 133953) ((-1137 . -1073) 133940) ((-1104 . -387) 133924) ((-793 . -387) 133908) ((-710 . -737) T) ((-710 . -805) T) ((-710 . -802) T) ((-592 . -1055) 133895) ((-529 . -1055) 133872) ((-60 . -57) 133834) ((-333 . -132) T) ((-325 . -1066) 133724) ((-322 . -1066) T) ((-171 . -1129) T) ((-791 . -387) 133708) ((-45 . -152) 133658) ((-1021 . -1009) 133640) ((-465 . -387) 133624) ((-418 . -174) T) ((-325 . -248) 133603) ((-322 . -248) T) ((-322 . -238) NIL) ((-303 . -1117) 133385) ((-227 . -132) T) ((-1137 . -111) 133370) ((-171 . -23) T) ((-810 . -148) 133349) ((-810 . -146) 133328) ((-257 . -650) 133234) ((-256 . -650) 133140) ((-328 . -293) 133106) ((-1174 . -525) 133039) ((-488 . -657) 132989) ((-493 . -908) 132856) ((-1150 . -1117) T) ((-227 . -1077) T) ((-826 . -318) 132794) ((-1104 . -913) 132729) ((-793 . -913) 132672) ((-791 . -913) 132656) ((-1307 . -38) 132626) ((-1305 . -38) 132596) ((-1258 . -1129) T) ((-866 . -1129) T) ((-465 . -913) 132573) ((-869 . -1117) T) ((-1258 . -23) T) ((-1137 . -627) 132545) ((-1079 . -132) T) ((-582 . -1129) T) ((-866 . -23) T) ((-634 . -737) T) ((-365 . -935) T) ((-362 . -935) T) ((-298 . -102) T) ((-354 . -935) T) ((-987 . -1100) T) ((-967 . -132) T) ((-827 . -234) 132490) ((-118 . -805) NIL) ((-118 . -802) NIL) ((-118 . -737) T) ((-1063 . -525) 132391) ((-705 . -924) NIL) ((-582 . -23) T) ((-492 . -132) T) ((-429 . -237) 132342) ((-686 . -318) 132280) ((-646 . -772) T) ((-618 . -772) T) ((-1249 . -861) NIL) ((-1097 . -1068) 132190) ((-1020 . -299) T) ((-705 . -659) 132140) ((-257 . -25) T) ((-361 . -1117) T) ((-257 . -21) T) ((-256 . -25) T) ((-256 . -21) T) ((-153 . -38) 132124) ((-2 . -102) T) ((-925 . -935) T) ((-1097 . -651) 131992) ((-493 . -1292) 131962) ((-1137 . -1066) T) ((-722 . -316) T) ((-369 . -1068) 131914) ((-363 . -1068) 131866) ((-355 . -1068) 131818) ((-369 . -651) 131770) ((-225 . -1055) 131747) ((-363 . -651) 131699) ((-108 . -1068) 131649) ((-355 . -651) 131601) ((-303 . -728) 131543) ((-712 . -1075) T) ((-498 . -463) T) ((-418 . -525) 131455) ((-108 . -651) 131405) ((-219 . -463) T) ((-1137 . -238) T) ((-304 . -152) 131355) ((-1016 . -625) 131316) ((-1016 . -624) 131298) ((-1006 . -624) 131280) ((-117 . -1075) T) ((-665 . -1073) 131264) ((-227 . -504) T) ((-410 . -624) 131246) ((-410 . -625) 131223) ((-1071 . -1292) 131193) ((-665 . -111) 131172) ((-681 . -915) 131095) ((-1159 . -500) 131079) ((-1309 . -657) 131038) ((-391 . -657) 131007) ((-63 . -452) T) ((-63 . -406) T) ((-1177 . -102) T) ((-882 . -132) T) ((-495 . -102) 130985) ((-1314 . -378) T) ((-1097 . -102) T) ((-1078 . -102) T) ((-361 . -728) 130930) ((-742 . -148) 130909) ((-742 . -146) 130888) ((-665 . -627) 130806) ((-1041 . -659) 130743) ((-534 . -1117) 130721) ((-369 . -102) T) ((-363 . -102) T) ((-355 . -102) T) ((-108 . -102) T) ((-515 . -1117) T) ((-364 . -659) 130666) ((-1190 . -650) 130614) ((-1142 . -650) 130562) ((-395 . -520) 130541) ((-844 . -859) 130520) ((-389 . -1239) T) ((-705 . -737) T) ((-1249 . -1009) 130472) ((-349 . -1075) T) ((-112 . -1235) T) ((-176 . -1075) T) ((-103 . -624) 130404) ((-1192 . -146) 130383) ((-1192 . -148) 130362) ((-389 . -567) T) ((-1191 . -148) 130341) ((-1191 . -146) 130320) ((-1185 . -146) 130227) ((-418 . -299) T) ((-1185 . -148) 130134) ((-1143 . -148) 130113) ((-1143 . -146) 130092) ((-328 . -38) 129933) ((-171 . -132) T) ((-322 . -806) NIL) ((-322 . -803) NIL) ((-665 . -1066) T) ((-48 . -659) 129883) ((-1130 . -1068) 129784) ((-905 . -627) 129761) ((-1130 . -651) 129683) ((-1184 . -102) T) ((-1011 . -102) T) ((-1010 . -21) T) ((-128 . -1027) 129667) ((-122 . -1027) 129651) ((-1010 . -25) T) ((-916 . -120) 129635) ((-1176 . -102) T) ((-1258 . -132) T) ((-1190 . -25) T) ((-353 . -1235) T) ((-1190 . -21) T) ((-866 . -132) T) ((-1142 . -25) T) ((-1142 . -21) T) ((-865 . -25) T) ((-865 . -21) T) ((-793 . -316) 129614) ((-1177 . -318) 129409) ((-1174 . -500) 129393) ((-1167 . -152) 129343) ((-658 . -102) 129321) ((-643 . -102) T) ((-1163 . -624) 129283) ((-582 . -132) T) ((-632 . -859) 129262) ((-1163 . -625) 129223) ((-1041 . -802) T) ((-1041 . -805) T) ((-1041 . -737) T) ((-826 . -915) 129092) ((-723 . -1073) 128915) ((-495 . -318) 128853) ((-464 . -428) 128823) ((-361 . -174) T) ((-298 . -38) 128810) ((-257 . -234) 128701) ((-256 . -234) 128592) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-278 . -102) T) ((-277 . -102) T) ((-353 . -1055) 128569) ((-276 . -102) T) 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. -1129) T) ((-328 . -915) 127245) ((-1242 . -624) 127227) ((-1199 . -1055) 127163) ((-1192 . -35) 127129) ((-1192 . -95) 127095) ((-1192 . -1223) 127061) ((-1192 . -1220) 127027) ((-1191 . -1220) 126993) ((-1191 . -1223) 126959) ((-1176 . -318) NIL) ((-89 . -407) T) ((-89 . -406) T) ((-1097 . -1169) 126938) ((-40 . -1235) T) ((-1191 . -95) 126904) ((-1051 . -23) T) ((-1191 . -35) 126870) ((-582 . -504) T) ((-1185 . -1220) 126836) ((-1185 . -1223) 126802) ((-1185 . -95) 126768) ((-1185 . -35) 126734) ((-371 . -1129) T) ((-369 . -1169) 126713) ((-363 . -1169) 126692) ((-355 . -1169) 126671) ((-1121 . -295) 126627) ((-1143 . -35) 126593) ((-1143 . -95) 126559) ((-108 . -1169) T) ((-1143 . -1223) 126525) ((-844 . -1075) 126504) ((-658 . -318) 126442) ((-643 . -318) 126293) ((-1143 . -1220) 126259) ((-723 . -1066) T) ((-1079 . -650) 126241) ((-1097 . -38) 126109) ((-967 . -650) 126057) ((-1021 . -148) T) ((-1021 . -146) NIL) ((-389 . -1129) T) ((-333 . -25) T) ((-331 . -23) T) ((-958 . 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110650) ((-245 . -908) 110517) ((-135 . -624) 110499) ((-117 . -624) 110481) ((-158 . -25) T) ((-1307 . -1117) T) ((-883 . -650) 110429) ((-1305 . -1117) T) ((-978 . -102) T) ((-746 . -102) T) ((-726 . -102) T) ((-464 . -102) T) ((-827 . -463) 110380) ((-44 . -1117) T) ((-1105 . -861) T) ((-1080 . -318) 110231) ((-675 . -132) T) ((-1071 . -657) 110200) ((-681 . -728) 110184) ((-298 . -1075) T) ((-365 . -132) T) ((-362 . -132) T) ((-354 . -132) T) ((-272 . -132) T) ((-252 . -132) T) ((-395 . -657) 110153) ((-429 . -102) T) ((-153 . -1117) T) ((-45 . -231) 110103) ((-1021 . -908) NIL) ((-810 . -1068) 110087) ((-973 . -861) 110066) ((-1016 . -659) 109968) ((-810 . -651) 109952) ((-245 . -1292) 109922) ((-1041 . -316) T) ((-303 . -1073) 109843) ((-925 . -132) T) ((-40 . -935) T) ((-498 . -411) 109825) ((-364 . -316) T) ((-219 . -411) 109807) ((-1097 . -422) 109791) ((-303 . -111) 109707) ((-1201 . -861) T) ((-1200 . -861) T) ((-883 . -25) T) ((-883 . -21) T) ((-1271 . -47) 109651) ((-349 . -624) 109633) ((-1190 . -237) T) ((-227 . -148) T) ((-176 . -624) 109615) ((-785 . -624) 109597) ((-129 . -861) T) ((-619 . -240) 109544) ((-486 . -240) 109494) ((-1307 . -728) 109464) ((-48 . -316) T) ((-1305 . -728) 109434) ((-65 . -627) 109363) ((-979 . -1117) T) ((-826 . -1117) 109115) ((-321 . -102) T) ((-916 . -1235) T) ((-48 . -1039) T) ((-1248 . -650) 109023) ((-700 . -102) 109001) ((-44 . -728) 108985) ((-561 . -102) T) ((-303 . -627) 108916) ((-67 . -393) T) ((-498 . -915) NIL) ((-67 . -406) T) ((-219 . -915) NIL) ((-673 . -23) T) ((-828 . -657) 108852) ((-681 . -772) T) ((-1232 . -1117) 108830) ((-361 . -1073) 108775) ((-686 . -1117) 108753) ((-1079 . -148) T) ((-967 . -148) 108732) ((-967 . -146) 108711) ((-810 . -102) T) ((-153 . -728) 108695) ((-492 . -148) 108674) ((-492 . -146) 108653) ((-361 . -111) 108582) ((-1097 . -1075) T) ((-331 . -861) 108561) ((-1277 . -990) 108530) ((-638 . -1117) T) ((-1270 . -990) 108492) ((-522 . -132) T) ((-518 . -132) T) ((-304 . -231) 108442) ((-369 . -1075) T) ((-363 . -1075) T) ((-355 . -1075) T) ((-303 . -1066) 108384) ((-1249 . -990) 108353) ((-389 . -861) T) ((-108 . -1075) T) ((-1016 . -737) T) ((-881 . -935) T) ((-854 . -806) 108332) ((-854 . -803) 108311) ((-429 . -318) 108250) ((-479 . -102) T) ((-606 . -990) 108219) ((-328 . -1117) T) ((-418 . -806) 108198) ((-418 . -803) 108177) ((-511 . -500) 108159) ((-1271 . -1055) 108125) ((-1269 . -21) T) ((-1269 . -25) T) ((-1248 . -21) T) ((-1248 . -25) T) ((-826 . -728) 108067) ((-361 . -627) 107997) ((-710 . -415) T) ((-1298 . -1235) T) ((-1130 . -422) 107966) ((-617 . -102) T) ((-1094 . -1235) T) ((-1020 . -378) NIL) ((-682 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) ((-155 . -102) T) ((-103 . -34) T) ((-1196 . -657) 107876) ((-748 . -1235) T) ((-742 . -1068) 107719) ((-44 . -772) T) ((-742 . -651) 107568) ((-604 . -102) T) ((-664 . -667) 107552) ((-77 . -407) T) ((-77 . -406) T) ((-142 . -1235) T) ((-882 . -148) T) ((-882 . -146) NIL) 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-102) T) ((-1191 . -102) T) ((-1185 . -102) T) ((-1177 . -1117) T) ((-1143 . -102) T) ((-224 . -34) T) ((-298 . -728) 103728) ((-1177 . -621) 103704) ((-604 . -318) NIL) ((-1277 . -1276) 103688) ((-495 . -1117) 103666) ((-1167 . -231) 103616) ((-401 . -624) 103598) ((-521 . -861) T) ((-1137 . -1235) T) ((-1277 . -1263) 103575) ((-1270 . -1268) 103536) ((-1270 . -1263) 103506) ((-1270 . -1266) 103490) ((-1249 . -1247) 103451) ((-1249 . -1263) 103428) ((-1249 . -1245) 103412) ((-632 . -624) 103394) ((-1192 . -293) 103360) ((-710 . -935) T) ((-1191 . -293) 103326) ((-1185 . -293) 103292) ((-1143 . -293) 103258) ((-1097 . -1117) T) ((-1078 . -1117) T) ((-48 . -311) T) ((-325 . -913) 103224) ((-322 . -913) NIL) ((-1078 . -1085) 103203) ((-1137 . -898) 103185) ((-810 . -38) 103169) ((-272 . -650) 103117) ((-252 . -650) 103065) ((-712 . -1073) 103052) ((-606 . -1263) 103029) ((-1137 . -1055) 103011) ((-328 . -174) 102942) ((-369 . -1117) T) ((-363 . -1117) T) ((-355 . -1117) T) ((-511 . -19) 102924) ((-1119 . -152) 102908) ((-882 . -237) NIL) ((-108 . -1117) T) ((-117 . -1073) 102895) ((-722 . -373) T) ((-511 . -615) 102870) ((-712 . -111) 102855) ((-1310 . -624) 102822) ((-1310 . -501) 102804) ((-1269 . -234) 102750) ((-1248 . -234) 102603) ((-447 . -102) T) ((-887 . -1280) T) ((-255 . -102) T) ((-45 . -1166) 102553) ((-117 . -111) 102538) ((-1287 . -624) 102520) ((-1258 . -237) T) ((-1243 . -624) 102502) ((-1241 . -861) T) ((-646 . -731) T) ((-618 . -731) T) ((-1229 . -1129) T) ((-1229 . -23) T) ((-1190 . -463) 102433) ((-1185 . -318) 102318) ((-1184 . -1117) T) ((-826 . -525) 102251) ((-1052 . -1235) T) ((-245 . -1068) 102152) ((-1176 . -1117) T) ((-1159 . -659) 102090) ((-958 . -152) 102074) ((-1143 . -318) 102061) ((-1142 . -463) 102012) ((-245 . -651) 101934) ((-1104 . -567) 101865) ((-1104 . -1239) 101844) ((-1097 . -728) 101712) ((-536 . -102) T) ((-531 . -102) 101662) ((-1021 . -1068) 101612) ((-1011 . -1117) T) ((-827 . -908) 101508) ((-793 . -1239) 101487) 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-1117) 100449) ((-643 . -621) 100424) ((-643 . -1117) T) ((-592 . -1239) T) ((-592 . -567) T) ((-529 . -1239) T) ((-529 . -567) T) ((-498 . -657) 100374) ((-485 . -234) 100320) ((-438 . -1068) 100304) ((-438 . -651) 100288) ((-369 . -728) 100240) ((-363 . -728) 100192) ((-349 . -1073) 100176) ((-355 . -728) 100128) ((-349 . -111) 100107) ((-176 . -1073) 100039) ((-219 . -657) 99989) ((-176 . -111) 99900) ((-108 . -728) 99850) ((-282 . -1117) T) ((-281 . -1117) T) ((-280 . -1117) T) ((-279 . -1117) T) ((-278 . -1117) T) ((-277 . -1117) T) ((-276 . -1117) T) ((-214 . -1117) T) ((-213 . -1117) T) ((-171 . -1223) 99828) ((-171 . -1220) 99806) ((-211 . -1117) T) ((-210 . -1117) T) ((-117 . -1066) T) ((-209 . -1117) T) ((-208 . -1117) T) ((-205 . -1117) T) ((-204 . -1117) T) ((-203 . -1117) T) ((-202 . -1117) T) ((-201 . -1117) T) ((-200 . -1117) T) ((-199 . -1117) T) ((-198 . -1117) T) ((-197 . -1117) T) ((-196 . -1117) T) ((-195 . -1117) T) ((-245 . -102) 99558) ((-171 . -35) 99536) ((-171 . -95) 99514) ((-665 . -1055) 99410) ((-493 . -1075) 99388) ((-1130 . -1117) 99140) ((-1159 . -34) T) ((-681 . -500) 99124) ((-73 . -1235) T) ((-105 . -624) 99106) ((-1309 . -624) 99088) ((-391 . -624) 99070) ((-349 . -627) 99022) ((-176 . -627) 98939) ((-1234 . -501) 98920) ((-742 . -38) 98769) ((-582 . -1223) T) ((-582 . -1220) T) ((-542 . -624) 98751) ((-531 . -318) 98689) ((-511 . -624) 98671) ((-511 . -625) 98653) ((-1234 . -624) 98619) ((-1185 . -1169) NIL) ((-1044 . -1088) 98588) ((-1044 . -1117) T) ((-1021 . -102) T) ((-988 . -102) T) ((-929 . -102) T) ((-905 . -1055) 98565) ((-1159 . -737) T) ((-1020 . -659) 98472) ((-487 . -1117) T) ((-474 . -1117) T) ((-597 . -23) T) ((-582 . -35) T) ((-582 . -95) T) ((-438 . -102) T) ((-1080 . -231) 98418) ((-1192 . -38) 98315) ((-877 . -737) T) ((-705 . -935) T) ((-522 . -25) T) ((-518 . -21) T) ((-518 . -25) T) ((-1191 . -38) 98156) ((-349 . -1066) T) ((-1185 . -38) 97952) ((-1097 . -174) T) ((-176 . -1066) T) ((-1143 . -38) 97849) ((-723 . -47) 97826) ((-369 . -174) T) ((-363 . -174) T) ((-530 . -57) 97800) ((-508 . -57) 97750) ((-361 . -1304) 97727) ((-227 . -463) T) ((-328 . -299) 97678) ((-355 . -174) T) ((-176 . -248) T) ((-1248 . -861) 97577) ((-108 . -174) T) ((-883 . -1009) 97561) ((-669 . -1129) T) ((-592 . -373) T) ((-592 . -338) 97548) ((-529 . -338) 97525) ((-529 . -373) T) ((-325 . -316) 97504) ((-322 . -316) T) ((-613 . -861) 97483) ((-1130 . -728) 97425) ((-531 . -291) 97409) ((-669 . -23) T) ((-429 . -232) 97393) ((-429 . -271) 97377) ((-322 . -1039) NIL) ((-346 . -23) T) ((-103 . -1027) 97361) ((-45 . -36) 97340) ((-623 . -1117) T) ((-361 . -378) T) ((-535 . -102) T) ((-506 . -27) T) ((-245 . -318) 97278) ((-1104 . -1129) T) ((-1308 . -659) 97252) ((-793 . -1129) T) ((-791 . -1129) T) ((-1196 . -422) 97236) ((-465 . -1129) T) ((-1079 . -463) T) ((-1168 . -1117) T) ((-967 . -463) 97187) ((-1132 . -1100) T) ((-110 . -1117) T) ((-1104 . -23) T) ((-1177 . -525) 96970) ((-828 . -1075) T) ((-793 . -23) T) 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-805) 92280) ((-854 . -802) 92259) ((-854 . -737) 92238) ((-369 . -299) T) ((-363 . -299) T) ((-355 . -299) T) ((-171 . -463) 92169) ((-438 . -38) 92153) ((-225 . -23) T) ((-108 . -299) T) ((-418 . -805) 92132) ((-418 . -802) 92111) ((-418 . -737) T) ((-511 . -297) 92086) ((-488 . -1073) 92051) ((-669 . -132) T) ((-632 . -627) 92020) ((-1130 . -525) 91953) ((-346 . -132) T) ((-171 . -413) 91932) ((-493 . -728) 91874) ((-826 . -295) 91851) ((-488 . -111) 91807) ((-664 . -1075) T) ((-1190 . -908) 91710) ((-1142 . -908) 91692) ((-827 . -1068) 91535) ((-1296 . -1100) T) ((-1258 . -463) 91466) ((-827 . -651) 91315) ((-1295 . -1100) T) ((-1104 . -132) T) ((-1071 . -728) 91257) ((-1044 . -525) 91190) ((-793 . -132) T) ((-791 . -132) T) ((-582 . -463) T) ((-632 . -1066) T) ((-603 . -1117) T) ((-544 . -175) T) ((-472 . -132) T) ((-465 . -132) T) ((-389 . -237) T) ((-1016 . -1235) T) ((-45 . -1117) T) ((-395 . -728) 91160) ((-828 . -1117) T) ((-487 . -525) 91093) ((-474 . -525) 91026) ((-1310 . -627) 91008) ((-464 . -377) 90978) ((-45 . -621) 90957) ((-410 . -1235) T) ((-325 . -311) T) ((-838 . -237) 90936) ((-488 . -627) 90886) ((-1249 . -318) 90771) ((-681 . -624) 90733) ((-59 . -861) 90712) ((-1021 . -411) 90694) ((-559 . -624) 90676) ((-810 . -657) 90635) ((-826 . -615) 90612) ((-527 . -861) 90591) ((-507 . -861) 90570) ((-1016 . -1055) 90466) ((-40 . -1239) T) ((-245 . -915) 90335) ((-50 . -132) T) ((-592 . -132) T) ((-529 . -132) T) ((-303 . -659) 90195) ((-353 . -338) 90172) ((-353 . -373) T) ((-331 . -332) 90149) ((-328 . -295) 90107) ((-40 . -567) T) ((-389 . -1220) T) ((-389 . -1223) T) ((-1052 . -1211) 90082) ((-1207 . -240) 90032) ((-1185 . -232) 89984) ((-1185 . -271) 89936) ((-339 . -1117) T) ((-389 . -95) T) ((-389 . -35) T) ((-1052 . -107) 89882) ((-488 . -1066) T) ((-1309 . -1073) 89866) ((-490 . -240) 89816) ((-1177 . -500) 89750) ((-1300 . -1068) 89734) ((-391 . -1073) 89718) ((-1300 . -651) 89688) ((-488 . -248) T) ((-827 . -102) T) ((-725 . -148) 89667) 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88465) ((-607 . -38) 88438) ((-606 . -38) 88335) ((-881 . -567) T) ((-225 . -132) T) ((-328 . -1019) 88301) ((-79 . -624) 88283) ((-723 . -316) 88262) ((-303 . -737) 88164) ((-835 . -102) T) ((-875 . -855) T) ((-303 . -484) 88143) ((-1300 . -102) T) ((-40 . -373) T) ((-883 . -148) 88122) ((-496 . -657) 88104) ((-883 . -146) 88083) ((-1176 . -500) 88065) ((-1309 . -1066) T) ((-493 . -525) 87998) ((-1163 . -1235) T) ((-979 . -624) 87980) ((-658 . -500) 87964) ((-643 . -500) 87895) ((-826 . -624) 87588) ((-48 . -27) T) ((-1196 . -728) 87485) ((-967 . -908) 87464) ((-664 . -1117) T) ((-872 . -871) T) ((-447 . -374) 87438) ((-742 . -657) 87348) ((-492 . -908) 87323) ((-1119 . -102) T) ((-987 . -1117) T) ((-875 . -1117) T) ((-827 . -318) 87310) ((-544 . -538) T) ((-544 . -587) T) ((-1305 . -392) 87282) ((-1071 . -525) 87215) ((-1177 . -295) 87191) ((-245 . -232) 87160) ((-245 . -271) 87129) ((-257 . -1068) 87030) ((-256 . -1068) 86931) ((-1297 . -728) 86901) ((-1184 . -93) T) ((-1011 . -93) 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-1117) T) ((-958 . -318) 83686) ((-712 . -659) 83658) ((-560 . -855) T) ((-219 . -1117) T) ((-325 . -935) 83637) ((-322 . -935) T) ((-322 . -831) NIL) ((-401 . -731) T) ((-881 . -23) T) ((-117 . -659) 83624) ((-485 . -146) 83603) ((-429 . -422) 83587) ((-485 . -148) 83566) ((-110 . -500) 83548) ((-320 . -627) 83529) ((-2 . -624) 83511) ((-188 . -102) T) ((-1176 . -19) 83493) ((-1176 . -615) 83468) ((-669 . -21) T) ((-669 . -25) T) ((-604 . -1161) T) ((-1130 . -295) 83445) ((-346 . -25) T) ((-346 . -21) T) ((-245 . -657) 83224) ((-506 . -373) T) ((-1307 . -1073) 83208) ((-1305 . -1073) 83192) ((-1300 . -38) 83162) ((-1269 . -1220) 83128) ((-1258 . -908) 83031) ((-1190 . -1068) 82854) ((-1159 . -1235) T) ((-1142 . -1068) 82697) ((-865 . -1068) 82681) ((-643 . -615) 82656) ((-1269 . -1223) 82622) ((-1269 . -95) 82588) ((-1269 . -237) 82540) ((-1190 . -651) 82369) ((-1142 . -651) 82218) ((-865 . -651) 82188) ((-1252 . -102) 82166) ((-1249 . -232) 82118) ((-560 . -1117) T) ((-1104 . -25) T) 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80969) ((-429 . -1075) T) ((-493 . -500) 80953) ((-438 . -657) 80912) ((-336 . -861) 80891) ((-349 . -659) 80865) ((-50 . -21) T) ((-50 . -25) T) ((-219 . -728) 80815) ((-171 . -735) 80786) ((-176 . -659) 80718) ((-592 . -21) T) ((-592 . -25) T) ((-529 . -25) T) ((-529 . -21) T) ((-486 . -152) 80668) ((-1078 . -624) 80650) ((-1010 . -102) T) ((-873 . -102) T) ((-827 . -915) 80550) ((-810 . -422) 80513) ((-40 . -132) T) ((-710 . -373) T) ((-712 . -737) T) ((-712 . -805) T) ((-712 . -802) T) ((-214 . -909) T) ((-591 . -1129) T) ((-575 . -1129) T) ((-506 . -1129) T) ((-369 . -624) 80495) ((-363 . -624) 80477) ((-355 . -624) 80459) ((-66 . -407) T) ((-66 . -406) T) ((-108 . -625) 80389) ((-108 . -624) 80331) ((-213 . -909) T) ((-973 . -152) 80315) ((-782 . -132) T) ((-681 . -627) 80233) ((-135 . -737) T) ((-117 . -737) T) ((-1269 . -35) 80199) ((-1071 . -500) 80183) ((-591 . -23) T) ((-575 . -23) T) ((-506 . -23) T) ((-1248 . -95) 80149) ((-1248 . -35) 80115) ((-1190 . -102) T) ((-1142 . -102) T) ((-865 . -102) T) ((-229 . -500) 80099) ((-1307 . -111) 80078) ((-1305 . -111) 80057) ((-44 . -1073) 80041) ((-1307 . -627) 79987) ((-1307 . -1066) T) ((-1258 . -1261) 79971) ((-866 . -863) 79955) ((-1196 . -299) 79934) ((-1121 . -1235) T) ((-110 . -295) 79884) ((-1020 . -1235) T) ((-129 . -152) 79866) ((-1159 . -913) 79825) ((-44 . -111) 79804) ((-1305 . -627) 79733) ((-1240 . -1117) T) ((-1199 . -1280) T) ((-1184 . -501) 79714) ((-681 . -1066) T) ((-1184 . -624) 79680) ((-1176 . -625) NIL) ((-485 . -237) 79632) ((-1080 . -621) 79607) ((-1011 . -501) 79588) ((-74 . -452) T) ((-74 . -406) T) ((-1080 . -1117) T) ((-153 . -1073) 79572) ((-1011 . -624) 79538) ((-681 . -238) 79517) ((-582 . -565) 79501) ((-365 . -148) 79480) ((-365 . -146) 79431) ((-362 . -148) 79410) ((-362 . -146) 79361) ((-354 . -148) 79340) ((-354 . -146) 79291) ((-272 . -146) 79270) ((-272 . -148) 79249) ((-252 . -148) 79228) ((-118 . -373) T) ((-252 . -146) 79207) ((-1176 . -624) 79189) ((-153 . -111) 79168) 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T) ((-397 . -102) T) ((-333 . -102) T) ((-220 . -1100) T) ((-978 . -1117) T) ((-153 . -1066) T) ((-742 . -422) 76496) ((-118 . -23) T) ((-1020 . -913) 76448) ((-746 . -1117) T) ((-726 . -1117) T) ((-1277 . -657) 76358) ((-464 . -1117) T) ((-418 . -1235) T) ((-325 . -441) 76342) ((-603 . -93) T) ((-1270 . -657) 76224) ((-1044 . -625) 76185) ((-1041 . -1239) T) ((-227 . -102) T) ((-1044 . -624) 76147) ((-827 . -271) 76131) ((-827 . -232) 76115) ((-826 . -627) 75913) ((-1249 . -657) 75750) ((-1041 . -567) T) ((-844 . -659) 75723) ((-364 . -1239) T) ((-487 . -624) 75685) ((-487 . -625) 75646) ((-474 . -625) 75607) ((-474 . -624) 75569) ((-607 . -657) 75528) ((-418 . -896) 75512) ((-328 . -1073) 75347) ((-418 . -898) 75272) ((-606 . -657) 75182) ((-854 . -1055) 75078) ((-498 . -525) NIL) ((-493 . -615) 75055) ((-592 . -234) 75042) ((-364 . -567) T) ((-529 . -234) 75029) ((-219 . -525) NIL) ((-883 . -463) T) ((-429 . -1117) T) ((-418 . -1055) 74893) ((-328 . -111) 74714) ((-705 . -373) T) 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. -659) 72798) ((-321 . -1117) T) ((-298 . -1073) 72785) ((-110 . -624) 72767) ((-110 . -625) 72749) ((-464 . -728) 72719) ((-827 . -259) 72658) ((-700 . -1117) 72636) ((-561 . -1117) T) ((-1192 . -1075) T) ((-1191 . -1075) T) ((-96 . -501) 72617) ((-1185 . -1075) T) ((-298 . -111) 72602) ((-1143 . -1075) T) ((-561 . -621) 72581) ((-96 . -624) 72547) ((-1021 . -859) T) ((-229 . -698) 72505) ((-705 . -1129) T) ((-1229 . -751) 72481) ((-1041 . -373) T) ((-849 . -846) 72463) ((-844 . -805) 72442) ((-418 . -913) 72401) ((-328 . -1066) T) ((-353 . -25) T) ((-353 . -21) T) ((-171 . -1068) 72311) ((-68 . -1235) T) ((-844 . -802) 72290) ((-429 . -728) 72264) ((-810 . -1117) T) ((-723 . -935) 72243) ((-710 . -132) T) ((-171 . -651) 72071) ((-705 . -23) T) ((-498 . -299) T) ((-844 . -737) 72050) ((-328 . -238) 72002) ((-328 . -248) 71981) ((-219 . -299) T) ((-130 . -378) T) ((-1269 . -463) 71960) ((-1248 . -463) 71939) ((-364 . -338) 71916) ((-364 . -373) T) ((-1157 . -624) 71898) ((-45 . -1273) 71848) ((-882 . -102) T) ((-655 . -291) 71832) ((-710 . -1077) T) ((-1296 . -102) T) ((-1295 . -102) T) ((-488 . -659) 71797) ((-479 . -1117) T) ((-45 . -615) 71722) ((-1176 . -297) 71697) ((-298 . -627) 71669) ((-40 . -650) 71608) ((-1258 . -1068) 71431) ((-866 . -1068) 71415) ((-48 . -373) T) ((-1123 . -624) 71397) ((-1258 . -651) 71226) ((-866 . -651) 71196) ((-643 . -297) 71171) ((-827 . -657) 71081) ((-582 . -1068) 71068) ((-493 . -624) 70761) ((-245 . -422) 70730) ((-967 . -318) 70717) ((-582 . -651) 70704) ((-65 . -1235) T) ((-1190 . -915) 70611) ((-1183 . -1117) T) ((-1080 . -525) 70455) ((-682 . -1117) T) ((-634 . -132) T) ((-492 . -318) 70442) ((-617 . -1117) T) ((-557 . -102) T) ((-118 . -132) T) ((-298 . -1066) T) ((-182 . -1117) T) ((-162 . -1117) T) ((-157 . -1117) T) ((-155 . -1117) T) ((-464 . -772) T) ((-31 . -1100) T) ((-978 . -174) 70393) ((-1142 . -915) 70377) ((-987 . -93) T) ((-1130 . -297) 70354) ((-1097 . -1073) 70264) ((-632 . -805) 70243) ((-604 . -1117) T) 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. -520) 64744) ((-883 . -908) 64665) ((-498 . -295) NIL) ((-493 . -297) 64642) ((-429 . -299) T) ((-364 . -132) T) ((-219 . -295) NIL) ((-705 . -504) NIL) ((-99 . -1129) T) ((-40 . -234) 64573) ((-171 . -38) 64401) ((-967 . -915) 64382) ((-1269 . -990) 64344) ((-1164 . -318) 64282) ((-492 . -915) 64259) ((-1248 . -990) 64228) ((-925 . -413) T) ((-1130 . -1066) 64206) ((-1271 . -567) T) ((-1167 . -615) 64185) ((-112 . -861) T) ((-1080 . -500) 64116) ((-591 . -21) T) ((-591 . -25) T) ((-575 . -21) T) ((-575 . -25) T) ((-506 . -25) T) ((-506 . -21) T) ((-1258 . -1169) 64094) ((-1130 . -238) 64046) ((-48 . -132) T) ((-1216 . -102) T) ((-245 . -1117) 63798) ((-882 . -411) 63775) ((-1105 . -102) T) ((-1093 . -102) T) ((-619 . -102) T) ((-486 . -102) T) ((-1258 . -38) 63604) ((-866 . -38) 63574) ((-1051 . -1068) 63548) ((-742 . -174) 63459) ((-664 . -624) 63441) ((-656 . -1100) T) ((-1051 . -651) 63425) ((-582 . -38) 63412) ((-987 . -501) 63393) ((-987 . -624) 63359) ((-973 . -102) 63309) 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51366) ((-865 . -422) 51350) ((-884 . -102) 51301) ((-1269 . -102) T) ((-1249 . -525) 51070) ((-1248 . -102) T) ((-1221 . -318) 51008) ((-1192 . -295) 50973) ((-1191 . -295) 50931) ((-536 . -93) T) ((-1185 . -295) 50759) ((-321 . -624) 50741) ((-1119 . -1117) T) ((-1097 . -659) 50615) ((-722 . -463) T) ((-700 . -624) 50547) ((-298 . -737) T) ((-108 . -924) NIL) ((-700 . -625) 50508) ((-612 . -624) 50490) ((-588 . -624) 50472) ((-561 . -625) NIL) ((-561 . -624) 50454) ((-540 . -624) 50436) ((-522 . -520) 50415) ((-498 . -1073) 50365) ((-485 . -1068) 50200) ((-518 . -520) 50179) ((-485 . -651) 50020) ((-219 . -1073) 49970) ((-369 . -659) 49922) ((-363 . -659) 49874) ((-227 . -859) T) ((-355 . -659) 49826) ((-613 . -102) 49776) ((-498 . -111) 49710) ((-493 . -378) 49689) ((-108 . -659) 49639) ((-364 . -234) 49626) ((-245 . -500) 49610) ((-353 . -148) 49592) ((-353 . -146) T) ((-171 . -380) 49563) ((-958 . -1283) 49547) ((-219 . -111) 49481) ((-883 . -318) 49446) ((-958 . -1117) 49396) 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. -102) T) ((-791 . -102) T) ((-1277 . -627) 22960) ((-1270 . -627) 22703) ((-472 . -102) T) ((-465 . -102) T) ((-1249 . -627) 22498) ((-245 . -806) 22477) ((-245 . -803) 22456) ((-660 . -102) T) ((-607 . -627) 22414) ((-606 . -627) 22296) ((-1258 . -299) 22207) ((-675 . -645) 22191) ((-188 . -624) 22173) ((-655 . -295) 22125) ((-1051 . -728) 22109) ((-582 . -299) T) ((-978 . -659) 22034) ((-1308 . -132) T) ((-746 . -659) 21994) ((-726 . -659) 21981) ((-283 . -102) T) ((-464 . -659) 21911) ((-50 . -102) T) ((-592 . -102) T) ((-529 . -102) T) ((-1277 . -1066) T) ((-1270 . -1066) T) ((-1249 . -1066) T) ((-518 . -657) 21893) ((-331 . -728) 21875) ((-1277 . -238) 21834) ((-1270 . -248) 21813) ((-1270 . -238) 21765) ((-1249 . -238) 21652) ((-1249 . -248) 21631) ((-1229 . -38) 21528) ((-607 . -1066) T) ((-606 . -1066) T) ((-1021 . -806) T) ((-1021 . -803) T) ((-988 . -806) T) ((-988 . -803) T) ((-883 . -1075) T) ((-109 . -624) 21510) ((-705 . -463) T) ((-389 . -728) 21475) ((-429 . -659) 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|tanintegrate| |rotatey| |rightDivide| |hasoln| |bindings| |iFTable| - |symmetricRemainder| |removeRedundantFactorsInPols| - |solveLinearPolynomialEquationByRecursion| |regime| |repeatUntilLoop| - |limitedint| |algintegrate| |redPol| |rombergo| |supersub| - |algebraicVariables| |primitiveElement| |physicalLength!| - |basisOfCenter| |rightGcd| |modularGcdPrimitive| |lists| |notelem| - |cosIfCan| |read!| |errorKind| |mapUnivariateIfCan| - |integralCoordinates| |simpleBounds?| |OMgetBVar| |removeCosSq| |clip| - |setEmpty!| |constantKernel| |youngDiagram| |c06fqf| |rightUnits| - |signature| |mkAnswer| |RemainderList| |d01alf| |represents| - |minGbasis| |uncouplingMatrices| |dmp2rfi| |traceMatrix| |iibinom| - |seriesSolve| |euclideanGroebner| |setMaxPoints3D| |numFunEvals3D| - |comparison| |goodPoint| |cycleTail| |deepExpand| |search| |expr| - |medialSet| |pascalTriangle| |const| |e02def| |iterationVar| |s01eaf| - |removeRoughlyRedundantFactorsInPol| |rename!| |virtualDegree| - |mkPrim| |initiallyReduced?| |viewPosDefault| - |exprHasWeightCosWXorSinWX| |f04maf| |aQuadratic| |outputList| - |schema| |polygon| |innerSolve1| |composites| |viewport2D| - |asechIfCan| |OMopenFile| |decomposeFunc| |max| |bitLength| |show| - |bat| |iiacos| |parametric?| |cAcsch| |ceiling| |meshPar2Var| - |semiResultantReduitEuclidean| |reducedContinuedFraction| |tablePow| - |roughUnitIdeal?| |univcase| |usingTable?| |e02ddf| |variable| - |bivariate?| |internalIntegrate| |mainVariables| |disjunction| - |categoryFrame| |trace| |traverse| |bigEndian| |frobenius| |rk4| - |iterators| |numberOfFactors| |numberOfComponents| |powmod| |voidMode| - |s18def| |Lazard2| |genericLeftTraceForm| |coerceListOfPairs| - |matrixConcat3D| |dual| |datalist| |screenResolution| |substitute| - |systemCommand| |birth| |gradient| |fintegrate| |incrementKthElement| - |char| |alternative?| |subst| |checkPrecision| |mapdiv| - |createThreeSpace| |f2st| |f07aef| |intersect| |patternMatchTimes| - |edf2ef| |s20acf| |numberOfComputedEntries| |bitior| |nextNormalPoly| - 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|noKaratsuba| |rightFactorIfCan| |exportedOperators| |insertRoot!| - |tubePointsDefault| |internalZeroSetSplit| |upperCase?| |nullary| - |tValues| |argumentListOf| |roughEqualIdeals?| |taylor| |comment| - |constDsolve| |mappingMode| |f01bsf| |adaptive| |getProperty| - |csc2sin| |e02ahf| |decompose| |lazyEvaluate| |laurent| |expIfCan| - |pdf2ef| |cross| |stosePrepareSubResAlgo| |mainKernel| |redpps| - |SFunction| |fractionPart| |indices| |puiseux| |factorFraction| - |computeInt| |permanent| |back| |matrix| |index| |linearDependence| - |partition| |integerBound| |quadratic| |zeroDimensional?| - |raisePolynomial| |complexEigenvectors| |mindeg| UP2UTS |quasiMonic?| - |iicosh| |leftQuotient| |overset?| |sinhIfCan| |inv| - |subQuasiComponent?| |lambda| |OMreceive| |leftNorm| |minimumDegree| - |exteriorDifferential| |dmpToHdmp| |alphabetic| |elseBranch| |isEquiv| - |lazyPseudoDivide| |tanh2coth| |ground?| |colorDef| |minPoly| - |createZechTable| |continuedFraction| |tryFunctionalDecomposition?| - |pair| |doubleResultant| |ground| |youngGroup| |purelyTranscendental?| - |OMgetEndBind| |ode2| |factorGroebnerBasis| |Lazard| |s17aff| - |anfactor| |ReduceOrder| |antiCommutative?| |directory| - |radicalOfLeftTraceForm| |removeCoshSq| |initiallyReduce| - |irreducible?| |powerAssociative?| |fprindINFO| |leadingMonomial| - |iteratedInitials| |iisech| |primeFrobenius| |heap| |sum| |iidsum| - |setErrorBound| |edf2efi| |closed| |reverse| |innerEigenvectors| - |leadingCoefficient| |qqq| |hypergeometric0F1| |dimension| |mathieu24| - |separateDegrees| |complexExpand| |s19abf| |leftRegularRepresentation| - |null?| |addMatch| |primitiveMonomials| |headRemainder| |capacity| - |exists?| |exponents| |retract| |before?| |elaborateFile| |iiexp| - |leftAlternative?| |remove!| |parametersOf| |reductum| - |oblateSpheroidal| |quatern| |SturmHabichtMultiple| - |basisOfRightAnnihilator| |var1Steps| |antisymmetric?| |integrate| - |hyperelliptic| |stoseLastSubResultant| |makeViewport3D| - |extractClosed| |df2mf| |lazyPseudoRemainder| |makeVariable| |failed?| - |rank| |primlimitedint| |polCase| |inHallBasis?| |evenlambert| - |interpolate| |sign| |zeroDim?| |upperCase| |ideal| |s13acf| - |orthonormalBasis| |leftOne| |UpTriBddDenomInv| |reseed| |unmakeSUP| - |anticoord| |OMreadFile| |patternVariable| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |generic?| |child| |semiResultantEuclidean2| + |member?| |getGoodPrime| |matrixConcat3D| |generateIrredPoly| + |factorSquareFree| |head| |ran| |in?| |set| |elliptic| |ListOfTerms| + |mdeg| |d01fcf| |mapGen| |numberOfComposites| |cothIfCan| |totalfract| + |queue| |c06gsf| |returnType!| |listLoops| + |factorSquareFreePolynomial| |doublyTransitive?| |getProperties| |xn| + |rightQuotient| |isAnd| |binding| |composites| + |combineFeatureCompatibility| |modularGcd| + |removeRedundantFactorsInPols| |areEquivalent?| |mindegTerm| + |ramified?| |sec2cos| |rootSimp| |mkcomm| |leftMinimalPolynomial| + |startTableInvSet!| |semiResultantEuclideannaif| |rename!| |identity| + |lists| |factors| |character?| |generalizedEigenvector| + |lfextendedint| |squareTop| |zag| |genericLeftNorm| |prologue| + |extension| |trueEqual| |zeroSetSplitIntoTriangularSystems| + |brillhartIrreducible?| |irCtor| |d03faf| |signature| |nextPrime| + |lookupFunction| |f01qdf| |realZeros| |iicosh| |rur| |argument| + |supRittWu?| |selectAndPolynomials| |pdf2ef| |lambert| + |chainSubResultants| |empty| |OMread| |rationalPoints| |UP2ifCan| + |f01rcf| |search| |connectTo| |zeroSquareMatrix| |expr| + |uncouplingMatrices| |numberOfMonomials| |maxint| |presub| |ode1| + |tryFunctionalDecomposition| |characteristicSerie| + |indiceSubResultant| |extendedSubResultantGcd| |pointData| |paren| + |removeDuplicates!| |f02aaf| |mapUnivariateIfCan| |outputList| + |univcase| |minPoints| |dmpToHdmp| |showClipRegion| |cyclic| |maxrow| + |createNormalPrimitivePoly| |printingInfo?| |iCompose| |wreath| |show| + |maxdeg| |exprHasWeightCosWXorSinWX| |univariatePolynomials| + |cycleEntry| |tubePoints| |noValueMode| |loopPoints| |interReduce| + |closed| |nonQsign| |printStatement| |zeroDimensional?| |mathieu23| + |variable| |removeRoughlyRedundantFactorsInPol| |drawComplex| + |modulus| |isTimes| |computeInt| |s18aff| |trace| |meshPar2Var| |cdr| + |var1Steps| |iterators| |calcRanges| |rightRegularRepresentation| + |leftTrace| |var2StepsDefault| |companionBlocks| |bivariate?| |e01daf| + |viewport2D| |normFactors| |wordInStrongGenerators| |datalist| + |radicalSimplify| |imagj| |matrixGcd| |systemCommand| + |balancedBinaryTree| |e02bcf| |makeVariable| |setColumn!| |char| + |functionIsContinuousAtEndPoints| |checkPrecision| |subst| |hconcat| + |minColIndex| |internalLastSubResultant| |stronglyReduce| |subscript| + |eisensteinIrreducible?| |OMgetBVar| |RittWuCompare| |bitior| + |generalPosition| |purelyAlgebraic?| |lifting1| |mirror| + |PollardSmallFactor| |slash| |beauzamyBound| |clikeUniv| |OMreadStr| + |insertRoot!| |genericRightTraceForm| |attributeData| + |rightExactQuotient| |lexGroebner| |sizeMultiplication| |precision| + |normal| |f01maf| |list?| |s18dcf| |contract| |support| |LiePoly| + |sturmVariationsOf| |leftAlternative?| |cond| |conditionP| |isPlus| + |concat| |Frobenius| |consnewpol| |bat| |currentScope| + |unrankImproperPartitions0| |rootKerSimp| |iiasin| |sech| |iiacsch| + |regime| |se2rfi| |alphanumeric| |bracket| |df2st| |viewWriteDefault| + |oneDimensionalArray| |leftMult| |csch| |operation| |prem| + |coth2trigh| |compound?| |element?| |bothWays| |objects| |float| + |find| |elaboration| |subscriptedVariables| |screenResolution3D| + |asinh| |gcdcofactprim| |dimensions| |addPointLast| |base| + |useEisensteinCriterion?| |totalLex| |ridHack1| |cubic| |setnext!| + |acosh| |socf2socdf| |lfintegrate| |simplify| |generalSqFr| |kind| + |vconcat| |subresultantSequence| |putProperty| |fortranReal| |arg1| + |tableau| |f01mcf| |leftDivide| |pseudoDivide| |atanh| + |sylvesterMatrix| |getMatch| |shallowExpand| |f01ref| |nthExpon| |op| + |getGraph| |equality| |jacobi| |internalInfRittWu?| |arg2| |expIfCan| + |f02aef| |acoth| |blankSeparate| |permutationRepresentation| + |argscript| |exportedOperators| |HermiteIntegrate| |autoReduced?| + |LiePolyIfCan| |writeInt8!| |FormatArabic| |asech| |e04naf| |numer| + |writeBytes!| |pop!| |addmod| |palgint0| |roughSubIdeal?| |conditions| + |setTopPredicate| |mainCoefficients| |sts2stst| |dimension| + |variables| |cRationalPower| |denom| |topFortranOutputStack| |besselY| + |d01aqf| |listBranches| |match| |coth2tanh| |options| |commaSeparate| + |multiple| |null?| |genericLeftDiscriminant| |overset?| + |identityMatrix| |rational| |bubbleSort!| |rootOfIrreduciblePoly| + |allRootsOf| |e04dgf| |applyQuote| |asinIfCan| + |irreducibleRepresentation| |tanIfCan| |factorials| |pi| |tree| + |edf2efi| |submod| |approximants| |s17dhf| |fortranDoubleComplex| + |superHeight| |c06fqf| |infinity| |ipow| |resultantReduit| |union| + |numberOfHues| |showIntensityFunctions| |any| |froot| |setleaves!| + |string| |ldf2vmf| |fill!| |indices| |bigEndian| |changeName| + |newTypeLists| |splitDenominator| |exponent| |rk4a| |ruleset| + |dioSolve| |rectangularMatrix| |s18acf| |brillhartTrials| + |subResultantGcd| |stiffnessAndStabilityFactor| |elRow1!| |heap| + |primextendedint| |isOp| |tanNa| |kernel| |partialDenominators| + |previous| |leadingIdeal| |gethi| |pile| |recur| |s19acf| + |bombieriNorm| |qqq| |mainMonomials| |stoseInvertibleSetreg| |list| + |complexNumeric| |multMonom| |numberOfComponents| |pastel| |sinh2csch| + |conjug| |factorByRecursion| |suchThat| |putGraph| |hostByteOrder| + |open?| |elseBranch| |compdegd| |draw| |unravel| |nextsousResultant2| + |npcoef| |adjoint| |trace2PowMod| |specialTrigs| |OMgetEndBind| + |cartesian| |modifyPointData| |subtractIfCan| + |numberOfIrreduciblePoly| |sumOfKthPowerDivisors| |d01ajf| |adaptive?| + |sech2cosh| |oddintegers| |top!| |f01brf| |localAbs| |asimpson| + |monomials| |euclideanSize| |negative?| |selectsecond| |changeBase| + |charthRoot| |iflist2Result| |simpleBounds?| |realElementary| + |LagrangeInterpolation| |inverse| |write!| |rightNorm| |headAst| + |opeval| |pquo| |rquo| |duplicates?| |position!| |expint| + |nextIrreduciblePoly| |prinb| |makeObject| |dihedral| |pdf2df| + |ScanFloatIgnoreSpacesIfCan| |reduction| |cyclicGroup| |lazyEvaluate| + |nary?| |monicDivide| |OMmakeConn| |center| |multiplyExponents| + |degree| |coef| |s17dcf| |roughUnitIdeal?| |innerSolve| + |primitiveElement| |roughBase?| |stack| + |setLegalFortranSourceExtensions| |pointPlot| |primlimintfrac| + |csubst| |indicialEquationAtInfinity| |label| |OMputEndAttr| + |toseInvertibleSet| |mkPrim| |vectorise| |basisOfRightAnnihilator| + |endSubProgram| |setprevious!| |cycleSplit!| |normalizedDivide| + |e01sbf| |name| |iroot| |getProperty| |d01alf| |quadratic| + |mainCharacterization| |mkIntegral| |messagePrint| |iterationVar| + |badValues| |oddInfiniteProduct| |body| |mainVariable?| + |axesColorDefault| |meshPar1Var| |Is| |schwerpunkt| |rangeIsFinite| + |nextsubResultant2| |typeForm| |rotate| |singularitiesOf| |e02aef| + |findConstructor| |index?| |baseRDE| |interpret| + |selectOptimizationRoutines| |f04maf| |patternMatch| |virtualDegree| + |padicallyExpand| |binaryTree| |rightPower| |c06ekf| |hspace| |iiacsc| + |getlo| |iitanh| |distance| |getSyntaxFormsFromFile| |getMeasure| + |alternating| |qinterval| |bitLength| |hasSolution?| |musserTrials| + |completeEchelonBasis| |belong?| |removeIrreducibleRedundantFactors| + |rightZero| |solveLinearPolynomialEquationByRecursion| + |createNormalPoly| |complexEigenvectors| |curveColorPalette| + |OMputAtp| |cardinality| |fmecg| |c02agf| |iicsc| |normalise| |point| + |completeHensel| |length| |lazyPseudoRemainder| |changeMeasure| + |readUInt32!| |extendedIntegrate| |bfEntry| + |rewriteSetByReducingWithParticularGenerators| + |createPrimitiveElement| |option| |constantKernel| |scripts| + |internalSubPolSet?| |cyclicEqual?| |s17aff| |aQuartic| |notelem| + |recoverAfterFail| |internalDecompose| |OMgetAttr| SEGMENT |irVar| + |iisqrt2| |eulerPhi| |leftExtendedGcd| |OMgetEndApp| + |lineColorDefault| |port| |innerint| |setPoly| |modularGcdPrimitive| + |satisfy?| |variable?| |intersect| |series| |adaptive3D?| |sechIfCan| + |explimitedint| |aromberg| |sequence| |boundOfCauchy| |ParCondList| + |viewPosDefault| |perfectSquare?| |charClass| |divisors| + |OMsupportsSymbol?| |primitivePart!| |expandTrigProducts| |t| + |internalIntegrate| |scalarMatrix| |perfectSqrt| |ptFunc| |nodes| + |lookup| |permutations| |resetNew| |redPol| |tube| |reopen!| + |alternatingGroup| |simpson| |leaf?| |e02agf| |setButtonValue| + |sorted?| |rightUnits| |setErrorBound| |createNormalElement| + |primintfldpoly| |s17aef| |d02gaf| |f07adf| |bernoulli| |min| |delay| + |integralLastSubResultant| |back| |limitPlus| |alphanumeric?| + |cyclePartition| |inverseLaplace| |PDESolve| |polar| |s18def| + |tanhIfCan| |swapColumns!| |f02adf| |nilFactor| |solveLinear| + |coerceListOfPairs| |fractionPart| |select!| |addBadValue| + |mainKernel| |createThreeSpace| |evaluateInverse| |mergeFactors| + |square?| |startTable!| |diagonal?| |rightFactorIfCan| |unknown| + |apply| |tubePlot| |reduceLODE| |mapExponents| |eyeDistance| + |divideIfCan!| |cAtan| |makeViewport2D| |measure2Result| + |internalZeroSetSplit| |getIdentifier| |aLinear| |first| |groebner| + |coefChoose| |rowEchLocal| |f04asf| |mapMatrixIfCan| |leftFactor| + |palgextint| |isPower| |xor| |imag| |euler| |localUnquote| + |separateFactors| |rest| |generalizedContinuumHypothesisAssumed| + |ReduceOrder| |certainlySubVariety?| |ode2| |range| |directProduct| + |antisymmetricTensors| |case| |incrementKthElement| |Hausdorff| + |randomR| |noKaratsuba| |binomThmExpt| |OMputSymbol| |unitNormal| + |extend| |headReduce| |leftUnit| GF2FG |Zero| |lowerCase!| |e02bdf| + |initiallyReduced?| |ramifiedAtInfinity?| |leadingExponent| |keys| + |comp| |true| |setProperty| |atanhIfCan| |tryFunctionalDecomposition?| + |void| |sayLength| |shiftRoots| |fillPascalTriangle| |One| |top| + |iiacoth| |setMaxPoints| |f04atf| |coordinate| |clipWithRanges| |cap| + |rightFactorCandidate| |continue| |s15adf| |binary| |empty?| |sin?| + |mainContent| |inverseIntegralMatrixAtInfinity| |showTheIFTable| + |hclf| |Gamma| |goodnessOfFit| |sort| |plusInfinity| |setStatus| + |fortranComplex| |leftLcm| |iibinom| |factorial| |elem?| + |complexElementary| |prolateSpheroidal| |iisech| |idealSimplify| + |minusInfinity| |solveid| |palgintegrate| |schema| |ignore?| |hessian| + |lieAdmissible?| |f02awf| |zero?| |var2Steps| |genericRightNorm| + |roman| |tubeRadius| |iomode| |id| |tanSum| |selectfirst| + |invertible?| |central?| |stopTableGcd!| |infRittWu?| + |reciprocalPolynomial| |host| |sortConstraints| |BasicMethod| + |splitConstant| |ratpart| |OMgetEndAttr| |elt| |quotientByP| |lo| + |s17agf| |atoms| |ddFact| |exptMod| |changeVar| |random| |fixedPoints| + |f02ajf| |OMserve| |inR?| |collectUnder| |next| |listexp| + |symmetricDifference| |spherical| |halfExtendedResultant1| |rspace| + |check| |stoseInvertible?reg| |fintegrate| |endOfFile?| |setrest!| + |hcrf| |weierstrass| |nextPrimitiveNormalPoly| |polyRicDE| + |modifyPoint| |badNum| |quickSort| |totolex| |basis| |OMgetObject| + |leastPower| |rubiksGroup| |sparsityIF| |complexSolve| + |stoseInvertible?| |principalIdeal| |physicalLength| |trim| + |doubleRank| |compiledFunction| |OMgetFloat| |nthRoot| + |integralAtInfinity?| |extensionDegree| |genericLeftTrace| |debug3D| + |iipow| |charpol| |ord| |hitherPlane| |complexNumericIfCan| + |karatsubaOnce| |commutative?| |rowEch| |rischDE| + |constantToUnaryFunction| |mainSquareFreePart| |complement| + |addPoint2| |insert| |youngDiagram| |abelianGroup| |unmakeSUP| + |someBasis| |randomLC| |subQuasiComponent?| |powers| + |basisOfLeftAnnihilator| |iiabs| |readUInt8!| |symmetricSquare| + |leader| |chvar| |lagrange| |push| |intensity| |rightUnit| |quote| + |rootRadius| |primintegrate| |c06ecf| |critpOrder| |OMgetError| + |viewWriteAvailable| |iicos| |df2ef| |compBound| |rationalIfCan| + |f02xef| |stirling2| |normDeriv2| |upDateBranches| |viewDefaults| + |cAtanh| |OMputEndError| |torsionIfCan| |maxPoints3D| |lowerCase| + |doubleComplex?| |enterInCache| |setEmpty!| |critM| |monicModulo| + |subResultantGcdEuclidean| |integers| |iidsum| |parametersOf| + |partialFraction| |resultantEuclideannaif| |iiatanh| |dark| + |binaryTournament| |palgRDE0| |subNode?| |addiag| |stFunc2| |vspace| + |mainVariable| |rational?| |makeViewport3D| |setOrder| |dequeue!| + |nullary| |s17akf| |inverseIntegralMatrix| |realSolve| |reify| + |e02bef| |setsubMatrix!| |structuralConstants| |symbolTable| + |gcdcofact| |e01saf| |seriesSolve| |whileLoop| |pow| |middle| + |tracePowMod| |f04mcf| |coordinates| |subset?| |checkRur| + |coefficients| |weight| |status| |relationsIdeal| |orbit| |goodPoint| + |postfix| |s18aef| |OMencodingSGML| |pushFortranOutputStack| + |setAttributeButtonStep| |isOpen?| |setUnion| |OMwrite| |normalize| + |reseed| |cAcosh| |clearTheIFTable| |extractProperty| |constantRight| + |popFortranOutputStack| |irDef| |lazy?| |width| |cycles| |lazyPquo| + |iicsch| |super| |cosIfCan| |rCoord| |computeCycleEntry| |tanQ| + |outputAsFortran| |cyclotomic| |appendPoint| |leftGcd| |s14aaf| + |irreducibleFactors| |tRange| |positiveSolve| |number?| Y |deref| + |fortranLogical| |findBinding| |bitCoef| |meshFun2Var| |d02bhf| + |cyclicParents| |solid| |exponential| |maxIndex| |SturmHabicht| + |infinityNorm| |binomial| |fortranLiteralLine| |denomLODE| + |variationOfParameters| |generalInfiniteProduct| |newSubProgram| + |subResultantsChain| |lepol| |subTriSet?| |reduceBasisAtInfinity| + |stFunc1| |semiSubResultantGcdEuclidean1| |internalSubQuasiComponent?| + |flexible?| |geometric| |linearAssociatedExp| |OMputError| |palgLODE0| + |pseudoQuotient| |clearCache| |fglmIfCan| |radicalEigenvectors| + |credPol| |dAndcExp| |lift| |table| |partialNumerators| + |totalDifferential| |cCsch| |hyperelliptic| |sumOfSquares| + |nativeModuleExtension| |leftOne| |harmonic| |digit| + |nthFractionalTerm| |reduce| |new| |basisOfMiddleNucleus| |jacobian| + |updateStatus!| |obj| |imagi| |tableForDiscreteLogarithm| + |subresultantVector| |rotatex| |quoted?| |normal?| |minordet| + |wordInGenerators| |exp1| |just| |cache| + |unprotectedRemoveRedundantFactors| |row| |bat1| |li| |digits| + |column| |denominator| |sign| |fortranInteger| |setvalue!| |isExpt| + |revert| |minGbasis| |retractable?| |pole?| |clearTable!| + |possiblyInfinite?| |lowerBound| |antiCommutator| |multinomial| + |algSplitSimple| |radicalSolve| |lifting| |quasiAlgebraicSet| |edf2ef| + |idealiser| |cPower| |setClosed| |factor| |ocf2ocdf| |hexDigit?| + |triangularSystems| |testModulus| |fixedDivisor| |unparse| + |OMopenFile| |iisec| |minPol| |degreePartition| |numberOfNormalPoly| + |positive?| |algebraicCoefficients?| |triangulate| + |rewriteIdealWithQuasiMonicGenerators| |iiatan| |createPrimitivePoly| + |makeResult| |removeRedundantFactors| |sinhIfCan| + |rightRankPolynomial| |plus!| |rk4| |vector| |genericLeftTraceForm| + |hostPlatform| |fractionFreeGauss!| |remove!| + |generalizedContinuumHypothesisAssumed?| |diagonalMatrix| |e02gaf| + |primitivePart| |OMclose| |userOrdered?| |differentiate| |symbolIfCan| + |OMputEndAtp| |OMgetString| |lazyIrreducibleFactors| |overlap| + |resize| |divisor| |predicate| |eq?| |wronskianMatrix| |qfactor| |box| + |eigenvector| |Vectorise| |pureLex| |unvectorise| |prinshINFO| + |internalAugment| |resultantEuclidean| |getButtonValue| |usingTable?| + |stoseInternalLastSubResultant| |magnitude| |ellipticCylindrical| + |safeCeiling| |clearFortranOutputStack| |size| |useSingleFactorBound| + |btwFact| |left| ** |monomial| |infiniteProduct| |besselK| |dom| + |test| |read!| |logical?| |lazyVariations| |coerceImages| + |semiIndiceSubResultantEuclidean| |byte| |differentialVariables| + |integralCoordinates| |innerSolve1| |extendedResultant| |right| + |multivariate| |lquo| |split| |factorAndSplit| + |nextNormalPrimitivePoly| |singleFactorBound| |imaginary| |string?| + |paraboloidal| |polyred| |unknownEndian| |makeop| |leadingIndex| + |retractIfCan| |cycle| |e02daf| |iicot| |build| + |getMultiplicationMatrix| |getVariableOrder| |outputMeasure| |s15aef| + |whatInfinity| |algebraicOf| |close| |linear| |unitCanonical| + |primeFrobenius| |irForm| |root?| |getMultiplicationTable| |wrregime| + |complexIntegrate| |setelt!| |completeEval| |insertMatch| |tan2cot| + |sqrt| |closedCurve| |resetAttributeButtons| |readLine!| + |semiResultantEuclidean1| |removeRoughlyRedundantFactorsInContents| + |showFortranOutputStack| |physicalLength!| |e01sff| |leaves| |hasoln| + |display| |polynomial| |high| |real| |title| |ravel| |curveColor| + |eigenvalues| |separate| |OMsend| |untab| |prefix| |units| + |lazyResidueClass| |insertionSort!| |numberOfImproperPartitions| + |rationalFunction| |inputBinaryFile| |basisOfRightNucleus| + |completeHermite| |GospersMethod| |points| |reshape| |rdregime| |mix| + |printStats!| |elaborate| |pascalTriangle| |parameters| |shape| |dn| + |iiacot| |node?| |elRow2!| |e04ucf| |leftZero| |int| |power| + |numberOfChildren| |cAsec| |cos2sec| |copies| |e| |cCoth| |coord| + |e02ahf| |e01bgf| |squareMatrix| |node| |capacity| |singular?| + |ODESolve| |rightDiscriminant| 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|partialQuotients| |rotatey| |LyndonWordsList| |child?| |assert| + |digamma| |wholeRadix| |chiSquare| |pointColor| |viewport3D| + |numerators| |curve| |generalizedEigenvectors| |convert| |zeroVector| + |gradient| |setAdaptive| |copyInto!| |midpoints| |discreteLog| |critT| + |subspace| |showAttributes| |argumentListOf| |LyndonCoordinates| + |level| |outputGeneral| |rename| |algint| |OMreadFile| |position| + |symFunc| |f04qaf| |tubeRadiusDefault| |genericRightDiscriminant| + |interpretString| |arrayStack| |mappingMode| |fortranLiteral| + |monomialIntPoly| |shanksDiscLogAlgorithm| |redPo| |lexTriangular| + |tanh2coth| |makeMulti| |copy!| |bit?| |makingStats?| |lyndon?| + |quatern| |scopes| |lfunc| |branchPoint?| |kovacic| |s19adf| |measure| + |mkAnswer| |setRow!| |compile| |createZechTable| |curryRight| + |readByte!| |fTable| |exp| |cCosh| |rombergo| |leastAffineMultiple| + |f02wef| |firstSubsetGray| |has?| |associatedSystem| + |subResultantChain| |setScreenResolution3D| |getCurve| |equation| + |expintfldpoly| |cyclicSubmodule| |removeCosSq| |cSec| |numeric| + |myDegree| |shiftLeft| |imagI| |radicalRoots| |decimal| + |OMgetEndObject| |systemSizeIF| |radical| |changeThreshhold| + |readInt16!| |selectPolynomials| |multiplyCoefficients| |OMReadError?| + |commonDenominator| |quasiRegular?| |complementaryBasis| |asechIfCan| + |entries| |OMconnectTCP| |OMgetEndBVar| |factorSFBRlcUnit| + |normalDeriv| |epilogue| |lintgcd| |kmax| |sdf2lst| |rotate!| + |parabolicCylindrical| |limit| |script| |external?| |lllp| F2FG + |doubleFloatFormat| |s18adf| |octon| |nonSingularModel| |extractIndex| + |every?| |printInfo| |divideExponents| |getRef| |upperCase| + |nextPartition| |countRealRoots| |mathieu11| |red| |modTree| + |enumerate| |symmetricGroup| |linearPolynomials| |insertBottom!| + |UnVectorise| |intcompBasis| |Ci| |explogs2trigs| + |mainDefiningPolynomial| |cAsech| |orthonormalBasis| |iidprod| + |bumprow| |tex| |graphImage| |f04mbf| |trunc| |complexZeros| + |basisOfCentroid| |bumptab1| |linkToFortran| |OMUnknownSymbol?| + |nothing| |newReduc| |palglimint| |comparison| |getOperands| + |reducedContinuedFraction| |s01eaf| |useSingleFactorBound?| + |leftScalarTimes!| |diag| |uniform| |clipPointsDefault| + |rewriteIdealWithRemainder| |infix| |zCoord| + |characteristicPolynomial| |subMatrix| |zerosOf| |shuffle| + |startStats!| |transcendent?| |inrootof| |normalElement| |sqfrFactor| + |zoom| |po| |enterPointData| |outputSpacing| |SturmHabichtSequence| + |infieldIntegrate| |radicalEigenvector| |bytes| |bandedHessian| + |f02bbf| |quasiMonic?| |removeSinSq| |qelt| |secIfCan| |multiset| + |setLabelValue| |getStream| |heapSort| |fracPart| |qsetelt| |type| + |expintegrate| |complexExpand| |youngGroup| |algDsolve| + |trailingCoefficient| |rem| |discriminant| |palgextint0| + |symmetricRemainder| |pseudoRemainder| |safeFloor| |d02kef| + |selectIntegrationRoutines| |nextItem| |screenResolution| |ref| |quo| + |xRange| |OMputEndObject| |initial| |linearAssociatedOrder| + |sylvesterSequence| |OMencodingBinary| |wordsForStrongGenerators| + |cons| |cCot| |tab| |wholeRagits| |basicSet| |yRange| |readBytes!| + |moduleSum| |yCoordinates| |setVariableOrder| |nthRootIfCan| + |outputForm| |dim| |integerIfCan| |Ei| |nthFactor| |e01bef| |div| + |zRange| |identification| |minimize| |call| + |dimensionOfIrreducibleRepresentation| |module| |solveInField| |map!| + |palgRDE| |isConnected?| |factorFraction| |buildSyntax| |exquo| + |rootPoly| |laplace| |redmat| |extractPoint| |problemPoints| |f01qcf| + |principalAncestors| |qsetelt!| |cot2tan| ~= |mapExpon| |BumInSepFFE| + |reducedSystem| |cschIfCan| |rightMinimalPolynomial| |cAcoth| + |lazyIntegrate| |modularFactor| |lyndonIfCan| |#| + |normalizedAssociate| |dihedralGroup| |flexibleArray| |crushedSet| + |factorsOfDegree| |oddlambert| |associatorDependence| ~ |zero| |rk4f| + |expressIdealMember| |iiexp| |coerce| |particularSolution| |log2| + |constantLeft| |selectSumOfSquaresRoutines| |closed?| |source| + |direction| |cscIfCan| |univariatePolynomial| |writable?| |construct| + |currentSubProgram| |validExponential| |readInt32!| |lazyPseudoDivide| + |And| |exteriorDifferential| |outputFixed| |contains?| + |iteratedInitials| |branchPointAtInfinity?| |typeLists| |updatD| + |surface| |rightRank| |bag| |/\\| |Or| |bandedJacobian| |acsch| + |taylorRep| |selectPDERoutines| |mapUp!| |convergents| + |mergeDifference| |makeSUP| |predicates| |\\/| |Not| |setMinPoints| + |mpsode| |printTypes| |critBonD| |numberOfPrimitivePoly| |eulerE| + |bezoutDiscriminant| |bernoulliB| UP2UTS |doubleDisc| |elColumn2!| + |gensym| |ScanArabic| |leadingCoefficientRicDE| |coHeight| |target| + |coerceS| |implies| |setlast!| |viewSizeDefault| |unit| + |computePowers| |isOr| |f02akf| |refine| |lazyPremWithDefault| + |noncommutativeJordanAlgebra?| |nthFlag| |explicitEntries?| + |listOfMonoms| |s14baf| |isAtom| |environment| |chebyshevT| |radPoly| + |divergence| |indicialEquations| |legendre| |toseInvertible?| + |baseRDEsys| |pointSizeDefault| |whitePoint| |traverse| |gbasis| + |restorePrecision| |printInfo!| |getPickedPoints| |cross| + |multiEuclideanTree| |linear?| |invertIfCan| |mainExpression| + |linearlyDependent?| |second| |open| |quartic| |maxPoints| |powern| + |numFunEvals| |createLowComplexityTable| |definingEquations| |iFTable| + |graphCurves| |cSin| |besselI| |third| |dot| |inverseColeman| + |countRealRootsMultiple| |linearMatrix| |basisOfLeftNucloid| + |viewDeltaXDefault| |f07fef| |hermite| |outputBinaryFile| |setValue!| + |exQuo| |makeSketch| |generalTwoFactor| |setchildren!| |coefficient| + |scalarTypeOf| FG2F |singularAtInfinity?| |expandPower| + |headRemainder| |integerBound| |OMsetEncoding| |nextPrimitivePoly| + |cSech| |interactiveEnv| |toseLastSubResultant| |OMlistSymbols| + |reset| |decrease| |readUInt16!| |safetyMargin| |bright| |operations| + |leftRemainder| |rightGcd| |gcdPrimitive| |makeTerm| |failed?| + |complexEigenvalues| F |leftQuotient| |writeLine!| + |createPrimitiveNormalPoly| |tanAn| |imports| |exactQuotient| + |ffactor| |fortranLinkerArgs| |frst| |deriv| |c06eaf| |augment| + |OMunhandledSymbol| |write| |iiperm| |reorder| |inc| + |pmComplexintegrate| |eval| |cycleElt| |OMgetAtp| |pair?| |bipolar| + |simpsono| |setelt| |save| |constant?| |setfirst!| + |localIntegralBasis| |s13adf| |acoshIfCan| |iisin| |dual| + |drawComplexVectorField| |nsqfree| |ratPoly| |createGenericMatrix| + |stopTable!| |leviCivitaSymbol| |outputFloating| |semicolonSeparate| + |round| |sn| |setFormula!| |ranges| |reduced?| |laurentRep| + |setPrologue!| |copy| |nlde| |numberOfComputedEntries| |region| + |dfRange| |sup| |error| |cTanh| |littleEndian| |lexico| |reverse!| + |f02aff| |zeroOf| |setLength!| |e02def| EQ |rootNormalize| + |maxRowIndex| |f04jgf| |even?| |dmp2rfi| |evaluate| |singRicDE| + |typeList| |rightCharacteristicPolynomial| |selectNonFiniteRoutines| + |curve?| |constDsolve| |sinhcosh| |janko2| |viewPhiDefault| |push!| + |isNot| |constantCoefficientRicDE| |graphStates| |f02bjf| |double?| + |minimumExponent| |escape| |plot| |rewriteSetWithReduction| + |aspFilename| |unexpand| |clipParametric| |graeffe| |invmod| |f2df| + |showTheRoutinesTable| |distdfact| |nextSubsetGray| |match?| + |upperCase!| |e01baf| |indicialEquation| |coerceL| + |removeSuperfluousCases| |autoCoerce| |size?| |smith| |monomial?| + |mapBivariate| |overlabel| |primes| |categoryFrame| |setTex!| |critB| + |rootDirectory| |minimumDegree| |encodingDirectory| |thetaCoord| + |alphabetic| |mapUnivariate| |trapezoidalo| |terms| |OMbindTCP| + |rootOf| |changeNameToObjf| |transpose| |factorPolynomial| + |jordanAlgebra?| |solveLinearPolynomialEquationByFractions| + |limitedIntegrate| |splitSquarefree| |deleteProperty!| |digit?| + |LowTriBddDenomInv| |iiasec| |localReal?| |makeGraphImage| |rst| + |c06gcf| |merge!| |bivariatePolynomials| |integralRepresents| + |B1solve| |replace| |complexForm| |lowerPolynomial| |d02gbf| |sort!| + |cExp| |testDim| |dimensionsOf| |entry| |quadraticForm| |adaptive| + |Si| |pr2dmp| |stronglyReduced?| |absolutelyIrreducible?| |subCase?| + |isobaric?| |viewpoint| |integralBasis| |domainTemplate| |cLog| + |trigs2explogs| |corrPoly| |listOfLists| |elaborateFile| |inf| + |distribute| |antiAssociative?| |voidMode| |null| |OMlistCDs| + |nullity| |eigenvectors| |listConjugateBases| |curryLeft| |acosIfCan| + |slex| |innerEigenvectors| |purelyTranscendental?| |s17ahf| |lazyPrem| + |OMputObject| |not| |removeSinhSq| |ldf2lst| |nullSpace| |c06gbf| + |less?| |ratDenom| |associative?| |f07fdf| |realEigenvalues| |cfirst| + |and| |monicCompleteDecompose| |FormatRoman| |numFunEvals3D| + |primitive?| |antisymmetric?| |categories| |horizConcat| + |invertibleSet| |LazardQuotient2| |linearDependenceOverZ| + |stoseInvertibleSet| |or| |delete| |firstDenom| |applyRules| + |quasiComponent| |e02akf| |stoseInvertibleSetsqfreg| |superscript| + |LyndonWordsList1| |pushdown| |swapRows!| |cycleTail| |hMonic| + |branchIfCan| |trigs| |OMputAttr| |compose| |edf2fi| |acotIfCan| + |integer?| |algintegrate| |sinIfCan| |normal01| |startTableGcd!| + |Aleph| |sample| |quotient| |atanIfCan| |droot| |close!| |rootBound| + |lfextlimint| |iisinh| |degreeSubResultant| |e02baf| |reducedForm| + |optAttributes| |collectUpper| |nodeOf?| |OMputInteger| |makeSeries| + |hex| |realEigenvectors| |seriesToOutputForm| |maxrank| |vedf2vef| + |firstNumer| |contractSolve| |leftRecip| |shade| |polynomialZeros| + |newLine| |useNagFunctions| |raisePolynomial| |halfExtendedResultant2| + |e02adf| |isQuotient| |sncndn| |optpair| |extractIfCan| + |functionIsOscillatory| |representationType| |sqfree| |lprop| |cTan| + |xCoord| |deepCopy| |leftUnits| |iprint| |reduceByQuasiMonic| + |polygamma| |polygon?| |skewSFunction| |rightTrace| |bfKeys| |monic?| + |squareFreePart| |c06ebf| |finite?| |simplifyLog| |forLoop| |repSq| + |psolve| |rootSplit| |polyPart| |depth| |perspective| |dictionary| + |numberOfVariables| |cup| |subSet| |d03eef| |withPredicates| |getCode| + |bringDown| |cn| |categoryMode| |setFieldInfo| |drawCurves| |s17ajf| + |exprHasAlgebraicWeight| |semiSubResultantGcdEuclidean2| |LyndonBasis| + |permanent| |height| |repeating?| |d01akf| |meatAxe| |rationalPower| + |decompose| |moebius| |rootPower| |semiLastSubResultantEuclidean| + |monomRDE| |fortranTypeOf| |dec| |moreAlgebraic?| |cAcsch| + |gcdPolynomial| |removeZero| |pdct| |concat!| |tubePointsDefault| + |removeRedundantFactorsInContents| |setOfMinN| |setMinPoints3D| + |numberOfOperations| |gcdprim| |power!| |d02cjf| |qPot| |multisect| + |expPot| |order| |log10| |is?| |tensorProduct| |clearTheSymbolTable| + |unary?| |normalForm| |fullPartialFraction| |mainForm| + |exponentialOrder| |generalLambert| |bitand| |radix| |checkForZero| + |isMult| |colorFunction| |nthCoef| |dualSignature| |f04arf| + |linearAssociatedLog| |univariate?| |norm| |df2fi| |lflimitedint| + |makeCos| |henselFact| |genericLeftMinimalPolynomial| + |semiDiscriminantEuclidean| |factorsOfCyclicGroupSize| |d02raf| + |clipSurface| |leftTraceMatrix| |cCos| |quadraticNorm| |s20adf| + |expenseOfEvaluation| |regularRepresentation| |minPoints3D| |nthr| + |euclideanGroebner| |mapdiv| |RemainderList| |fullDisplay| |s21bcf| + |mathieu22| |triangular?| |mat| |rischDEsys| |debug| |An| |failed| + |enqueue!| |gderiv| |SturmHabichtMultiple| |SFunction| |denomRicDE| + |arity| |getOrder| |substring?| D |equiv| |diophantineSystem| + |product| |degreeSubResultantEuclidean| |imagJ| |graphState| |f02axf| + |scan| |makeYoungTableau| |hermiteH| |clearDenominator| |yellow| + |extractBottom!| |df2mf| |padecf| |coleman| |suffix?| |clipBoolean| + |exponential1| |stosePrepareSubResAlgo| |truncate| |unitNormalize| + |setleft!| |numericalIntegration| |contours| |axes| |llprop| + |repeatUntilLoop| |nil| |associator| |cosSinInfo| |tail| |log| + |univariate| |prefix?| |prepareSubResAlgo| |real?| |laguerreL| + |Lazard| |readable?| |transform| |LazardQuotient| |f02fjf| |init| + |increase| |polygon| |leftRegularRepresentation| |isList| |besselJ| + |minrank| |macroExpand| |rangePascalTriangle| |medialSet| |cyclic?| + |radicalOfLeftTraceForm| |sumSquares| |plotPolar| |varList| + |OMputEndBind| |generic| |nextColeman| |currentCategoryFrame| + |cyclotomicFactorization| |critMonD1| |approximate| |complexLimit| + |OMgetVariable| |reverseLex| |toseSquareFreePart| |neglist| + |sizePascalTriangle| |constantOpIfCan| |complex| |probablyZeroDim?| + |max| |yCoord| |ScanRoman| |padicFraction| |processTemplate| + |totalDegree| |positiveRemainder| |computeCycleLength| |primeFactor| + |expenseOfEvaluationIF| |rotatez| |monicLeftDivide| + |removeConstantTerm| |conjugate| |infieldint| |print| |iilog| |solve| + |stoseInvertible?sqfreg| |properties| |extendedEuclidean| |c05nbf| + |toroidal| |infix?| |romberg| |resolve| |e04ycf| |invmultisect| + |translate| |powerSum| |invertibleElseSplit?| |lieAlgebra?| |mask| + |squareFreeLexTriangular| |declare| |OMgetSymbol| |laguerre| |pack!| + |more?| |scaleRoots| |firstUncouplingMatrix| |crest| |fprindINFO| + |acothIfCan| |coshIfCan| |quoByVar| |numberOfDivisors| |Beta| + |groebnerFactorize| |weights| |asecIfCan| |factor1| |cotIfCan| + |supDimElseRittWu?| |leftCharacteristicPolynomial| |OMputEndApp| + |prime?| |cylindrical| |palglimint0| |bitTruth| |green| + |selectMultiDimensionalRoutines| |integralBasisAtInfinity| |updatF| + |optional?| GE |vark| |numericIfCan| |solid?| |light| + |createLowComplexityNormalBasis| |OMputEndBVar| |complete| + |scanOneDimSubspaces| GT |getOperator| |airyAi| |karatsuba| |edf2df| + |goto| |fractRadix| |randnum| |s21baf| |say| |OMputVariable| + |components| LE |sequences| |cycleRagits| |delta| |moduloP| + |alternative?| |hdmpToDmp| |binarySearchTree| |readInt8!| LT + |sizeLess?| |conditionsForIdempotents| |numberOfFactors| |deepExpand| + |signatureAst| |e01bff| |fortranCharacter| |frobenius| + |setIntersection| |internal?| |plus| |f04adf| |upperCase?| |ef2edf| + |s17dlf| |writeByte!| |resetVariableOrder| |parabolic| |d01amf| + |outputAsScript| |OMconnOutDevice| |children| |normalized?| + |genericRightMinimalPolynomial| |powmod| |shift| + |integralMatrixAtInfinity| |prefixRagits| |csch2sinh| |recolor| + |extendIfCan| |OMgetApp| |remove| |ParCond| |eigenMatrix| + |setImagSteps| |redpps| |rightTraceMatrix| + |halfExtendedSubResultantGcd1| |pushucoef| |cosh2sech| + |listYoungTableaus| |mapDown!| |over| |leftPower| |OMUnknownCD?| + |times| |monicRightFactorIfCan| |insertTop!| + |unrankImproperPartitions1| |mesh| |showAll?| |last| + |rationalApproximation| |morphism| |parseString| |partitions| + |lastSubResultantElseSplit| |generator| |aQuadratic| |iisqrt3| + |logpart| |mantissa| |algebraicDecompose| |collectQuasiMonic| + |symmetricTensors| |assoc| |genericRightTrace| |s17adf| + |factorGroebnerBasis| |stFuncN| |iiasinh| |useEisensteinCriterion| + |transcendentalDecompose| |lfinfieldint| |numberOfFractionalTerms| + |cyclicEntries| |antiCommutative?| |eof?| UTS2UP |quasiRegular| + |OMreceive| |e02zaf| BY |fixPredicate| |symmetric?| |before?| + |condition| |ratDsolve| |part?| |d02ejf| |s19abf| |rightScalarTimes!| + |monom| |fortranCompilerName| |callForm?| |linSolve| |content| + |OMgetEndAtp| |printHeader| |rowEchelon| |deepestTail| |ode| + |UpTriBddDenomInv| |omError| |symbol?| |mightHaveRoots| |Nul| + |acscIfCan| |s17acf| |removeZeroes| |monicRightDivide| + |leadingBasisTerm| |OMputBVar| |largest| |OMencodingXML| |erf| + |makeCrit| |mainVariables| |getExplanations| |c06gqf| |output| + |common| |showScalarValues| |patternMatchTimes| |pointLists| |mapmult| + |leftRankPolynomial| |weakBiRank| |denominators| |curry| |Lazard2| + |e04fdf| |permutation| |printCode| |makeSin| |cAcsc| |constant| + |generalizedInverse| |integral| |irreducibleFactor| + |inputOutputBinaryFile| |constructor| |split!| |sh| |finiteBasis| + |linearDependence| |leftExactQuotient| |dilog| |powerAssociative?| + |relativeApprox| NOT |create| |extractClosed| |tablePow| |incr| + |presuper| |groebner?| |mvar| |point?| |sin| |function| |ricDsolve| + |initializeGroupForWordProblem| OR |interval| |extendedint| |key?| + |hi| |nor| |binaryFunction| |isAbsolutelyIrreducible?| |move| |cos| + |extract!| |stiffnessAndStabilityOfODEIF| |d01bbf| AND |rightTrim| + |fixedPointExquo| |homogeneous?| |factorOfDegree| |cCsc| |lyndon| + |separant| |tan| |d01apf| |infinite?| |logIfCan| |outputAsTex| + |leftTrim| |deepestInitial| |e01bhf| |reducedDiscriminant| + |simplifyExp| |reindex| |cot| |distFact| |derivationCoordinates| + |addMatchRestricted| |chiSquare1| |linearPart| |componentUpperBound| + |realRoots| |hue| |setStatus!| |sec| |groebgen| |cot2trig| |entry?| + |permutationGroup| |splitNodeOf!| |perfectNthPower?| |KrullNumber| + |monicDecomposeIfCan| |evenInfiniteProduct| |csc| |symbol| |shufflein| + |pToHdmp| |quadratic?| |e02dcf| |chebyshevU| |lastSubResultant| + |d03edf| |wholePart| |setDifference| |asin| |expression| |moebiusMu| + |csc2sin| |normalizeAtInfinity| |traceMatrix| |repeating| |tab1| + |setPosition| |twoFactor| |f01rdf| |acos| |functorData| |integer| + |nil?| |destruct| |directSum| |showTheSymbolTable| |derivative| + |rightMult| |f01qef| |legendreP| |biRank| |splitLinear| |atan| + |removeRoughlyRedundantFactorsInPols| |showArrayValues| |setright!| + |viewZoomDefault| |setref| |solveLinearlyOverQ| + |coercePreimagesImages| |findCycle| |anfactor| + |stripCommentsAndBlanks| |acot| |s19aaf| |abs| |f2st| |hasPredicate?| + |cAcos| |extractTop!| |readLineIfCan!| |expandLog| |rightRemainder| + |asec| |jordanAdmissible?| |changeWeightLevel| * |normalizeIfCan| + |subHeight| |minus!| |lhs| |createMultiplicationTable| |lex| + |triangSolve| |kroneckerDelta| |acsc| |rightAlternative?| + |complexRoots| |lcm| |dflist| |karatsubaDivide| + |fortranCarriageReturn| |rhs| |nand| |approxSqrt| |f02agf| |cSinh| + |sinh| |lazyPseudoQuotient| |low| |represents| |mulmod| |one?| + |generate| |diff| |laplacian| |lighting| |plenaryPower| |principal?| + |cosh| |createIrreduciblePoly| |idealiserMatrix| |anticoord| |append| + |hash| = |currentEnv| |clearTheFTable| |returns| |tValues| |isImplies| + |pattern| |floor| |tanh| |count| |gcd| |symbolTableOf| + |complexNormalize| |cAcot| |commutativeEquality| |incrementBy| + |normInvertible?| |associates?| |groebSolve| |initTable!| + |showTheFTable| |nonLinearPart| |coth| |e02ajf| |false| |lp| + |atrapezoidal| < |removeSuperfluousQuasiComponents| |decomposeFunc| + |expand| |category| |rationalPoint?| |getZechTable| |pmintegrate| + |ptree| |sin2csc| |solve1| |flatten| |rightRecip| |inGroundField?| + |OMParseError?| > |root| |filterWhile| |domain| |intPatternMatch| + |conjugates| |diagonal| |loadNativeModule| |poisson| + |oblateSpheroidal| |pushup| |sub| <= |parent| |generators| + |filterUntil| |package| |iiasech| |asinhIfCan| |interpolate| |message| + |tanh2trigh| |minimalPolynomial| |unit?| |overbar| >= |externalList| + |matrixDimensions| |select| |cycleLength| |separateDegrees| + |defineProperty| |OMgetEndError| |polCase| |prod| |algebraicSort| + |hdmpToP| |exactQuotient!| |packageCall| |double| |drawStyle| |space| + |delete!| |polarCoordinates| |parts| |exponents| + |integralDerivationMatrix| |genus| |bezoutResultant| |weighted| + |squareFreePolynomial| |arbitrary| |complex?| |OMopenString| + |viewDeltaYDefault| |figureUnits| |c06fpf| |characteristicSet| + |dominantTerm| |zeroSetSplit| + |makeprod| |setAdaptive3D| + |palginfieldint| |mappingAst| |summation| |parents| |s21bbf| |rarrow| + |linearlyDependentOverZ?| |qualifier| |univariatePolynomialsGcds| - + |controlPanel| |determinant| |inspect| |blue| |solveRetract| + |createMultiplicationMatrix| |maximumExponent| |getBadValues| + |completeSmith| |f02abf| / |c02aff| |pToDmp| |remainder| |rule| + |prindINFO| |reflect| |birth| |tanintegrate| + |solveLinearPolynomialEquation| |makeRecord| |collect| |difference| + |univariateSolve| |createRandomElement| |twist| |s17dgf| + |lastSubResultantEuclidean| |outerProduct| |setCondition!| + |trapezoidal| |functionIsFracPolynomial?| |algebraic?| + |internalIntegrate0| |pleskenSplit| |e01sef| |byteBuffer| |bounds| + |declare!| |fibonacci| |initiallyReduce| |assign| |removeDuplicates| + |selectFiniteRoutines| |startPolynomial| |selectOrPolynomials| + |roughBasicSet| |operators| |zeroDimPrimary?| + |resultantReduitEuclidean| |selectODEIVPRoutines| + |intermediateResultsIF| |computeBasis| |outputArgs| |lllip| + |noLinearFactor?| |coerceP| |bivariateSLPEBR| |irreducible?| |s21bdf| + |minPoly| |imagE| |factorSquareFreeByRecursion| |headReduced?| |rules| + |discriminantEuclidean| |algebraicVariables| |composite| |palgLODE| + |nullary?| |rdHack1| |e02ddf| |halfExtendedSubResultantGcd2| + |showAllElements| |nextNormalPoly| |basisOfLeftNucleus| |setEpilogue!| + |iitan| |definingInequation| |step| |taylorIfCan| |makeUnit| + |finiteBound| |prepareDecompose| |errorInfo| |cAsinh| |inconsistent?| + |stirling1| |swap!| |linGenPos| |airyBi| |backOldPos| |zeroDim?| + |any?| |constantOperator| |stoseSquareFreePart| |returnTypeOf| + |tan2trig| |unitVector| |segment| |diagonalProduct| |quotedOperators| + |topPredicate| |leastMonomial| |stopMusserTrials| |sumOfDivisors| + |genericPosition| |palgint| |cyclicCopy| |signAround| |f04faf| + |htrigs| |outlineRender| |zeroDimPrime?| |transcendenceDegree| + |expextendedint| |block| |OMconnInDevice| |ip4Address| |bindings| + |c05adf| |s13acf| |parametric?| |iiacosh| |commutator| |OMputString| + |atom?| |writeUInt8!| |scripted?| |pushuconst| |alphabetic?| + |integral?| |iExquo| |primlimitedint| |recip| |normalDenom| + |pushNewContour| |putProperties| |leadingSupport| |merge| + |associatedEquations| |key| |cAsin| |resultant| |multiple?| + |setScreenResolution| |errorKind| |leftDiscriminant| |closeComponent| + |color| |clip| |connect| |maxColIndex| |value| |upperBound| + |divisorCascade| |drawToScale| |linears| |filename| |exists?| + |factorList| |bits| |closedCurve?| |exprToXXP| |HenselLift| + |taylorQuoByVar| |optional| |polyRDE| |supersub| |imagK| + |approxNthRoot| |mathieu12| |times!| |rightLcm| |lazyGintegrate| + |duplicates| |formula| |parse| |d01asf| |car| |minset| |nextSublist| + |prime| |squareFreePrim| |initials| |explicitlyFinite?| |stop| + |substitute| |nextLatticePermutation| |component| |insert!| + |setProperties| |s14abf| |evenlambert| |mr| |arguments| + |resetBadValues| |front| |var1StepsDefault| |leftRank| |seed| + |readIfCan!| |bumptab| |fortranDouble| |disjunction| |relerror| + |getConstant| |intChoose| |rischNormalize| |limitedint| + |chineseRemainder| |imagk| |iifact| |infLex?| |d01gbf| |nrows| + |result| |subPolSet?| |shiftRight| |c05pbf| |ceiling| |accuracyIF| + |d01anf| |stoseIntegralLastSubResultant| |members| + |SturmHabichtCoefficients| |odd?| |ncols| |groebnerIdeal| |OMputBind| + |universe| |rk4qc| |symmetricProduct| |sPol| |subNodeOf?| + |patternVariable| |latex| |bsolve| |e04mbf| |setMaxPoints3D| + |shrinkable| |mapSolve| |tower| |explicitlyEmpty?| |preprocess| + |symmetricPower| |minRowIndex| |routines| |e04gcf| |colorDef| |iiacos| + |divideIfCan| |c06frf| |squareFree| |rootProduct| |scale| |freeOf?| + |rootsOf| |bezoutMatrix| |totalGroebner| |indiceSubResultantEuclidean| + |compactFraction| |taylor| |comment| |conjunction| |OMputApp| + |setPredicates| |thenBranch| |hexDigit| |zeroMatrix| |knownInfBasis| + |mainMonomial| |numerator| |laurent| |semiResultantReduitEuclidean| + |elementary| |qroot| LODO2FUN |toScale| |e02dff| |choosemon| + |property| |expt| |puiseux| |basisOfCommutingElements| + |continuedFraction| |quasiMonicPolynomials| |makeFR| |matrix| |index| + |rroot| |mainValue| |reducedQPowers| |diagonals| |deleteRoutine!| + |pointColorPalette| |monomRDEsys| RF2UTS |jokerMode| |midpoint| + |cyclotomicDecomposition| |elements| |semiDegreeSubResultantEuclidean| + |uniform01| |inv| |aCubic| |lambda| |critMTonD1| |highCommonTerms| + |primextintfrac| |dmpToP| |leftNorm| |exprHasLogarithmicWeights| + |elliptic?| |s20acf| |att2Result| |float?| |setRealSteps| |ground?| + |f01bsf| |exprToGenUPS| |partition| |jacobiIdentity?| |pair| + |doubleResultant| |ground| |prinpolINFO| |showRegion| |iiGamma| + |primaryDecomp| |fixedPoint| |rightExtendedGcd| |unaryFunction| + |mesh?| |addPoint| |squareFreeFactors| |directory| + |identitySquareMatrix| |decreasePrecision| |increasePrecision| + |OMencodingUnknown| |mainPrimitivePart| |leadingMonomial| + |primPartElseUnitCanonical| |factorset| |hypergeometric0F1| + |viewThetaDefault| |hasHi| |sum| |basisOfRightNucloid| + |possiblyNewVariety?| |phiCoord| |reverse| |OMgetType| |pade| + |leadingCoefficient| |pomopo!| |style| |rightOne| |setClipValue| + |integrate| |simplifyPower| |listRepresentation| |ideal| |graphs| + |primitiveMonomials| |leftFactorIfCan| |d01gaf| |makeEq| + |numericalOptimization| |resultantnaif| |e02bbf| |retract| + |bipolarCylindrical| |varselect| |basisOfCenter| |flagFactor| + |lSpaceBasis| |reductum| |addMatch| |pol| |increment| |lowerCase?| + |makeFloatFunction| |OMputFloat| |OMsupportsCD?| |s17def| + |roughEqualIdeals?| |divide| |torsion?| |multiEuclidean| + |trivialIdeal?| |inRadical?| |characteristic| |rank| + |removeSquaresIfCan| |sincos| |putColorInfo| |const| + |stopTableInvSet!| |mindeg| |mathieu24| |primPartElseUnitCanonical!| + |rightDivide| |monomialIntegrate| |f04axf| |bottom!| + |hasTopPredicate?| |definingPolynomial| |iicoth| |exprToUPS| + |argumentList!| |OMgetInteger| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-908 $ #3=(-1194)) -3765 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-913 (-1194)) |has| |#1| (-913 (-1194))) ((-915 #3#) -3765 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-898 (-389)) |has| |#1| (-898 (-389))) ((-898 (-575)) |has| |#1| (-898 (-575))) ((-896 |#1|) . T) ((-924) -12 (|has| |#1| (-316)) (|has| |#1| (-924))) ((-935) -3765 (|has| |#1| (-359)) (|has| |#1| (-373)) (|has| |#1| (-316))) ((-1019) -12 (|has| |#1| (-1019)) (|has| |#1| (-1220))) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 |#1|) . T) ((-1068 #0#) -3765 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1068 |#1|) . T) ((-1068 $) . T) ((-1073 #0#) -3765 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1073 |#1|) . T) ((-1073 $) . T) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1169) |has| |#1| (-359)) ((-1220) |has| |#1| (-1220)) ((-1223) |has| |#1| (-1220)) ((-1235) . 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T) ((-234 $) -3763 (|has| |#1| (-359)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) -3763 (|has| |#1| (-359)) (|has| |#1| (-238))) ((-237) -3763 (|has| |#1| (-359)) (|has| |#1| (-237)) (|has| |#1| (-238))) ((-271 |#1|) . T) ((-248) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-293) |has| |#1| (-1220)) ((-295 |#1| $) |has| |#1| (-295 |#1| |#1|)) ((-299) -3763 (|has| |#1| (-567)) (|has| |#1| (-359)) (|has| |#1| (-373)) (|has| |#1| (-316))) ((-316) -3763 (|has| |#1| (-359)) (|has| |#1| (-373)) (|has| |#1| (-316))) ((-318 |#1|) |has| |#1| (-318 |#1|)) ((-373) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-413) |has| |#1| (-359)) ((-378) -3763 (|has| |#1| (-378)) (|has| |#1| (-359))) ((-359) |has| |#1| (-359)) ((-380 |#1| #1#) . T) ((-420 |#1| #1#) . T) ((-348 |#1|) . T) ((-387 |#1|) . T) ((-411 |#1|) . T) ((-422 |#1|) . 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T) ((-908 $ #3=(-1194)) -3763 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-913 (-1194)) |has| |#1| (-913 (-1194))) ((-915 #3#) -3763 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-898 (-389)) |has| |#1| (-898 (-389))) ((-898 (-575)) |has| |#1| (-898 (-575))) ((-896 |#1|) . T) ((-924) -12 (|has| |#1| (-316)) (|has| |#1| (-924))) ((-935) -3763 (|has| |#1| (-359)) (|has| |#1| (-373)) (|has| |#1| (-316))) ((-1019) -12 (|has| |#1| (-1019)) (|has| |#1| (-1220))) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 |#1|) . T) ((-1068 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1068 |#1|) . T) ((-1068 $) . T) ((-1073 #0#) -3763 (|has| |#1| (-359)) (|has| |#1| (-373))) ((-1073 |#1|) . T) ((-1073 $) . T) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1169) |has| |#1| (-359)) ((-1220) |has| |#1| (-1220)) ((-1223) |has| |#1| (-1220)) ((-1235) . 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(-782)) NIL (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066)))) (($ $ (-655 (-1194))) NIL (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066)))) (($ $ (-1194)) NIL (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066)))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1066))) (($ $ (-1 |#2| |#2|) (-782)) NIL (|has| |#2| (-1066)))) (-3981 (((-112) $ $) NIL (|has| |#2| (-861)))) (-3956 (((-112) $ $) NIL (|has| |#2| (-861)))) (-3914 (((-112) $ $) 27 (|has| |#2| (-1117)))) (-3970 (((-112) $ $) NIL (|has| |#2| (-861)))) (-3943 (((-112) $ $) 66 (|has| |#2| (-861)))) (-4038 (($ $ |#2|) NIL (|has| |#2| (-373)))) (-4028 (($ $ $) NIL (|has| |#2| (-21))) (($ $) NIL (|has| |#2| (-21)))) (-4016 (($ $ $) 34 (|has| |#2| (-25)))) (** (($ $ (-782)) NIL (|has| |#2| (-1066))) (($ $ (-936)) NIL (|has| |#2| (-1066)))) (* (($ $ $) 46 (|has| |#2| (-1066))) (($ $ |#2|) 44 (|has| |#2| (-737))) (($ |#2| $) 45 (|has| |#2| (-737))) (($ (-575) $) NIL (|has| |#2| (-21))) (($ (-782) $) NIL (|has| |#2| (-23))) (($ (-936) $) NIL (|has| |#2| (-25)))) (-2871 (((-782) $) NIL (|has| $ (-6 -4460))))) +((-1975 (*1 *1 *2) (-12 (-5 *2 (-1285 *4)) (-4 *4 (-1235)) (-4 *1 (-243 *3 *4)))) (-4126 (*1 *1 *2) (-12 (-5 *2 (-936)) (-4 *1 (-243 *3 *4)) (-4 *4 (-1066)) (-4 *4 (-1235)))) (-2988 (*1 *2 *1 *1) (-12 (-4 *1 (-243 *3 *2)) (-4 *2 (-1235)) (-4 *2 (-1066))))) +(-13 (-615 (-575) |t#2|) (-624 (-1285 |t#2|)) (-10 -8 (-6 -4460) (-15 -1975 ($ (-1285 |t#2|))) (IF (|has| |t#2| (-1117)) (-6 (-422 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1066)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-232 |t#2|)) (-6 (-387 |t#2|)) (-15 -4126 ($ (-936))) (-15 -2988 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-737)) (-6 (-651 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-378)) (-6 (-378)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-728 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4457)) (-6 -4457) |%noBranch|) (IF (|has| |t#2| (-861)) (-6 (-861)) |%noBranch|) (IF (|has| |t#2| (-804)) (-6 (-804)) |%noBranch|) (IF (|has| |t#2| (-373)) (-6 (-1292 |t#2|)) |%noBranch|))) +(((-21) -3763 (|has| |#2| (-1066)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -3763 (|has| |#2| (-1066)) (|has| |#2| (-804)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -3763 (|has| |#2| (-1066)) (|has| |#2| (-804)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -3763 (|has| |#2| (-1117)) (|has| |#2| (-1066)) (|has| |#2| (-861)) (|has| |#2| (-804)) (|has| |#2| (-737)) (|has| |#2| (-378)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3763 (|has| |#2| (-1066)) (|has| |#2| (-373)) (|has| |#2| (-174))) ((-132) -3763 (|has| |#2| (-1066)) (|has| |#2| (-804)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-627 #0=(-418 (-575))) -12 (|has| |#2| (-1055 (-418 (-575)))) (|has| |#2| (-1117))) ((-627 (-575)) -3763 (|has| |#2| (-1066)) (-12 (|has| |#2| (-1055 (-575))) (|has| |#2| (-1117)))) ((-627 |#2|) |has| |#2| (-1117)) ((-624 (-873)) -3763 (|has| |#2| (-1117)) (|has| |#2| (-1066)) (|has| |#2| (-861)) (|has| |#2| (-804)) (|has| |#2| (-737)) (|has| |#2| (-378)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-624 (-873))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-624 (-1285 |#2|)) . T) ((-234 $) -3763 (-12 (|has| |#2| (-237)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1066)))) ((-232 |#2|) |has| |#2| (-1066)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1066))) ((-237) -3763 (-12 (|has| |#2| (-237)) (|has| |#2| (-1066))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1066)))) ((-271 |#2|) |has| |#2| (-1066)) ((-295 #1=(-575) |#2|) . T) ((-297 #1# |#2|) . T) ((-318 |#2|) -12 (|has| |#2| (-318 |#2|)) (|has| |#2| (-1117))) ((-378) |has| |#2| (-378)) ((-387 |#2|) |has| |#2| (-1066)) ((-422 |#2|) |has| |#2| (-1117)) ((-500 |#2|) . T) ((-615 #1# |#2|) . T) ((-525 |#2| |#2|) -12 (|has| |#2| (-318 |#2|)) (|has| |#2| (-1117))) ((-657 (-575)) -3763 (|has| |#2| (-1066)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-657 |#2|) -3763 (|has| |#2| (-1066)) (|has| |#2| (-737)) (|has| |#2| (-373)) (|has| |#2| (-174))) ((-657 $) |has| |#2| (-1066)) ((-659 #2=(-575)) -12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066))) ((-659 |#2|) -3763 (|has| |#2| (-1066)) (|has| |#2| (-373)) (|has| |#2| (-174))) ((-659 $) |has| |#2| (-1066)) ((-651 |#2|) -3763 (|has| |#2| (-737)) (|has| |#2| (-373)) (|has| |#2| (-174))) ((-650 #2#) -12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066))) ((-650 |#2|) |has| |#2| (-1066)) ((-728 |#2|) -3763 (|has| |#2| (-373)) (|has| |#2| (-174))) ((-737) |has| |#2| (-1066)) ((-803) |has| |#2| (-804)) ((-804) |has| |#2| (-804)) ((-805) |has| |#2| (-804)) ((-806) |has| |#2| (-804)) ((-861) -3763 (|has| |#2| (-861)) (|has| |#2| (-804))) ((-908 $ #3=(-1194)) -3763 (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066)))) ((-913 (-1194)) -12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066))) ((-915 #3#) -3763 (-12 (|has| |#2| (-915 (-1194))) (|has| |#2| (-1066))) (-12 (|has| |#2| (-913 (-1194))) (|has| |#2| (-1066)))) ((-1055 #0#) -12 (|has| |#2| (-1055 (-418 (-575)))) (|has| |#2| (-1117))) ((-1055 (-575)) -12 (|has| |#2| (-1055 (-575))) (|has| |#2| (-1117))) ((-1055 |#2|) |has| |#2| (-1117)) ((-1068 |#2|) -3763 (|has| |#2| (-1066)) (|has| |#2| (-737)) (|has| |#2| (-373)) (|has| |#2| (-174))) ((-1073 |#2|) -3763 (|has| |#2| (-1066)) (|has| |#2| (-373)) (|has| |#2| (-174))) ((-1066) |has| |#2| (-1066)) ((-1075) |has| |#2| (-1066)) ((-1129) |has| |#2| (-1066)) ((-1117) -3763 (|has| |#2| (-1117)) (|has| |#2| (-1066)) (|has| |#2| (-861)) (|has| |#2| (-804)) (|has| |#2| (-737)) (|has| |#2| (-378)) (|has| |#2| (-373)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1235) . T) ((-1292 |#2|) |has| |#2| (-373))) +((-3436 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2302 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-2544 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -3436 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2302 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2544 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-782) (-1235) (-1235)) (T -244)) +((-2544 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-782)) (-4 *6 (-1235)) (-4 *7 (-1235)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2302 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-782)) (-4 *6 (-1235)) (-4 *2 (-1235)) (-5 *1 (-244 *5 *6 *2)))) (-3436 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-782)) (-4 *7 (-1235)) (-4 *5 (-1235)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) +(-10 -7 (-15 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(((-418 (-575)) $) NIL (-12 (|has| |#2| (-1055 (-418 (-575)))) (|has| |#2| (-1117)))) ((|#2| $) 28 (|has| |#2| (-1117)))) (-2862 (((-700 (-575)) (-1285 $)) NIL (-12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066)))) (((-700 (-575)) (-700 $)) NIL (-12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066)))) (((-2 (|:| -3415 (-700 (-575))) (|:| |vec| (-1285 (-575)))) (-700 $) (-1285 $)) NIL (-12 (|has| |#2| (-650 (-575))) (|has| |#2| (-1066)))) (((-2 (|:| -3415 (-700 |#2|)) (|:| |vec| (-1285 |#2|))) (-700 $) (-1285 $)) NIL (|has| |#2| (-1066))) (((-700 |#2|) (-700 $)) NIL (|has| |#2| (-1066))) (((-700 |#2|) (-1285 $)) NIL (|has| |#2| (-1066)))) (-4162 (((-3 $ "failed") $) 58 (|has| |#2| (-1066)))) (-2073 (($) NIL (|has| |#2| (-378)))) (-2857 ((|#2| $ (-575) |#2|) NIL (|has| $ (-6 -4461)))) (-2786 ((|#2| $ (-575)) 56)) (-3999 (((-655 |#2|) $) 14 (|has| $ (-6 -4460)))) (-3900 (((-112) $) NIL (|has| |#2| (-1066)))) (-3541 (((-112) $ (-782)) NIL)) (-2569 (((-575) $) 19 (|has| (-575) (-861)))) (-1914 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-418 (-575)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-627 #0#) -3765 (|has| |#1| (-1055 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575))))) ((-627 (-575)) . T) ((-627 |#1|) . T) ((-627 |#2|) . T) ((-627 |#3|) . T) ((-627 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-624 (-873)) . T) ((-174) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-625 (-547)) -12 (|has| |#1| (-625 (-547))) (|has| |#3| (-625 (-547)))) ((-625 (-904 (-389))) -12 (|has| |#1| (-625 (-904 (-389)))) (|has| |#3| (-625 (-904 (-389))))) ((-625 (-904 (-575))) -12 (|has| |#1| (-625 (-904 (-575)))) (|has| |#3| (-625 (-904 (-575))))) ((-234 $) -3765 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -3765 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-271 |#1|) . T) ((-299) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-318 $) . T) ((-335 |#1| |#4|) . T) ((-387 |#1|) . T) ((-422 |#1|) . T) ((-463) -3765 (|has| |#1| (-924)) (|has| |#1| (-463))) ((-525 |#2| |#1|) |has| |#1| (-238)) ((-525 |#2| $) |has| |#1| (-238)) ((-525 |#3| |#1|) . T) ((-525 |#3| $) . T) ((-525 $ $) . T) ((-567) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-657 #0#) |has| |#1| (-38 (-418 (-575)))) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 $) . T) ((-659 #0#) |has| |#1| (-38 (-418 (-575)))) ((-659 #1=(-575)) |has| |#1| (-650 (-575))) ((-659 |#1|) . T) ((-659 $) . T) ((-651 #0#) |has| |#1| (-38 (-418 (-575)))) ((-651 |#1|) |has| |#1| (-174)) ((-651 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-650 #1#) |has| |#1| (-650 (-575))) ((-650 |#1|) . T) ((-728 #0#) |has| |#1| (-38 (-418 (-575)))) ((-728 |#1|) |has| |#1| (-174)) ((-728 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-737) . T) ((-908 $ #2=(-1194)) -3765 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-908 $ |#3|) . T) ((-913 (-1194)) |has| |#1| (-913 (-1194))) ((-913 |#3|) . T) ((-915 #2#) -3765 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-915 |#3|) . T) ((-898 (-389)) -12 (|has| |#1| (-898 (-389))) (|has| |#3| (-898 (-389)))) ((-898 (-575)) -12 (|has| |#1| (-898 (-575))) (|has| |#3| (-898 (-575)))) ((-964 |#1| |#4| |#3|) . T) ((-924) |has| |#1| (-924)) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 |#1|) . T) ((-1055 |#2|) . T) ((-1055 |#3|) . T) ((-1068 #0#) |has| |#1| (-38 (-418 (-575)))) ((-1068 |#1|) . T) ((-1068 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-1073 #0#) |has| |#1| (-38 (-418 (-575)))) ((-1073 |#1|) . T) ((-1073 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1235) . T) ((-1239) |has| |#1| (-924))) -((-2861 (((-112) $ $) 19 (|has| |#1| (-1117)))) (-1596 ((|#1| $) 55)) (-2010 ((|#1| $) 45)) (-1845 (((-112) $ (-782)) 8)) (-3011 (($) 7 T CONST)) (-4162 (($ $) 61)) (-1789 (($ $) 49)) (-2620 ((|#1| |#1| $) 47)) (-4065 ((|#1| $) 46)) (-4001 (((-655 |#1|) $) 31 (|has| $ (-6 -4460)))) (-3896 (((-112) $ (-782)) 9)) (-3955 (((-655 |#1|) $) 30 (|has| $ (-6 -4460)))) (-2625 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1117)) (|has| $ (-6 -4460))))) (-2847 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4461)))) (-2550 (($ (-1 |#1| |#1|) $) 36)) (-4026 (((-112) $ (-782)) 10)) (-1839 (((-782) $) 62)) (-2288 (((-1176) $) 22 (|has| |#1| (-1117)))) (-4012 ((|#1| $) 40)) (-1997 ((|#1| |#1| $) 53)) (-3488 ((|#1| |#1| $) 52)) (-3862 (($ |#1| $) 41)) (-3343 (((-782) $) 56)) (-3912 (((-1137) $) 21 (|has| |#1| (-1117)))) (-2392 ((|#1| $) 63)) (-3691 ((|#1| $) 51)) (-2004 ((|#1| $) 50)) (-2454 ((|#1| $) 42)) (-3207 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4460)))) (-3048 (($ $ (-655 (-303 |#1|))) 27 (-12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (($ $ (-303 |#1|)) 26 (-12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117)))) (($ $ (-655 |#1|) (-655 |#1|)) 24 (-12 (|has| |#1| (-318 |#1|)) (|has| |#1| (-1117))))) (-3753 (((-112) $ $) 14)) (-2818 ((|#1| |#1| $) 59)) (-4076 (((-112) $) 11)) (-1938 (($) 12)) (-2906 ((|#1| $) 60)) (-1505 (($) 58) (($ (-655 |#1|)) 57)) (-3323 (((-782) $) 44)) (-3925 (((-782) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4460))) (((-782) |#1| $) 29 (-12 (|has| |#1| (-1117)) (|has| $ (-6 -4460))))) (-3078 (($ $) 13)) (-2883 (((-873) $) 18 (|has| |#1| (-624 (-873))))) (-1959 ((|#1| $) 54)) (-4400 (((-112) $ $) 23 (|has| |#1| (-1117)))) (-1511 (($ (-655 |#1|)) 43)) (-4315 ((|#1| $) 64)) (-3771 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4460)))) (-3914 (((-112) $ $) 20 (|has| |#1| (-1117)))) (-2871 (((-782) $) 6 (|has| $ (-6 -4460))))) +((-1470 (*1 *2 *3) (-12 (-4 *4 (-1066)) (-4 *3 (-861)) (-4 *5 (-274 *3)) (-4 *6 (-804)) (-5 *2 (-1 *1 (-782))) (-4 *1 (-259 *4 *3 *5 *6)))) (-2425 (*1 *2 *1) (-12 (-4 *1 (-259 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-655 *4)))) (-3369 (*1 *2 *1 *3) (-12 (-4 *1 (-259 *4 *3 *5 *6)) (-4 *4 (-1066)) (-4 *3 (-861)) (-4 *5 (-274 *3)) (-4 *6 (-804)) (-5 *2 (-782)))) (-3369 (*1 *2 *1) (-12 (-4 *1 (-259 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-782)))) (-1753 (*1 *2 *1 *3) (-12 (-4 *1 (-259 *4 *3 *5 *6)) (-4 *4 (-1066)) (-4 *3 (-861)) (-4 *5 (-274 *3)) (-4 *6 (-804)) (-5 *2 (-782)))) (-3552 (*1 *2 *1) (-12 (-4 *1 (-259 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-655 (-782))))) (-2213 (*1 *2 *1) (-12 (-4 *1 (-259 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-782)))) (-3552 (*1 *2 *1 *3) (-12 (-4 *1 (-259 *4 *3 *5 *6)) (-4 *4 (-1066)) (-4 *3 (-861)) (-4 *5 (-274 *3)) (-4 *6 (-804)) (-5 *2 (-655 (-782))))) (-2213 (*1 *2 *1 *3) (-12 (-4 *1 (-259 *4 *3 *5 *6)) (-4 *4 (-1066)) (-4 *3 (-861)) (-4 *5 (-274 *3)) (-4 *6 (-804)) (-5 *2 (-782)))) (-3187 (*1 *2 *1) (-12 (-4 *1 (-259 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-112)))) (-2141 (*1 *2 *1) (-12 (-4 *1 (-259 *3 *4 *2 *5)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-804)) (-4 *2 (-274 *4)))) (-2814 (*1 *1 *1) (-12 (-4 *1 (-259 *2 *3 *4 *5)) (-4 *2 (-1066)) (-4 *3 (-861)) (-4 *4 (-274 *3)) (-4 *5 (-804)))) (-3783 (*1 *1 *1) (-12 (-4 *1 (-259 *2 *3 *4 *5)) (-4 *2 (-1066)) (-4 *3 (-861)) (-4 *4 (-274 *3)) (-4 *5 (-804)))) (-1470 (*1 *2 *1) (-12 (-4 *3 (-238)) (-4 *3 (-1066)) (-4 *4 (-861)) (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-1 *1 (-782))) (-4 *1 (-259 *3 *4 *5 *6))))) +(-13 (-964 |t#1| |t#4| |t#3|) (-232 |t#1|) (-1055 |t#2|) (-10 -8 (-15 -1470 ((-1 $ (-782)) |t#2|)) (-15 -2425 ((-655 |t#2|) $)) (-15 -3369 ((-782) $ |t#2|)) (-15 -3369 ((-782) $)) (-15 -1753 ((-782) $ |t#2|)) (-15 -3552 ((-655 (-782)) $)) (-15 -2213 ((-782) $)) (-15 -3552 ((-655 (-782)) $ |t#2|)) (-15 -2213 ((-782) $ |t#2|)) (-15 -3187 ((-112) $)) (-15 -2141 (|t#3| $)) (-15 -2814 ($ $)) (-15 -3783 ($ $)) (IF (|has| |t#1| (-238)) (PROGN (-6 (-525 |t#2| |t#1|)) (-6 (-525 |t#2| $)) (-6 (-318 $)) (-15 -1470 ((-1 $ (-782)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-418 (-575)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-627 #0#) -3763 (|has| |#1| (-1055 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575))))) ((-627 (-575)) . T) ((-627 |#1|) . T) ((-627 |#2|) . T) ((-627 |#3|) . T) ((-627 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-624 (-873)) . T) ((-174) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-625 (-547)) -12 (|has| |#1| (-625 (-547))) (|has| |#3| (-625 (-547)))) ((-625 (-904 (-389))) -12 (|has| |#1| (-625 (-904 (-389)))) (|has| |#3| (-625 (-904 (-389))))) ((-625 (-904 (-575))) -12 (|has| |#1| (-625 (-904 (-575)))) (|has| |#3| (-625 (-904 (-575))))) ((-234 $) -3763 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -3763 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-271 |#1|) . T) ((-299) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-318 $) . T) ((-335 |#1| |#4|) . T) ((-387 |#1|) . T) ((-422 |#1|) . T) ((-463) -3763 (|has| |#1| (-924)) (|has| |#1| (-463))) ((-525 |#2| |#1|) |has| |#1| (-238)) ((-525 |#2| $) |has| |#1| (-238)) ((-525 |#3| |#1|) . T) ((-525 |#3| $) . T) ((-525 $ $) . T) ((-567) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-657 #0#) |has| |#1| (-38 (-418 (-575)))) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 $) . T) ((-659 #0#) |has| |#1| (-38 (-418 (-575)))) ((-659 #1=(-575)) |has| |#1| (-650 (-575))) ((-659 |#1|) . T) ((-659 $) . T) ((-651 #0#) |has| |#1| (-38 (-418 (-575)))) ((-651 |#1|) |has| |#1| (-174)) ((-651 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-650 #1#) |has| |#1| (-650 (-575))) ((-650 |#1|) . T) ((-728 #0#) |has| |#1| (-38 (-418 (-575)))) ((-728 |#1|) |has| |#1| (-174)) ((-728 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463))) ((-737) . T) ((-908 $ #2=(-1194)) -3763 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-908 $ |#3|) . T) ((-913 (-1194)) |has| |#1| (-913 (-1194))) ((-913 |#3|) . T) ((-915 #2#) -3763 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-915 |#3|) . T) ((-898 (-389)) -12 (|has| |#1| (-898 (-389))) (|has| |#3| (-898 (-389)))) ((-898 (-575)) -12 (|has| |#1| (-898 (-575))) (|has| |#3| (-898 (-575)))) ((-964 |#1| |#4| |#3|) . T) ((-924) |has| |#1| (-924)) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 |#1|) . T) ((-1055 |#2|) . T) ((-1055 |#3|) . T) ((-1068 #0#) |has| |#1| (-38 (-418 (-575)))) ((-1068 |#1|) . T) ((-1068 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-1073 #0#) |has| |#1| (-38 (-418 (-575)))) ((-1073 |#1|) . T) ((-1073 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-174))) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1235) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-418 (-575))) . T) ((-38 |#1|) . T) ((-38 $) . T) ((-102) . T) ((-111 #0# #0#) . T) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-627 #0#) . T) ((-627 (-575)) . T) ((-627 #1=(-1194)) |has| |#1| (-1055 (-1194))) ((-627 |#1|) . T) ((-627 $) . T) ((-624 (-873)) . T) ((-174) . T) ((-625 (-227)) |has| |#1| (-1039)) ((-625 (-389)) |has| |#1| (-1039)) ((-625 (-547)) |has| |#1| (-625 (-547))) ((-625 (-904 (-389))) |has| |#1| (-625 (-904 (-389)))) ((-625 (-904 (-575))) |has| |#1| (-625 (-904 (-575)))) ((-234 $) -3763 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-232 |#1|) . T) ((-238) |has| |#1| (-238)) ((-237) -3763 (|has| |#1| (-237)) (|has| |#1| (-238))) ((-271 |#1|) . T) ((-248) . T) ((-295 |#1| $) |has| |#1| (-295 |#1| |#1|)) ((-299) . T) ((-316) . T) ((-318 |#1|) |has| |#1| (-318 |#1|)) ((-373) . T) ((-348 |#1|) . T) ((-387 |#1|) . T) ((-411 |#1|) . T) ((-463) . 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T) ((-935) |has| |#1| (-373)) ((-1009 |#2|) |has| |#1| (-373)) ((-1019) |has| |#1| (-38 (-418 (-575)))) ((-1039) -12 (|has| |#1| (-373)) (|has| |#2| (-1039))) ((-1055 (-418 (-575))) -12 (|has| |#1| (-373)) (|has| |#2| (-1055 (-575)))) ((-1055 (-575)) -12 (|has| |#1| (-373)) (|has| |#2| (-1055 (-575)))) ((-1055 #2#) -12 (|has| |#1| (-373)) (|has| |#2| (-1055 (-1194)))) ((-1055 |#2|) . T) ((-1068 #1#) -3765 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-1068 |#1|) . T) ((-1068 |#2|) |has| |#1| (-373)) ((-1068 $) -3765 (|has| |#1| (-567)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1073 #1#) -3765 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-1073 |#1|) . T) ((-1073 |#2|) |has| |#1| (-373)) ((-1073 $) -3765 (|has| |#1| (-567)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1169) -12 (|has| |#1| (-373)) (|has| |#2| (-1169))) ((-1220) |has| |#1| (-38 (-418 (-575)))) ((-1223) |has| |#1| (-38 (-418 (-575)))) ((-1235) . 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T) ((-23) . T) ((-47 |#1| #0=(-575)) . T) ((-25) . T) ((-38 #1=(-418 (-575))) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-373)) ((-38 $) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-35) |has| |#1| (-38 (-418 (-575)))) ((-95) |has| |#1| (-38 (-418 (-575)))) ((-102) . T) ((-111 #1# #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-373)) ((-111 $ $) -3763 (|has| |#1| (-567)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-132) . T) ((-146) -3763 (-12 (|has| |#1| (-373)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -3763 (-12 (|has| |#1| (-373)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-627 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-627 (-575)) . T) ((-627 #2=(-1194)) -12 (|has| |#1| (-373)) (|has| |#2| (-1055 (-1194)))) ((-627 |#1|) |has| |#1| (-174)) ((-627 |#2|) . 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T) ((-659 |#2|) |has| |#1| (-373)) ((-659 $) . T) ((-651 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-651 |#1|) |has| |#1| (-174)) ((-651 |#2|) |has| |#1| (-373)) ((-651 $) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-650 #3#) -12 (|has| |#1| (-373)) (|has| |#2| (-650 (-575)))) ((-650 |#2|) |has| |#1| (-373)) ((-728 #1#) -3763 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-728 |#1|) |has| |#1| (-174)) ((-728 |#2|) |has| |#1| (-373)) ((-728 $) -3763 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-737) . 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T) ((-174) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-625 (-547)) -12 (|has| (-1099) (-625 (-547))) (|has| |#1| (-625 (-547)))) ((-625 (-904 (-389))) -12 (|has| (-1099) (-625 (-904 (-389)))) (|has| |#1| (-625 (-904 (-389))))) ((-625 (-904 (-575))) -12 (|has| (-1099) (-625 (-904 (-575)))) (|has| |#1| (-625 (-904 (-575))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-271 |#1|) . T) ((-295 (-418 $) (-418 $)) |has| |#1| (-567)) ((-295 |#1| |#1|) . T) ((-295 $ $) . T) ((-299) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-316) |has| |#1| (-373)) ((-318 $) . T) ((-335 |#1| #0#) . T) ((-387 |#1|) . T) ((-422 |#1|) . T) ((-463) -3765 (|has| |#1| (-924)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-525 #2# |#1|) . T) ((-525 #2# $) . T) ((-525 $ $) . T) ((-567) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-657 #1#) |has| |#1| (-38 (-418 (-575)))) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 $) . T) ((-659 #1#) |has| |#1| (-38 (-418 (-575)))) ((-659 #3=(-575)) |has| |#1| (-650 (-575))) ((-659 |#1|) . T) ((-659 $) . T) ((-651 #1#) |has| |#1| (-38 (-418 (-575)))) ((-651 |#1|) |has| |#1| (-174)) ((-651 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-650 #3#) |has| |#1| (-650 (-575))) ((-650 |#1|) . T) ((-728 #1#) |has| |#1| (-38 (-418 (-575)))) ((-728 |#1|) |has| |#1| (-174)) ((-728 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-737) . T) ((-908 $ #2#) . T) ((-908 $ #4=(-1194)) -3765 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-913 #2#) . T) ((-913 (-1194)) |has| |#1| (-913 (-1194))) ((-915 #2#) . T) ((-915 #4#) -3765 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-898 (-389)) -12 (|has| (-1099) (-898 (-389))) (|has| |#1| (-898 (-389)))) ((-898 (-575)) -12 (|has| (-1099) (-898 (-575))) (|has| |#1| (-898 (-575)))) ((-964 |#1| #0# #2#) . T) ((-924) |has| |#1| (-924)) ((-935) |has| |#1| (-373)) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 #2#) . T) ((-1055 |#1|) . T) ((-1068 #1#) |has| |#1| (-38 (-418 (-575)))) ((-1068 |#1|) . T) ((-1068 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1073 #1#) |has| |#1| (-38 (-418 (-575)))) ((-1073 |#1|) . T) ((-1073 $) -3765 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1169) |has| |#1| (-1169)) ((-1235) . T) ((-1239) |has| |#1| (-924))) -((-1606 (((-655 (-1099)) $) 34)) (-4406 (($ $) 31)) (-2417 (($ |#2| |#3|) NIL) (($ $ (-1099) |#3|) 28) (($ $ (-655 (-1099)) (-655 |#3|)) 27)) (-4371 (($ $) 14)) (-4383 ((|#2| $) 12)) (-2645 ((|#3| $) 10))) -(((-1262 |#1| |#2| |#3|) (-10 -8 (-15 -1606 ((-655 (-1099)) |#1|)) (-15 -2417 (|#1| |#1| (-655 (-1099)) (-655 |#3|))) (-15 -2417 (|#1| |#1| (-1099) |#3|)) (-15 -4406 (|#1| |#1|)) (-15 -2417 (|#1| |#2| |#3|)) (-15 -2645 (|#3| |#1|)) (-15 -4371 (|#1| |#1|)) (-15 -4383 (|#2| |#1|))) (-1263 |#2| |#3|) (-1066) (-803)) (T -1262)) -NIL -(-10 -8 (-15 -1606 ((-655 (-1099)) |#1|)) (-15 -2417 (|#1| |#1| (-655 (-1099)) (-655 |#3|))) (-15 -2417 (|#1| |#1| (-1099) |#3|)) (-15 -4406 (|#1| |#1|)) (-15 -2417 (|#1| |#2| |#3|)) (-15 -2645 (|#3| |#1|)) (-15 -4371 (|#1| |#1|)) (-15 -4383 (|#2| |#1|))) -((-2861 (((-112) $ $) 7)) (-3799 (((-112) $) 17)) (-1606 (((-655 (-1099)) $) 86)) (-1441 (((-1194) $) 118)) (-3370 (((-2 (|:| -3800 $) (|:| -4447 $) (|:| |associate| $)) $) 63 (|has| |#1| (-567)))) (-1540 (($ $) 64 (|has| |#1| (-567)))) (-3286 (((-112) $) 66 (|has| |#1| (-567)))) (-4080 (($ $ |#2|) 113) (($ $ |#2| |#2|) 112)) (-2144 (((-1174 (-2 (|:| |k| |#2|) (|:| |c| |#1|))) $) 119)) (-2597 (((-3 $ "failed") $ $) 20)) (-3011 (($) 18 T CONST)) (-4406 (($ $) 72)) (-1747 (((-3 $ "failed") $) 37)) (-2789 (((-112) $) 85)) (-2673 ((|#2| $) 115) ((|#2| $ |#2|) 114)) (-1542 (((-112) $) 35)) (-3461 (($ $ (-936)) 116)) (-2376 (((-112) $) 74)) (-2417 (($ |#1| |#2|) 73) (($ $ (-1099) |#2|) 88) (($ $ (-655 (-1099)) (-655 |#2|)) 87)) (-2550 (($ (-1 |#1| |#1|) $) 75)) (-4371 (($ $) 77)) (-4383 ((|#1| $) 78)) (-2288 (((-1176) $) 10)) (-3912 (((-1137) $) 11)) (-4276 (($ $ |#2|) 110)) (-2851 (((-3 $ "failed") $ $) 62 (|has| |#1| (-567)))) (-3048 (((-1174 |#1|) $ |#1|) 109 (|has| |#1| (-15 ** (|#1| |#1| |#2|))))) (-2070 ((|#1| $ |#2|) 120) (($ $ $) 96 (|has| |#2| (-1129)))) (-2389 (($ $ (-1194)) 108 (-12 (|has| |#1| (-913 (-1194))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-655 (-1194))) 106 (-12 (|has| |#1| (-913 (-1194))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-1194) (-782)) 105 (-12 (|has| |#1| (-913 (-1194))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $ (-655 (-1194)) (-655 (-782))) 104 (-12 (|has| |#1| (-913 (-1194))) (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (($ $) 100 (|has| |#1| (-15 * (|#1| |#2| |#1|)))) (($ $ (-782)) 98 (|has| |#1| (-15 * (|#1| |#2| |#1|))))) (-2645 ((|#2| $) 76)) (-2972 (($ $) 84)) (-2883 (((-873) $) 12) (($ (-575)) 33) (($ (-418 (-575))) 69 (|has| |#1| (-38 (-418 (-575))))) (($ $) 61 (|has| |#1| (-567))) (($ |#1|) 59 (|has| |#1| (-174)))) (-2012 ((|#1| $ |#2|) 71)) (-1518 (((-3 $ "failed") $) 60 (|has| |#1| (-146)))) (-3759 (((-782)) 32 T CONST)) (-1751 ((|#1| $) 117)) (-4400 (((-112) $ $) 9)) (-1780 (((-112) $ $) 65 (|has| |#1| (-567)))) (-3494 ((|#1| $ |#2|) 111 (-12 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) (|has| |#1| (-15 -2883 (|#1| (-1194))))))) (-1996 (($) 19 T CONST)) (-2009 (($) 34 T CONST)) 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(-2918 (*1 *2 *1) (-12 (-4 *1 (-1261 *3)) (-4 *3 (-1066)) (-5 *2 (-1190 *3)))) (-2132 (*1 *1 *2) (-12 (-5 *2 (-1190 *3)) (-4 *3 (-1066)) (-4 *1 (-1261 *3)))) (-1752 (*1 *1 *1 *2) (-12 (-5 *2 (-782)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)))) (-2720 (*1 *1 *1 *2) (|partial| -12 (-5 *2 (-782)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)))) (-1749 (*1 *2 *1 *1) (-12 (-4 *3 (-1066)) (-5 *2 (-2 (|:| -3262 *1) (|:| -4041 *1))) (-4 *1 (-1261 *3)))) (-3888 (*1 *2 *1 *3) (-12 (-5 *3 (-782)) (-4 *4 (-1066)) (-5 *2 (-2 (|:| -3262 *1) (|:| -4041 *1))) (-4 *1 (-1261 *4)))) (-4246 (*1 *1 *1 *2) (-12 (-5 *2 (-782)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)))) (-2681 (*1 *1 *1 *2) (-12 (-5 *2 (-782)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)))) (-2804 (*1 *1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)))) (-2382 (*1 *1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)))) (-2801 (*1 *2 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-174)))) (-4171 (*1 *2 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-174)))) (-2065 (*1 *2 *2 *2) (-12 (-5 *2 (-418 *1)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)) (-4 *3 (-567)))) (-3369 (*1 *2 *1 *1) (-12 (-4 *1 (-1261 *3)) (-4 *3 (-1066)) (-4 *3 (-567)) (-5 *2 (-782)))) (-1665 (*1 *1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-567)))) (-4095 (*1 *1 *1 *1) (|partial| -12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-567)))) (-4095 (*1 *2 *2 *1) (|partial| -12 (-5 *2 (-418 *1)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)) (-4 *3 (-567)))) (-2284 (*1 *1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-567)))) (-1568 (*1 *2 *1 *1) (-12 (-4 *3 (-567)) (-4 *3 (-1066)) (-5 *2 (-2 (|:| -1754 *3) (|:| -3262 *1) (|:| -4041 *1))) (-4 *1 (-1261 *3)))) (-2486 (*1 *2 *1 *1) (-12 (-4 *3 (-463)) (-4 *3 (-1066)) (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) (-4 *1 (-1261 *3)))) (-2065 (*1 *2 *3 *2) (-12 (-5 *3 (-418 *1)) (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-373)))) (-4388 (*1 *1 *1) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-38 (-418 (-575))))))) +(-13 (-964 |t#1| (-782) (-1099)) (-295 |t#1| |t#1|) (-295 $ $) (-238) (-232 |t#1|) (-10 -8 (-15 -1770 ((-1285 |t#1|) $ (-782))) (-15 -2918 ((-1190 |t#1|) $)) (-15 -2132 ($ (-1190 |t#1|))) (-15 -1752 ($ $ (-782))) (-15 -2720 ((-3 $ "failed") $ (-782))) (-15 -1749 ((-2 (|:| -3262 $) (|:| -4041 $)) $ $)) (-15 -3888 ((-2 (|:| -3262 $) (|:| -4041 $)) $ (-782))) (-15 -4246 ($ $ (-782))) (-15 -2681 ($ $ (-782))) (-15 -2804 ($ $ $)) (-15 -2382 ($ $ (-1 |t#1| |t#1|) $)) (IF (|has| |t#1| (-1169)) (-6 (-1169)) |%noBranch|) (IF (|has| |t#1| (-174)) (PROGN (-15 -2801 (|t#1| $)) (-15 -4171 (|t#1| $ $))) |%noBranch|) (IF (|has| |t#1| (-567)) (PROGN (-6 (-295 (-418 $) (-418 $))) (-15 -2065 ((-418 $) (-418 $) (-418 $))) (-15 -3369 ((-782) $ $)) (-15 -1665 ($ $ $)) (-15 -4095 ((-3 $ "failed") $ $)) (-15 -4095 ((-3 (-418 $) "failed") (-418 $) $)) (-15 -2284 ($ $ $)) (-15 -1568 ((-2 (|:| -1754 |t#1|) (|:| -3262 $) (|:| -4041 $)) $ $))) |%noBranch|) (IF (|has| |t#1| (-463)) (-15 -2486 ((-2 (|:| |primePart| $) (|:| |commonPart| $)) $ $)) |%noBranch|) (IF (|has| |t#1| (-373)) (PROGN (-6 (-316)) (-6 -4456) (-15 -2065 (|t#1| (-418 $) |t#1|))) |%noBranch|) (IF (|has| |t#1| (-38 (-418 (-575)))) (-15 -4388 ($ $)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| #0=(-782)) . T) ((-25) . T) ((-38 #1=(-418 (-575))) |has| |#1| (-38 (-418 (-575)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-418 (-575)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-627 #1#) -3763 (|has| |#1| (-1055 (-418 (-575)))) (|has| |#1| (-38 (-418 (-575))))) ((-627 (-575)) . T) ((-627 #2=(-1099)) . T) ((-627 |#1|) . T) ((-627 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-624 (-873)) . T) ((-174) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-625 (-547)) -12 (|has| (-1099) (-625 (-547))) (|has| |#1| (-625 (-547)))) ((-625 (-904 (-389))) -12 (|has| (-1099) (-625 (-904 (-389)))) (|has| |#1| (-625 (-904 (-389))))) ((-625 (-904 (-575))) -12 (|has| (-1099) (-625 (-904 (-575)))) (|has| |#1| (-625 (-904 (-575))))) ((-234 $) . T) ((-232 |#1|) . T) ((-238) . T) ((-237) . T) ((-271 |#1|) . T) ((-295 (-418 $) (-418 $)) |has| |#1| (-567)) ((-295 |#1| |#1|) . T) ((-295 $ $) . T) ((-299) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-316) |has| |#1| (-373)) ((-318 $) . T) ((-335 |#1| #0#) . T) ((-387 |#1|) . T) ((-422 |#1|) . T) ((-463) -3763 (|has| |#1| (-924)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-525 #2# |#1|) . T) ((-525 #2# $) . T) ((-525 $ $) . T) ((-567) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-657 #1#) |has| |#1| (-38 (-418 (-575)))) ((-657 (-575)) . T) ((-657 |#1|) . T) ((-657 $) . T) ((-659 #1#) |has| |#1| (-38 (-418 (-575)))) ((-659 #3=(-575)) |has| |#1| (-650 (-575))) ((-659 |#1|) . T) ((-659 $) . T) ((-651 #1#) |has| |#1| (-38 (-418 (-575)))) ((-651 |#1|) |has| |#1| (-174)) ((-651 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-650 #3#) |has| |#1| (-650 (-575))) ((-650 |#1|) . T) ((-728 #1#) |has| |#1| (-38 (-418 (-575)))) ((-728 |#1|) |has| |#1| (-174)) ((-728 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373))) ((-737) . T) ((-908 $ #2#) . T) ((-908 $ #4=(-1194)) -3763 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-913 #2#) . T) ((-913 (-1194)) |has| |#1| (-913 (-1194))) ((-915 #2#) . T) ((-915 #4#) -3763 (|has| |#1| (-915 (-1194))) (|has| |#1| (-913 (-1194)))) ((-898 (-389)) -12 (|has| (-1099) (-898 (-389))) (|has| |#1| (-898 (-389)))) ((-898 (-575)) -12 (|has| (-1099) (-898 (-575))) (|has| |#1| (-898 (-575)))) ((-964 |#1| #0# #2#) . T) ((-924) |has| |#1| (-924)) ((-935) |has| |#1| (-373)) ((-1055 (-418 (-575))) |has| |#1| (-1055 (-418 (-575)))) ((-1055 (-575)) |has| |#1| (-1055 (-575))) ((-1055 #2#) . T) ((-1055 |#1|) . T) ((-1068 #1#) |has| |#1| (-38 (-418 (-575)))) ((-1068 |#1|) . T) ((-1068 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1073 #1#) |has| |#1| (-38 (-418 (-575)))) ((-1073 |#1|) . T) ((-1073 $) -3763 (|has| |#1| (-924)) (|has| |#1| (-567)) (|has| |#1| (-463)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1066) . T) ((-1075) . T) ((-1129) . T) ((-1117) . T) ((-1169) |has| |#1| (-1169)) ((-1235) . 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T) ((-651 #1#) -3765 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-651 |#1|) |has| |#1| (-174)) ((-651 $) -3765 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-728 #1#) -3765 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-728 |#1|) |has| |#1| (-174)) ((-728 $) -3765 (|has| |#1| (-567)) (|has| |#1| (-373))) ((-737) . T) ((-908 $ #2=(-1194)) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194)))) ((-913 #2#) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194)))) ((-915 #2#) -12 (|has| |#1| (-15 * (|#1| (-418 (-575)) |#1|))) (|has| |#1| (-913 (-1194)))) ((-990 |#1| #0# (-1099)) . T) ((-935) |has| |#1| (-373)) ((-1019) |has| |#1| (-38 (-418 (-575)))) ((-1055 |#2|) . T) ((-1068 #1#) -3765 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-1068 |#1|) . T) ((-1068 $) -3765 (|has| |#1| (-567)) (|has| |#1| (-373)) (|has| |#1| (-174))) ((-1073 #1#) -3765 (|has| |#1| (-373)) (|has| |#1| (-38 (-418 (-575))))) ((-1073 |#1|) . 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NIL NIL NIL) (-1300 3209808 3211549 3211645 "XDPOLY" 3211650 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1299 3208615 3209215 3209258 "XALG" 3209263 NIL XALG (NIL T) -9 NIL 3209374 NIL) (-1298 3202057 3206592 3207086 "WUTSET" 3208207 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1297 3200313 3201109 3201432 "WP" 3201868 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1296 3199915 3200135 3200205 "WHILEAST" 3200265 T WHILEAST (NIL) -8 NIL NIL NIL) (-1295 3199387 3199632 3199726 "WHEREAST" 3199843 T WHEREAST (NIL) -8 NIL NIL NIL) (-1294 3198273 3198471 3198766 "WFFINTBS" 3199184 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1293 3196177 3196604 3197066 "WEIER" 3197845 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1292 3195223 3195673 3195715 "VSPACE" 3195851 NIL VSPACE (NIL T) -9 NIL 3195925 NIL) (-1291 3195061 3195088 3195179 "VSPACE-" 3195184 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1290 3194870 3194912 3194980 "VOID" 3195015 T VOID (NIL) -8 NIL NIL NIL) (-1289 3193006 3193365 3193771 "VIEW" 3194486 T VIEW (NIL) -7 NIL NIL NIL) (-1288 3189430 3190069 3190806 "VIEWDEF" 3192291 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1287 3178734 3180978 3183151 "VIEW3D" 3187279 T VIEW3D (NIL) -8 NIL NIL NIL) (-1286 3170985 3172645 3174224 "VIEW2D" 3177177 T VIEW2D (NIL) -8 NIL NIL NIL) (-1285 3166338 3170755 3170847 "VECTOR" 3170928 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1284 3164915 3165174 3165492 "VECTOR2" 3166068 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1283 3158357 3162666 3162709 "VECTCAT" 3163704 NIL VECTCAT (NIL T) -9 NIL 3164291 NIL) (-1282 3157371 3157625 3158015 "VECTCAT-" 3158020 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1281 3156825 3157022 3157142 "VARIABLE" 3157286 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1280 3156758 3156763 3156793 "UTYPE" 3156798 T UTYPE (NIL) -9 NIL NIL NIL) (-1279 3155588 3155742 3156004 "UTSODETL" 3156584 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1278 3153028 3153488 3154012 "UTSODE" 3155129 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1277 3144866 3150654 3151143 "UTS" 3152597 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1276 3135430 3140800 3140843 "UTSCAT" 3141955 NIL UTSCAT (NIL T) -9 NIL 3142713 NIL) (-1275 3132778 3133500 3134489 "UTSCAT-" 3134494 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1274 3132405 3132448 3132581 "UTS2" 3132729 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3126631 3129243 3129286 "URAGG" 3131356 NIL URAGG (NIL T) -9 NIL 3132079 NIL) (-1272 3123570 3124433 3125556 "URAGG-" 3125561 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1271 3119279 3122205 3122670 "UPXSSING" 3123234 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1270 3111345 3118526 3118799 "UPXS" 3119064 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1269 3104418 3111249 3111321 "UPXSCONS" 3111326 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1268 3093825 3100621 3100683 "UPXSCCA" 3101257 NIL UPXSCCA (NIL T T) -9 NIL 3101490 NIL) (-1267 3093463 3093548 3093722 "UPXSCCA-" 3093727 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1266 3082722 3089291 3089334 "UPXSCAT" 3089982 NIL UPXSCAT (NIL T) -9 NIL 3090591 NIL) (-1265 3082152 3082231 3082410 "UPXS2" 3082637 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1264 3080806 3081059 3081410 "UPSQFREE" 3081895 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1263 3074014 3077074 3077129 "UPSCAT" 3078209 NIL UPSCAT (NIL T T) -9 NIL 3078974 NIL) (-1262 3073218 3073425 3073752 "UPSCAT-" 3073757 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3058487 3066345 3066388 "UPOLYC" 3068489 NIL UPOLYC (NIL T) -9 NIL 3069710 NIL) (-1260 3049815 3052241 3055388 "UPOLYC-" 3055393 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1259 3049442 3049485 3049618 "UPOLYC2" 3049766 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1258 3041164 3049125 3049254 "UP" 3049361 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1257 3040503 3040610 3040774 "UPMP" 3041053 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1256 3040056 3040137 3040276 "UPDIVP" 3040416 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1255 3038624 3038873 3039189 "UPDECOMP" 3039805 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1254 3037855 3037967 3038153 "UPCDEN" 3038508 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1253 3037374 3037443 3037592 "UP2" 3037780 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1252 3035841 3036578 3036855 "UNISEG" 3037132 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1251 3035056 3035183 3035388 "UNISEG2" 3035684 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1250 3034116 3034296 3034522 "UNIFACT" 3034872 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1249 3017045 3033293 3033544 "ULS" 3033923 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3004908 3016949 3017021 "ULSCONS" 3017026 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1247 2985971 2998096 2998158 "ULSCCAT" 2998796 NIL ULSCCAT (NIL T T) -9 NIL 2999085 NIL) (-1246 2985021 2985266 2985654 "ULSCCAT-" 2985659 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1245 2974085 2980568 2980611 "ULSCAT" 2981474 NIL ULSCAT (NIL T) -9 NIL 2982205 NIL) (-1244 2973515 2973594 2973773 "ULS2" 2974000 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 2972634 2973144 2973251 "UINT8" 2973362 T UINT8 (NIL) -8 NIL NIL 2973447) (-1242 2971752 2972262 2972369 "UINT64" 2972480 T UINT64 (NIL) -8 NIL NIL 2972565) (-1241 2970870 2971380 2971487 "UINT32" 2971598 T UINT32 (NIL) -8 NIL NIL 2971683) (-1240 2969988 2970498 2970605 "UINT16" 2970716 T UINT16 (NIL) -8 NIL NIL 2970801) (-1239 2968291 2969248 2969278 "UFD" 2969490 T UFD (NIL) -9 NIL 2969604 NIL) (-1238 2968085 2968131 2968226 "UFD-" 2968231 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1237 2967167 2967350 2967566 "UDVO" 2967891 T UDVO (NIL) -7 NIL NIL NIL) (-1236 2964983 2965392 2965863 "UDPO" 2966731 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1235 2964916 2964921 2964951 "TYPE" 2964956 T TYPE (NIL) -9 NIL NIL NIL) (-1234 2964676 2964871 2964902 "TYPEAST" 2964907 T TYPEAST (NIL) -8 NIL NIL NIL) (-1233 2963647 2963849 2964089 "TWOFACT" 2964470 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1232 2962670 2963056 2963291 "TUPLE" 2963447 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1231 2960361 2960880 2961419 "TUBETOOL" 2962153 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1230 2959210 2959415 2959656 "TUBE" 2960154 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1229 2953939 2958182 2958465 "TS" 2958962 NIL TS (NIL T) -8 NIL NIL NIL) (-1228 2942579 2946698 2946795 "TSETCAT" 2952064 NIL TSETCAT (NIL T T T T) -9 NIL 2953595 NIL) (-1227 2937311 2938911 2940802 "TSETCAT-" 2940807 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1226 2931950 2932797 2933726 "TRMANIP" 2936447 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1225 2931391 2931454 2931617 "TRIMAT" 2931882 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1224 2929257 2929494 2929851 "TRIGMNIP" 2931140 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1223 2928777 2928890 2928920 "TRIGCAT" 2929133 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1222 2928446 2928525 2928666 "TRIGCAT-" 2928671 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1221 2925291 2927304 2927585 "TREE" 2928200 NIL TREE (NIL T) -8 NIL NIL NIL) (-1220 2924565 2925093 2925123 "TRANFUN" 2925158 T TRANFUN (NIL) -9 NIL 2925224 NIL) (-1219 2923844 2924035 2924315 "TRANFUN-" 2924320 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1218 2923648 2923680 2923741 "TOPSP" 2923805 T TOPSP (NIL) -7 NIL NIL NIL) (-1217 2922996 2923111 2923265 "TOOLSIGN" 2923529 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1216 2921630 2922173 2922412 "TEXTFILE" 2922779 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1215 2919542 2920083 2920512 "TEX" 2921223 T TEX (NIL) -8 NIL NIL NIL) (-1214 2919323 2919354 2919426 "TEX1" 2919505 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1213 2918971 2919034 2919124 "TEMUTL" 2919255 T TEMUTL (NIL) -7 NIL NIL NIL) (-1212 2917125 2917405 2917730 "TBCMPPK" 2918694 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1211 2908902 2915285 2915341 "TBAGG" 2915741 NIL TBAGG (NIL T T) -9 NIL 2915952 NIL) (-1210 2903972 2905460 2907214 "TBAGG-" 2907219 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1209 2903356 2903463 2903608 "TANEXP" 2903861 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1208 2902867 2903131 2903221 "TALGOP" 2903301 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1207 2896257 2902724 2902817 "TABLE" 2902822 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1206 2895669 2895768 2895906 "TABLEAU" 2896154 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1205 2890277 2891497 2892745 "TABLBUMP" 2894455 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1204 2889499 2889646 2889827 "SYSTEM" 2890118 T SYSTEM (NIL) -8 NIL NIL NIL) (-1203 2885958 2886657 2887440 "SYSSOLP" 2888750 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1202 2885756 2885913 2885944 "SYSPTR" 2885949 T SYSPTR (NIL) -8 NIL NIL NIL) (-1201 2884792 2885297 2885416 "SYSNNI" 2885602 NIL SYSNNI (NIL NIL) -8 NIL NIL 2885687) (-1200 2884091 2884550 2884629 "SYSINT" 2884689 NIL SYSINT (NIL NIL) -8 NIL NIL 2884734) (-1199 2880423 2881369 2882079 "SYNTAX" 2883403 T SYNTAX (NIL) -8 NIL NIL NIL) (-1198 2877581 2878183 2878815 "SYMTAB" 2879813 T SYMTAB (NIL) -8 NIL NIL NIL) (-1197 2872830 2873732 2874715 "SYMS" 2876620 T SYMS (NIL) -8 NIL NIL NIL) (-1196 2870065 2872288 2872518 "SYMPOLY" 2872635 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1195 2869582 2869657 2869780 "SYMFUNC" 2869977 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1194 2865602 2866894 2867707 "SYMBOL" 2868791 T SYMBOL (NIL) -8 NIL NIL NIL) (-1193 2859141 2860830 2862550 "SWITCH" 2863904 T SWITCH (NIL) -8 NIL NIL NIL) (-1192 2852375 2857962 2858265 "SUTS" 2858896 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2844441 2851622 2851895 "SUPXS" 2852160 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1190 2836111 2844059 2844185 "SUP" 2844350 NIL SUP (NIL T) -8 NIL NIL NIL) (-1189 2835270 2835397 2835614 "SUPFRACF" 2835979 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1188 2834891 2834950 2835063 "SUP2" 2835205 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1187 2833339 2833613 2833969 "SUMRF" 2834590 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1186 2832674 2832740 2832932 "SUMFS" 2833260 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1185 2815638 2831851 2832102 "SULS" 2832481 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1184 2815240 2815460 2815530 "SUCHTAST" 2815590 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1183 2814535 2814765 2814905 "SUCH" 2815148 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1182 2808402 2809441 2810400 "SUBSPACE" 2813623 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1181 2807832 2807922 2808086 "SUBRESP" 2808290 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1180 2801200 2802497 2803808 "STTF" 2806568 NIL STTF (NIL T) -7 NIL NIL NIL) (-1179 2795373 2796493 2797640 "STTFNC" 2800100 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1178 2786686 2788555 2790349 "STTAYLOR" 2793614 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1177 2779816 2786550 2786633 "STRTBL" 2786638 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1176 2775180 2779771 2779802 "STRING" 2779807 T STRING (NIL) -8 NIL NIL NIL) (-1175 2770009 2774523 2774553 "STRICAT" 2774612 T STRICAT (NIL) -9 NIL 2774674 NIL) (-1174 2762762 2767628 2768239 "STREAM" 2769433 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1173 2762272 2762349 2762493 "STREAM3" 2762679 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1172 2761254 2761437 2761672 "STREAM2" 2762085 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1171 2760942 2760994 2761087 "STREAM1" 2761196 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1170 2759958 2760139 2760370 "STINPROD" 2760758 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1169 2759510 2759720 2759750 "STEP" 2759830 T STEP (NIL) -9 NIL 2759908 NIL) (-1168 2758697 2758999 2759147 "STEPAST" 2759384 T STEPAST (NIL) -8 NIL NIL NIL) (-1167 2752129 2758596 2758673 "STBL" 2758678 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1166 2747224 2751320 2751363 "STAGG" 2751516 NIL STAGG (NIL T) -9 NIL 2751605 NIL) (-1165 2744926 2745528 2746400 "STAGG-" 2746405 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1164 2743073 2744696 2744788 "STACK" 2744869 NIL STACK (NIL T) -8 NIL NIL NIL) (-1163 2735768 2741214 2741670 "SREGSET" 2742703 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1162 2728193 2729562 2731075 "SRDCMPK" 2734374 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1161 2721078 2725603 2725633 "SRAGG" 2726936 T SRAGG (NIL) -9 NIL 2727544 NIL) (-1160 2720095 2720350 2720729 "SRAGG-" 2720734 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1159 2714466 2719042 2719463 "SQMATRIX" 2719721 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1158 2708151 2711184 2711911 "SPLTREE" 2713811 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1157 2704114 2704807 2705453 "SPLNODE" 2707577 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1156 2703161 2703394 2703424 "SPFCAT" 2703868 T SPFCAT (NIL) -9 NIL NIL NIL) (-1155 2701898 2702108 2702372 "SPECOUT" 2702919 T SPECOUT (NIL) -7 NIL NIL NIL) (-1154 2693008 2694880 2694910 "SPADXPT" 2699586 T SPADXPT (NIL) -9 NIL 2701750 NIL) (-1153 2692769 2692809 2692878 "SPADPRSR" 2692961 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1152 2690818 2692724 2692755 "SPADAST" 2692760 T SPADAST (NIL) -8 NIL NIL NIL) (-1151 2682763 2684536 2684579 "SPACEC" 2688952 NIL SPACEC (NIL T) -9 NIL 2690768 NIL) (-1150 2680893 2682695 2682744 "SPACE3" 2682749 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1149 2679645 2679816 2680107 "SORTPAK" 2680698 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1148 2677737 2678040 2678452 "SOLVETRA" 2679309 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1147 2676787 2677009 2677270 "SOLVESER" 2677510 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1146 2672091 2672979 2673974 "SOLVERAD" 2675839 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1145 2667906 2668515 2669244 "SOLVEFOR" 2671458 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1144 2662176 2667255 2667352 "SNTSCAT" 2667357 NIL SNTSCAT (NIL T T T T) -9 NIL 2667427 NIL) (-1143 2656282 2660499 2660890 "SMTS" 2661866 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1142 2650878 2656170 2656247 "SMP" 2656252 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1141 2649037 2649338 2649736 "SMITH" 2650575 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1140 2641328 2645616 2645719 "SMATCAT" 2647070 NIL SMATCAT (NIL NIL T T T) -9 NIL 2647620 NIL) (-1139 2638046 2638931 2640189 "SMATCAT-" 2640194 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1138 2635712 2637282 2637325 "SKAGG" 2637586 NIL SKAGG (NIL T) -9 NIL 2637721 NIL) (-1137 2631988 2635185 2635369 "SINT" 2635521 T SINT (NIL) -8 NIL NIL 2635683) (-1136 2631760 2631798 2631864 "SIMPAN" 2631944 T SIMPAN (NIL) -7 NIL NIL NIL) (-1135 2631039 2631295 2631435 "SIG" 2631642 T SIG (NIL) -8 NIL NIL NIL) (-1134 2629877 2630098 2630373 "SIGNRF" 2630798 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1133 2628710 2628861 2629145 "SIGNEF" 2629706 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1132 2628016 2628293 2628417 "SIGAST" 2628608 T SIGAST (NIL) -8 NIL NIL NIL) (-1131 2625706 2626160 2626666 "SHP" 2627557 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1130 2619711 2625607 2625683 "SHDP" 2625688 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1129 2619284 2619476 2619506 "SGROUP" 2619599 T SGROUP (NIL) -9 NIL 2619661 NIL) (-1128 2619142 2619168 2619241 "SGROUP-" 2619246 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1127 2615933 2616631 2617354 "SGCF" 2618441 T SGCF (NIL) -7 NIL NIL NIL) (-1126 2610301 2615380 2615477 "SFRTCAT" 2615482 NIL SFRTCAT (NIL T T T T) -9 NIL 2615521 NIL) (-1125 2603722 2604740 2605876 "SFRGCD" 2609284 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1124 2596848 2597921 2599107 "SFQCMPK" 2602655 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1123 2596468 2596557 2596668 "SFORT" 2596789 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1122 2595586 2596308 2596429 "SEXOF" 2596434 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1121 2594693 2595467 2595535 "SEX" 2595540 T SEX (NIL) -8 NIL NIL NIL) (-1120 2590474 2591189 2591284 "SEXCAT" 2593906 NIL SEXCAT (NIL T T T T T) -9 NIL 2594466 NIL) (-1119 2587627 2590408 2590456 "SET" 2590461 NIL SET (NIL T) -8 NIL NIL NIL) (-1118 2585851 2586340 2586645 "SETMN" 2587368 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1117 2585347 2585499 2585529 "SETCAT" 2585705 T SETCAT (NIL) -9 NIL 2585815 NIL) (-1116 2585039 2585117 2585247 "SETCAT-" 2585252 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1115 2581400 2583500 2583543 "SETAGG" 2584413 NIL SETAGG (NIL T) -9 NIL 2584753 NIL) (-1114 2580858 2580974 2581211 "SETAGG-" 2581216 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1113 2580301 2580554 2580655 "SEQAST" 2580779 T SEQAST (NIL) -8 NIL NIL NIL) (-1112 2579500 2579794 2579855 "SEGXCAT" 2580141 NIL SEGXCAT (NIL T T) -9 NIL 2580261 NIL) (-1111 2578506 2579166 2579348 "SEG" 2579353 NIL SEG (NIL T) -8 NIL NIL NIL) (-1110 2577485 2577699 2577742 "SEGCAT" 2578264 NIL SEGCAT (NIL T) -9 NIL 2578485 NIL) (-1109 2576417 2576848 2577056 "SEGBIND" 2577312 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1108 2576038 2576097 2576210 "SEGBIND2" 2576352 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1107 2575611 2575839 2575916 "SEGAST" 2575983 T SEGAST (NIL) -8 NIL NIL NIL) (-1106 2574830 2574956 2575160 "SEG2" 2575455 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1105 2574201 2574765 2574812 "SDVAR" 2574817 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1104 2566639 2573971 2574101 "SDPOL" 2574106 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1103 2565232 2565498 2565817 "SCPKG" 2566354 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1102 2564396 2564568 2564760 "SCOPE" 2565062 T SCOPE (NIL) -8 NIL NIL NIL) (-1101 2563616 2563750 2563929 "SCACHE" 2564251 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1100 2563262 2563448 2563478 "SASTCAT" 2563483 T SASTCAT (NIL) -9 NIL 2563496 NIL) (-1099 2562749 2563097 2563173 "SAOS" 2563208 T SAOS (NIL) -8 NIL NIL NIL) (-1098 2562314 2562349 2562522 "SAERFFC" 2562708 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1097 2556164 2562211 2562291 "SAE" 2562296 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1096 2555757 2555792 2555951 "SAEFACT" 2556123 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1095 2554078 2554392 2554793 "RURPK" 2555423 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1094 2552715 2553021 2553326 "RULESET" 2553912 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1093 2549938 2550468 2550926 "RULE" 2552396 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1092 2549550 2549732 2549815 "RULECOLD" 2549890 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1091 2549340 2549368 2549439 "RTVALUE" 2549501 T RTVALUE (NIL) -8 NIL NIL NIL) (-1090 2548811 2549057 2549151 "RSTRCAST" 2549268 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1089 2543659 2544454 2545374 "RSETGCD" 2548010 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1088 2532889 2537968 2538065 "RSETCAT" 2542184 NIL RSETCAT (NIL T T T T) -9 NIL 2543281 NIL) (-1087 2530816 2531355 2532179 "RSETCAT-" 2532184 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1086 2523202 2524578 2526098 "RSDCMPK" 2529415 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1085 2521181 2521648 2521722 "RRCC" 2522808 NIL RRCC (NIL T T) -9 NIL 2523152 NIL) (-1084 2520532 2520706 2520985 "RRCC-" 2520990 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1083 2519975 2520228 2520329 "RPTAST" 2520453 T RPTAST (NIL) -8 NIL NIL NIL) (-1082 2493638 2503087 2503154 "RPOLCAT" 2513820 NIL RPOLCAT (NIL T T T) -9 NIL 2516980 NIL) (-1081 2485136 2487476 2490598 "RPOLCAT-" 2490603 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1080 2476067 2483347 2483829 "ROUTINE" 2484676 T ROUTINE (NIL) -8 NIL NIL NIL) (-1079 2472814 2475693 2475833 "ROMAN" 2475949 T ROMAN (NIL) -8 NIL NIL NIL) (-1078 2471058 2471674 2471934 "ROIRC" 2472619 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1077 2467290 2469574 2469604 "RNS" 2469908 T RNS (NIL) -9 NIL 2470182 NIL) (-1076 2465799 2466182 2466716 "RNS-" 2466791 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1075 2465202 2465610 2465640 "RNG" 2465645 T RNG (NIL) -9 NIL 2465666 NIL) (-1074 2464205 2464567 2464769 "RNGBIND" 2465053 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1073 2463604 2463992 2464035 "RMODULE" 2464040 NIL RMODULE (NIL T) -9 NIL 2464067 NIL) (-1072 2462440 2462534 2462870 "RMCAT2" 2463505 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1071 2459290 2461786 2462083 "RMATRIX" 2462202 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1070 2452117 2454377 2454492 "RMATCAT" 2457851 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2458833 NIL) (-1069 2451492 2451639 2451946 "RMATCAT-" 2451951 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1068 2450893 2451114 2451157 "RLINSET" 2451351 NIL RLINSET (NIL T) -9 NIL 2451442 NIL) (-1067 2450460 2450535 2450663 "RINTERP" 2450812 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1066 2449518 2450072 2450102 "RING" 2450158 T RING (NIL) -9 NIL 2450250 NIL) (-1065 2449310 2449354 2449451 "RING-" 2449456 NIL RING- (NIL T) -8 NIL NIL NIL) (-1064 2448151 2448388 2448646 "RIDIST" 2449074 T RIDIST (NIL) -7 NIL NIL NIL) (-1063 2439440 2447619 2447825 "RGCHAIN" 2447999 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1062 2438790 2439196 2439237 "RGBCSPC" 2439295 NIL RGBCSPC (NIL T) -9 NIL 2439347 NIL) (-1061 2437948 2438329 2438370 "RGBCMDL" 2438602 NIL RGBCMDL (NIL T) -9 NIL 2438716 NIL) (-1060 2434942 2435556 2436226 "RF" 2437312 NIL RF (NIL T) -7 NIL NIL NIL) (-1059 2434588 2434651 2434754 "RFFACTOR" 2434873 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1058 2434313 2434348 2434445 "RFFACT" 2434547 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1057 2432430 2432794 2433176 "RFDIST" 2433953 T RFDIST (NIL) -7 NIL NIL NIL) (-1056 2431883 2431975 2432138 "RETSOL" 2432332 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1055 2431519 2431599 2431642 "RETRACT" 2431775 NIL RETRACT (NIL T) -9 NIL 2431862 NIL) (-1054 2431368 2431393 2431480 "RETRACT-" 2431485 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1053 2430970 2431190 2431260 "RETAST" 2431320 T RETAST (NIL) -8 NIL NIL NIL) (-1052 2423708 2430623 2430750 "RESULT" 2430865 T RESULT (NIL) -8 NIL NIL NIL) (-1051 2422299 2422977 2423176 "RESRING" 2423611 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1050 2421935 2421984 2422082 "RESLATC" 2422236 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1049 2421640 2421675 2421782 "REPSQ" 2421894 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1048 2419062 2419642 2420244 "REP" 2421060 T REP (NIL) -7 NIL NIL NIL) (-1047 2418759 2418794 2418905 "REPDB" 2419021 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1046 2412659 2414048 2415271 "REP2" 2417571 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1045 2409036 2409717 2410525 "REP1" 2411886 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1044 2401732 2407177 2407633 "REGSET" 2408666 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1043 2400497 2400880 2401130 "REF" 2401517 NIL REF (NIL T) -8 NIL NIL NIL) (-1042 2399874 2399977 2400144 "REDORDER" 2400381 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1041 2395842 2399087 2399314 "RECLOS" 2399702 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1040 2394894 2395075 2395290 "REALSOLV" 2395649 T REALSOLV (NIL) -7 NIL NIL NIL) (-1039 2394740 2394781 2394811 "REAL" 2394816 T REAL (NIL) -9 NIL 2394851 NIL) (-1038 2391223 2392025 2392909 "REAL0Q" 2393905 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1037 2386824 2387812 2388873 "REAL0" 2390204 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1036 2386295 2386541 2386635 "RDUCEAST" 2386752 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1035 2385700 2385772 2385979 "RDIV" 2386217 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1034 2384768 2384942 2385155 "RDIST" 2385522 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1033 2383365 2383652 2384024 "RDETRS" 2384476 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1032 2381177 2381631 2382169 "RDETR" 2382907 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1031 2379802 2380080 2380477 "RDEEFS" 2380893 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1030 2378311 2378617 2379042 "RDEEF" 2379490 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1029 2372372 2375292 2375322 "RCFIELD" 2376617 T RCFIELD (NIL) -9 NIL 2377348 NIL) (-1028 2370436 2370940 2371636 "RCFIELD-" 2371711 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1027 2366705 2368537 2368580 "RCAGG" 2369664 NIL RCAGG (NIL T) -9 NIL 2370129 NIL) (-1026 2366333 2366427 2366590 "RCAGG-" 2366595 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1025 2365668 2365780 2365945 "RATRET" 2366217 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1024 2365221 2365288 2365409 "RATFACT" 2365596 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1023 2364529 2364649 2364801 "RANDSRC" 2365091 T RANDSRC (NIL) -7 NIL NIL NIL) (-1022 2364263 2364307 2364380 "RADUTIL" 2364478 T RADUTIL (NIL) -7 NIL NIL NIL) (-1021 2357284 2363094 2363405 "RADIX" 2363986 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1020 2347952 2357126 2357256 "RADFF" 2357261 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1019 2347599 2347674 2347704 "RADCAT" 2347864 T RADCAT (NIL) -9 NIL NIL NIL) (-1018 2347381 2347429 2347529 "RADCAT-" 2347534 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1017 2345479 2347151 2347243 "QUEUE" 2347324 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1016 2341927 2345412 2345460 "QUAT" 2345465 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1015 2341558 2341601 2341732 "QUATCT2" 2341878 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2334571 2338008 2338050 "QUATCAT" 2338841 NIL QUATCAT (NIL T) -9 NIL 2339607 NIL) (-1013 2330710 2331747 2333137 "QUATCAT-" 2333233 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1012 2328175 2329786 2329829 "QUAGG" 2330210 NIL QUAGG (NIL T) -9 NIL 2330385 NIL) (-1011 2327777 2327997 2328067 "QQUTAST" 2328127 T QQUTAST (NIL) -8 NIL NIL NIL) (-1010 2326790 2327290 2327455 "QFORM" 2327658 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1009 2317364 2322692 2322734 "QFCAT" 2323402 NIL QFCAT (NIL T) -9 NIL 2324403 NIL) (-1008 2312709 2313972 2315646 "QFCAT-" 2315742 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1007 2312340 2312383 2312514 "QFCAT2" 2312660 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2311795 2311905 2312037 "QEQUAT" 2312230 T QEQUAT (NIL) -8 NIL NIL NIL) (-1005 2304921 2305994 2307180 "QCMPACK" 2310728 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1004 2302459 2302907 2303337 "QALGSET" 2304576 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1003 2301694 2301870 2302106 "QALGSET2" 2302277 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1002 2300379 2300603 2300922 "PWFFINTB" 2301467 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1001 2298554 2298722 2299078 "PUSHVAR" 2300193 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1000 2294443 2295497 2295540 "PTRANFN" 2297451 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-999 2292845 2293136 2293458 "PTPACK" 2294154 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-998 2292477 2292534 2292643 "PTFUNC2" 2292782 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-997 2286922 2291319 2291360 "PTCAT" 2291656 NIL PTCAT (NIL T) -9 NIL 2291809 NIL) (-996 2286580 2286615 2286739 "PSQFR" 2286881 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-995 2285175 2285473 2285807 "PSEUDLIN" 2286278 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-994 2271938 2274309 2276633 "PSETPK" 2282935 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-993 2264956 2267696 2267792 "PSETCAT" 2270813 NIL PSETCAT (NIL T T T T) -9 NIL 2271627 NIL) (-992 2262792 2263426 2264247 "PSETCAT-" 2264252 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-991 2262141 2262306 2262334 "PSCURVE" 2262602 T PSCURVE (NIL) -9 NIL 2262769 NIL) (-990 2258139 2259655 2259720 "PSCAT" 2260564 NIL PSCAT (NIL T T T) -9 NIL 2260804 NIL) (-989 2257202 2257418 2257818 "PSCAT-" 2257823 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-988 2255561 2256271 2256534 "PRTITION" 2256959 T PRTITION (NIL) -8 NIL NIL NIL) (-987 2255036 2255282 2255374 "PRTDAST" 2255489 T PRTDAST (NIL) -8 NIL NIL NIL) (-986 2244126 2246340 2248528 "PRS" 2252898 NIL PRS (NIL T T) -7 NIL NIL NIL) (-985 2241937 2243476 2243516 "PRQAGG" 2243699 NIL PRQAGG (NIL T) -9 NIL 2243801 NIL) (-984 2241273 2241578 2241606 "PROPLOG" 2241745 T PROPLOG (NIL) -9 NIL 2241860 NIL) (-983 2240877 2240934 2241057 "PROPFUN2" 2241196 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-982 2240192 2240313 2240485 "PROPFUN1" 2240738 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-981 2238373 2238939 2239236 "PROPFRML" 2239928 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-980 2237842 2237949 2238077 "PROPERTY" 2238265 T PROPERTY (NIL) -8 NIL NIL NIL) (-979 2231900 2236008 2236828 "PRODUCT" 2237068 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-978 2229178 2231358 2231592 "PR" 2231711 NIL PR (NIL T T) -8 NIL NIL NIL) (-977 2228974 2229006 2229065 "PRINT" 2229139 T PRINT (NIL) -7 NIL NIL NIL) (-976 2228314 2228431 2228583 "PRIMES" 2228854 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-975 2226379 2226780 2227246 "PRIMELT" 2227893 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-974 2226108 2226157 2226185 "PRIMCAT" 2226309 T PRIMCAT (NIL) -9 NIL NIL NIL) (-973 2222223 2226046 2226091 "PRIMARR" 2226096 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-972 2221230 2221408 2221636 "PRIMARR2" 2222041 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-971 2220873 2220929 2221040 "PREASSOC" 2221168 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-970 2220348 2220481 2220509 "PPCURVE" 2220714 T PPCURVE (NIL) -9 NIL 2220850 NIL) (-969 2219943 2220143 2220226 "PORTNUM" 2220285 T PORTNUM (NIL) -8 NIL NIL NIL) (-968 2217302 2217701 2218293 "POLYROOT" 2219524 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-967 2211395 2216906 2217066 "POLY" 2217175 NIL POLY (NIL T) -8 NIL NIL NIL) (-966 2210778 2210836 2211070 "POLYLIFT" 2211331 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-965 2207053 2207502 2208131 "POLYCATQ" 2210323 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-964 2193582 2198800 2198865 "POLYCAT" 2202379 NIL POLYCAT (NIL T T T) -9 NIL 2204257 NIL) (-963 2186809 2188733 2191197 "POLYCAT-" 2191202 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-962 2186396 2186464 2186584 "POLY2UP" 2186735 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-961 2186028 2186085 2186194 "POLY2" 2186333 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-960 2184713 2184952 2185228 "POLUTIL" 2185802 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-959 2183068 2183345 2183676 "POLTOPOL" 2184435 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-958 2178533 2183004 2183050 "POINT" 2183055 NIL POINT (NIL T) -8 NIL NIL NIL) (-957 2176720 2177077 2177452 "PNTHEORY" 2178178 T PNTHEORY (NIL) -7 NIL NIL NIL) (-956 2175178 2175475 2175874 "PMTOOLS" 2176418 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-955 2174771 2174849 2174966 "PMSYM" 2175094 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-954 2174279 2174348 2174523 "PMQFCAT" 2174696 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-953 2173634 2173744 2173900 "PMPRED" 2174156 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-952 2173027 2173113 2173275 "PMPREDFS" 2173535 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-951 2171691 2171899 2172277 "PMPLCAT" 2172789 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-950 2171223 2171302 2171454 "PMLSAGG" 2171606 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-949 2170696 2170772 2170954 "PMKERNEL" 2171141 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-948 2170313 2170388 2170501 "PMINS" 2170615 NIL PMINS (NIL T) -7 NIL NIL NIL) (-947 2169755 2169824 2170033 "PMFS" 2170238 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-946 2168983 2169101 2169306 "PMDOWN" 2169632 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-945 2168150 2168308 2168489 "PMASS" 2168822 T PMASS (NIL) -7 NIL NIL NIL) (-944 2167423 2167533 2167696 "PMASSFS" 2168037 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-943 2167078 2167146 2167240 "PLOTTOOL" 2167349 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-942 2161685 2162889 2164037 "PLOT" 2165950 T PLOT (NIL) -8 NIL NIL NIL) (-941 2157489 2158533 2159454 "PLOT3D" 2160784 T PLOT3D (NIL) -8 NIL NIL NIL) (-940 2156401 2156578 2156813 "PLOT1" 2157293 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-939 2131792 2136467 2141318 "PLEQN" 2151667 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-938 2131110 2131232 2131412 "PINTERP" 2131657 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-937 2130803 2130850 2130953 "PINTERPA" 2131057 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-936 2130019 2130567 2130654 "PI" 2130694 T PI (NIL) -8 NIL NIL 2130761) (-935 2128316 2129291 2129319 "PID" 2129501 T PID (NIL) -9 NIL 2129635 NIL) (-934 2128067 2128104 2128179 "PICOERCE" 2128273 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-933 2127387 2127526 2127702 "PGROEB" 2127923 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-932 2122974 2123788 2124693 "PGE" 2126502 T PGE (NIL) -7 NIL NIL NIL) (-931 2121097 2121344 2121710 "PGCD" 2122691 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-930 2120435 2120538 2120699 "PFRPAC" 2120981 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-929 2117075 2118983 2119336 "PFR" 2120114 NIL PFR (NIL T) -8 NIL NIL NIL) (-928 2115464 2115708 2116033 "PFOTOOLS" 2116822 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-927 2113997 2114236 2114587 "PFOQ" 2115221 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-926 2112498 2112710 2113066 "PFO" 2113781 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-925 2109051 2112387 2112456 "PF" 2112461 NIL PF (NIL NIL) -8 NIL NIL NIL) (-924 2106385 2107656 2107684 "PFECAT" 2108269 T PFECAT (NIL) -9 NIL 2108653 NIL) (-923 2105830 2105984 2106198 "PFECAT-" 2106203 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-922 2104433 2104685 2104986 "PFBRU" 2105579 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-921 2102299 2102651 2103083 "PFBR" 2104084 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-920 2098345 2099811 2100458 "PERM" 2101685 NIL PERM (NIL T) -8 NIL NIL NIL) (-919 2093579 2094552 2095422 "PERMGRP" 2097508 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-918 2091698 2092658 2092699 "PERMCAT" 2093099 NIL PERMCAT (NIL T) -9 NIL 2093397 NIL) (-917 2091351 2091392 2091516 "PERMAN" 2091651 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-916 2088839 2091016 2091138 "PENDTREE" 2091262 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-915 2087768 2087983 2088024 "PDSPC" 2088557 NIL PDSPC (NIL T) -9 NIL 2088802 NIL) (-914 2086871 2087089 2087451 "PDSPC-" 2087456 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-913 2085753 2086521 2086562 "PDRING" 2086567 NIL PDRING (NIL T) -9 NIL 2086595 NIL) (-912 2082968 2083746 2084414 "PDEPROB" 2085105 T PDEPROB (NIL) -8 NIL NIL NIL) (-911 2080513 2081017 2081572 "PDEPACK" 2082433 T PDEPACK (NIL) -7 NIL NIL NIL) (-910 2079425 2079615 2079866 "PDECOMP" 2080312 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-909 2077004 2077847 2077875 "PDECAT" 2078662 T PDECAT (NIL) -9 NIL 2079375 NIL) (-908 2076633 2076688 2076742 "PDDOM" 2076907 NIL PDDOM (NIL T T) -9 NIL 2076987 NIL) (-907 2076452 2076482 2076589 "PDDOM-" 2076594 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-906 2076203 2076236 2076326 "PCOMP" 2076413 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-905 2074381 2075004 2075301 "PBWLB" 2075932 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-904 2066854 2068454 2069792 "PATTERN" 2073064 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-903 2066486 2066543 2066652 "PATTERN2" 2066791 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-902 2064243 2064631 2065088 "PATTERN1" 2066075 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-901 2061611 2062192 2062673 "PATRES" 2063808 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-900 2061175 2061242 2061374 "PATRES2" 2061538 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-899 2059058 2059463 2059870 "PATMATCH" 2060842 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-898 2058568 2058777 2058818 "PATMAB" 2058925 NIL PATMAB (NIL T) -9 NIL 2059008 NIL) (-897 2057086 2057422 2057680 "PATLRES" 2058373 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-896 2056632 2056755 2056796 "PATAB" 2056801 NIL PATAB (NIL T) -9 NIL 2056973 NIL) (-895 2054814 2055209 2055632 "PARTPERM" 2056229 T PARTPERM (NIL) -7 NIL NIL NIL) (-894 2054435 2054498 2054600 "PARSURF" 2054745 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-893 2054067 2054124 2054233 "PARSU2" 2054372 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-892 2053831 2053871 2053938 "PARSER" 2054020 T PARSER (NIL) -7 NIL NIL NIL) (-891 2053452 2053515 2053617 "PARSCURV" 2053762 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-890 2053084 2053141 2053250 "PARSC2" 2053389 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-889 2052723 2052781 2052878 "PARPCURV" 2053020 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-888 2052355 2052412 2052521 "PARPC2" 2052660 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-887 2051416 2051728 2051910 "PARAMAST" 2052193 T PARAMAST (NIL) -8 NIL NIL NIL) (-886 2050936 2051022 2051141 "PAN2EXPR" 2051317 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-885 2049713 2050057 2050285 "PALETTE" 2050728 T PALETTE (NIL) -8 NIL NIL NIL) (-884 2048106 2048718 2049078 "PAIR" 2049399 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-883 2041885 2047363 2047558 "PADICRC" 2047960 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-882 2035009 2041229 2041414 "PADICRAT" 2041732 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-881 2033324 2034946 2034991 "PADIC" 2034996 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-880 2030434 2031998 2032038 "PADICCT" 2032619 NIL PADICCT (NIL NIL) -9 NIL 2032901 NIL) (-879 2029391 2029591 2029859 "PADEPAC" 2030221 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-878 2028603 2028736 2028942 "PADE" 2029253 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-877 2026990 2027811 2028091 "OWP" 2028407 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-876 2026483 2026696 2026793 "OVERSET" 2026913 T OVERSET (NIL) -8 NIL NIL NIL) (-875 2025529 2026088 2026260 "OVAR" 2026351 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-874 2024793 2024914 2025075 "OUT" 2025388 T OUT (NIL) -7 NIL NIL NIL) (-873 2013665 2015902 2018102 "OUTFORM" 2022613 T OUTFORM (NIL) -8 NIL NIL NIL) (-872 2013001 2013262 2013389 "OUTBFILE" 2013558 T OUTBFILE (NIL) -8 NIL NIL NIL) (-871 2012308 2012473 2012501 "OUTBCON" 2012819 T OUTBCON (NIL) -9 NIL 2012985 NIL) (-870 2011909 2012021 2012178 "OUTBCON-" 2012183 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-869 2011289 2011638 2011727 "OSI" 2011840 T OSI (NIL) -8 NIL NIL NIL) (-868 2010819 2011157 2011185 "OSGROUP" 2011190 T OSGROUP (NIL) -9 NIL 2011212 NIL) (-867 2009564 2009791 2010076 "ORTHPOL" 2010566 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-866 2007115 2009399 2009520 "OREUP" 2009525 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-865 2004518 2006806 2006933 "ORESUP" 2007057 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-864 2002046 2002546 2003107 "OREPCTO" 2004007 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-863 1995732 1997933 1997974 "OREPCAT" 2000322 NIL OREPCAT (NIL T) -9 NIL 2001426 NIL) (-862 1992879 1993661 1994719 "OREPCAT-" 1994724 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-861 1992030 1992328 1992356 "ORDSET" 1992665 T ORDSET (NIL) -9 NIL 1992829 NIL) (-860 1991461 1991609 1991833 "ORDSET-" 1991838 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-859 1990026 1990817 1990845 "ORDRING" 1991047 T ORDRING (NIL) -9 NIL 1991172 NIL) (-858 1989671 1989765 1989909 "ORDRING-" 1989914 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-857 1989051 1989514 1989542 "ORDMON" 1989547 T ORDMON (NIL) -9 NIL 1989568 NIL) (-856 1988213 1988360 1988555 "ORDFUNS" 1988900 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-855 1987551 1987970 1987998 "ORDFIN" 1988063 T ORDFIN (NIL) -9 NIL 1988137 NIL) (-854 1984110 1986137 1986546 "ORDCOMP" 1987175 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-853 1983376 1983503 1983689 "ORDCOMP2" 1983970 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-852 1979957 1980867 1981681 "OPTPROB" 1982582 T OPTPROB (NIL) -8 NIL NIL NIL) (-851 1976759 1977398 1978102 "OPTPACK" 1979273 T OPTPACK (NIL) -7 NIL NIL NIL) (-850 1974446 1975212 1975240 "OPTCAT" 1976059 T OPTCAT (NIL) -9 NIL 1976709 NIL) (-849 1973830 1974123 1974228 "OPSIG" 1974361 T OPSIG (NIL) -8 NIL NIL NIL) (-848 1973598 1973637 1973703 "OPQUERY" 1973784 T OPQUERY (NIL) -7 NIL NIL NIL) (-847 1970729 1971909 1972413 "OP" 1973127 NIL OP (NIL T) -8 NIL NIL NIL) (-846 1970103 1970329 1970370 "OPERCAT" 1970582 NIL OPERCAT (NIL T) -9 NIL 1970679 NIL) (-845 1969858 1969914 1970031 "OPERCAT-" 1970036 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-844 1966671 1968655 1969024 "ONECOMP" 1969522 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-843 1965976 1966091 1966265 "ONECOMP2" 1966543 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1965395 1965501 1965631 "OMSERVER" 1965866 T OMSERVER (NIL) -7 NIL NIL NIL) (-841 1962257 1964835 1964875 "OMSAGG" 1964936 NIL OMSAGG (NIL T) -9 NIL 1965000 NIL) (-840 1960880 1961143 1961425 "OMPKG" 1961995 T OMPKG (NIL) -7 NIL NIL NIL) (-839 1960310 1960413 1960441 "OM" 1960740 T OM (NIL) -9 NIL NIL NIL) (-838 1958857 1959859 1960028 "OMLO" 1960191 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-837 1957817 1957964 1958184 "OMEXPR" 1958683 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-836 1957108 1957363 1957499 "OMERR" 1957701 T OMERR (NIL) -8 NIL NIL NIL) (-835 1956259 1956529 1956689 "OMERRK" 1956968 T OMERRK (NIL) -8 NIL NIL NIL) (-834 1955710 1955936 1956044 "OMENC" 1956171 T OMENC (NIL) -8 NIL NIL NIL) (-833 1949605 1950790 1951961 "OMDEV" 1954559 T OMDEV (NIL) -8 NIL NIL NIL) (-832 1948674 1948845 1949039 "OMCONN" 1949431 T OMCONN (NIL) -8 NIL NIL NIL) (-831 1947195 1948171 1948199 "OINTDOM" 1948204 T OINTDOM (NIL) -9 NIL 1948225 NIL) (-830 1944533 1945883 1946220 "OFMONOID" 1946890 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-829 1943905 1944470 1944515 "ODVAR" 1944520 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-828 1941328 1943650 1943805 "ODR" 1943810 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-827 1933820 1941104 1941230 "ODPOL" 1941235 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-826 1927795 1933692 1933797 "ODP" 1933802 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-825 1926561 1926776 1927051 "ODETOOLS" 1927569 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-824 1923528 1924186 1924902 "ODESYS" 1925894 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-823 1918410 1919318 1920343 "ODERTRIC" 1922603 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-822 1917836 1917918 1918112 "ODERED" 1918322 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-821 1914724 1915272 1915949 "ODERAT" 1917259 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-820 1911683 1912148 1912745 "ODEPRRIC" 1914253 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-819 1909626 1910222 1910708 "ODEPROB" 1911217 T ODEPROB (NIL) -8 NIL NIL NIL) (-818 1906146 1906631 1907278 "ODEPRIM" 1909105 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-817 1905395 1905497 1905757 "ODEPAL" 1906038 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-816 1901557 1902348 1903212 "ODEPACK" 1904551 T ODEPACK (NIL) -7 NIL NIL NIL) (-815 1900618 1900725 1900947 "ODEINT" 1901446 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-814 1894719 1896144 1897591 "ODEIFTBL" 1899191 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-813 1890117 1890903 1891855 "ODEEF" 1893878 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-812 1889466 1889555 1889778 "ODECONST" 1890022 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-811 1887591 1888252 1888280 "ODECAT" 1888885 T ODECAT (NIL) -9 NIL 1889416 NIL) (-810 1884446 1887296 1887418 "OCT" 1887501 NIL OCT (NIL T) -8 NIL NIL NIL) (-809 1884084 1884127 1884254 "OCTCT2" 1884397 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-808 1878695 1881130 1881170 "OC" 1882267 NIL OC (NIL T) -9 NIL 1883125 NIL) (-807 1875922 1876670 1877660 "OC-" 1877754 NIL OC- (NIL T T) -8 NIL NIL NIL) (-806 1875274 1875742 1875770 "OCAMON" 1875775 T OCAMON (NIL) -9 NIL 1875796 NIL) (-805 1874805 1875146 1875174 "OASGP" 1875179 T OASGP (NIL) -9 NIL 1875199 NIL) (-804 1874066 1874555 1874583 "OAMONS" 1874623 T OAMONS (NIL) -9 NIL 1874666 NIL) (-803 1873480 1873913 1873941 "OAMON" 1873946 T OAMON (NIL) -9 NIL 1873966 NIL) (-802 1872738 1873256 1873284 "OAGROUP" 1873289 T OAGROUP (NIL) -9 NIL 1873309 NIL) (-801 1872428 1872478 1872566 "NUMTUBE" 1872682 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-800 1866001 1867519 1869055 "NUMQUAD" 1870912 T NUMQUAD (NIL) -7 NIL NIL NIL) (-799 1861757 1862745 1863770 "NUMODE" 1864996 T NUMODE (NIL) -7 NIL NIL NIL) (-798 1859112 1859992 1860020 "NUMINT" 1860943 T NUMINT (NIL) -9 NIL 1861707 NIL) (-797 1858060 1858257 1858475 "NUMFMT" 1858914 T NUMFMT (NIL) -7 NIL NIL NIL) (-796 1844419 1847364 1849896 "NUMERIC" 1855567 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-795 1838789 1843868 1843963 "NTSCAT" 1843968 NIL NTSCAT (NIL T T T T) -9 NIL 1844007 NIL) (-794 1837983 1838148 1838341 "NTPOLFN" 1838628 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-793 1825971 1834808 1835620 "NSUP" 1837204 NIL NSUP (NIL T) -8 NIL NIL NIL) (-792 1825603 1825660 1825769 "NSUP2" 1825908 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-791 1815740 1825377 1825510 "NSMP" 1825515 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-790 1814172 1814473 1814830 "NREP" 1815428 NIL NREP (NIL T) -7 NIL NIL NIL) (-789 1812763 1813015 1813373 "NPCOEF" 1813915 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-788 1811829 1811944 1812160 "NORMRETR" 1812644 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-787 1809870 1810160 1810569 "NORMPK" 1811537 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-786 1809555 1809583 1809707 "NORMMA" 1809836 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-785 1809355 1809512 1809541 "NONE" 1809546 T NONE (NIL) -8 NIL NIL NIL) (-784 1809144 1809173 1809242 "NONE1" 1809319 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-783 1808641 1808703 1808882 "NODE1" 1809076 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-782 1806922 1807773 1808028 "NNI" 1808375 T NNI (NIL) -8 NIL NIL 1808610) (-781 1805342 1805655 1806019 "NLINSOL" 1806590 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-780 1801583 1802578 1803477 "NIPROB" 1804463 T NIPROB (NIL) -8 NIL NIL NIL) (-779 1800340 1800574 1800876 "NFINTBAS" 1801345 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-778 1799514 1799990 1800031 "NETCLT" 1800203 NIL NETCLT (NIL T) -9 NIL 1800285 NIL) (-777 1798222 1798453 1798734 "NCODIV" 1799282 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-776 1797984 1798021 1798096 "NCNTFRAC" 1798179 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-775 1796164 1796528 1796948 "NCEP" 1797609 NIL NCEP (NIL T) -7 NIL NIL NIL) (-774 1795015 1795788 1795816 "NASRING" 1795926 T NASRING (NIL) -9 NIL 1796006 NIL) (-773 1794810 1794854 1794948 "NASRING-" 1794953 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-772 1793917 1794442 1794470 "NARNG" 1794587 T NARNG (NIL) -9 NIL 1794678 NIL) (-771 1793609 1793676 1793810 "NARNG-" 1793815 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-770 1792488 1792695 1792930 "NAGSP" 1793394 T NAGSP (NIL) -7 NIL NIL NIL) (-769 1783760 1785444 1787117 "NAGS" 1790835 T NAGS (NIL) -7 NIL NIL NIL) (-768 1782308 1782616 1782947 "NAGF07" 1783449 T NAGF07 (NIL) -7 NIL NIL NIL) (-767 1776846 1778137 1779444 "NAGF04" 1781021 T NAGF04 (NIL) -7 NIL NIL NIL) (-766 1769814 1771428 1773061 "NAGF02" 1775233 T NAGF02 (NIL) -7 NIL NIL NIL) (-765 1765038 1766138 1767255 "NAGF01" 1768717 T NAGF01 (NIL) -7 NIL NIL NIL) (-764 1758666 1760232 1761817 "NAGE04" 1763473 T NAGE04 (NIL) -7 NIL NIL NIL) (-763 1749835 1751956 1754086 "NAGE02" 1756556 T NAGE02 (NIL) -7 NIL NIL NIL) (-762 1745788 1746735 1747699 "NAGE01" 1748891 T NAGE01 (NIL) -7 NIL NIL NIL) (-761 1743583 1744117 1744675 "NAGD03" 1745250 T NAGD03 (NIL) -7 NIL NIL NIL) (-760 1735333 1737261 1739215 "NAGD02" 1741649 T NAGD02 (NIL) -7 NIL NIL NIL) (-759 1729144 1730569 1732009 "NAGD01" 1733913 T NAGD01 (NIL) -7 NIL NIL NIL) (-758 1725353 1726175 1727012 "NAGC06" 1728327 T NAGC06 (NIL) -7 NIL NIL NIL) (-757 1723818 1724150 1724506 "NAGC05" 1725017 T NAGC05 (NIL) -7 NIL NIL NIL) (-756 1723194 1723313 1723457 "NAGC02" 1723694 T NAGC02 (NIL) -7 NIL NIL NIL) (-755 1722153 1722736 1722776 "NAALG" 1722855 NIL NAALG (NIL T) -9 NIL 1722916 NIL) (-754 1721988 1722017 1722107 "NAALG-" 1722112 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-753 1715938 1717046 1718233 "MULTSQFR" 1720884 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-752 1715257 1715332 1715516 "MULTFACT" 1715850 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-751 1707928 1711842 1711895 "MTSCAT" 1712965 NIL MTSCAT (NIL T T) -9 NIL 1713480 NIL) (-750 1707640 1707694 1707786 "MTHING" 1707868 NIL MTHING (NIL T) -7 NIL NIL NIL) (-749 1707432 1707465 1707525 "MSYSCMD" 1707600 T MSYSCMD (NIL) -7 NIL NIL NIL) (-748 1703514 1706187 1706507 "MSET" 1707145 NIL MSET (NIL T) -8 NIL NIL NIL) (-747 1700583 1703075 1703116 "MSETAGG" 1703121 NIL MSETAGG (NIL T) -9 NIL 1703155 NIL) (-746 1696425 1697962 1698707 "MRING" 1699883 NIL MRING (NIL T T) -8 NIL NIL NIL) (-745 1695991 1696058 1696189 "MRF2" 1696352 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-744 1695609 1695644 1695788 "MRATFAC" 1695950 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-743 1693221 1693516 1693947 "MPRFF" 1695314 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-742 1687429 1693075 1693172 "MPOLY" 1693177 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-741 1686919 1686954 1687162 "MPCPF" 1687388 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-740 1686433 1686476 1686660 "MPC3" 1686870 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1685628 1685709 1685930 "MPC2" 1686348 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-738 1683929 1684266 1684656 "MONOTOOL" 1685288 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-737 1683154 1683471 1683499 "MONOID" 1683718 T MONOID (NIL) -9 NIL 1683865 NIL) (-736 1682700 1682819 1683000 "MONOID-" 1683005 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-735 1672435 1678478 1678537 "MONOGEN" 1679211 NIL MONOGEN (NIL T T) -9 NIL 1679667 NIL) (-734 1669653 1670388 1671388 "MONOGEN-" 1671507 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-733 1668486 1668932 1668960 "MONADWU" 1669352 T MONADWU (NIL) -9 NIL 1669590 NIL) (-732 1667858 1668017 1668265 "MONADWU-" 1668270 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-731 1667217 1667461 1667489 "MONAD" 1667696 T MONAD (NIL) -9 NIL 1667808 NIL) (-730 1666902 1666980 1667112 "MONAD-" 1667117 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-729 1665191 1665815 1666094 "MOEBIUS" 1666655 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-728 1664469 1664873 1664913 "MODULE" 1664918 NIL MODULE (NIL T) -9 NIL 1664957 NIL) (-727 1664037 1664133 1664323 "MODULE-" 1664328 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-726 1661717 1662401 1662728 "MODRING" 1663861 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-725 1658661 1659822 1660343 "MODOP" 1661246 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-724 1657249 1657728 1658005 "MODMONOM" 1658524 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-723 1647204 1655540 1655954 "MODMON" 1656886 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-722 1644360 1646048 1646324 "MODFIELD" 1647079 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-721 1643337 1643641 1643831 "MMLFORM" 1644190 T MMLFORM (NIL) -8 NIL NIL NIL) (-720 1642863 1642906 1643085 "MMAP" 1643288 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-719 1640942 1641709 1641750 "MLO" 1642173 NIL MLO (NIL T) -9 NIL 1642415 NIL) (-718 1638308 1638824 1639426 "MLIFT" 1640423 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-717 1637699 1637783 1637937 "MKUCFUNC" 1638219 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-716 1637298 1637368 1637491 "MKRECORD" 1637622 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-715 1636345 1636507 1636735 "MKFUNC" 1637109 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-714 1635733 1635837 1635993 "MKFLCFN" 1636228 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-713 1635010 1635112 1635297 "MKBCFUNC" 1635626 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-712 1631685 1634564 1634700 "MINT" 1634894 T MINT (NIL) -8 NIL NIL NIL) (-711 1630497 1630740 1631017 "MHROWRED" 1631440 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-710 1625877 1629032 1629437 "MFLOAT" 1630112 T MFLOAT (NIL) -8 NIL NIL NIL) (-709 1625234 1625310 1625481 "MFINFACT" 1625789 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-708 1621549 1622397 1623281 "MESH" 1624370 T MESH (NIL) -7 NIL NIL NIL) (-707 1619939 1620251 1620604 "MDDFACT" 1621236 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-706 1616734 1619098 1619139 "MDAGG" 1619394 NIL MDAGG (NIL T) -9 NIL 1619537 NIL) (-705 1605621 1616027 1616234 "MCMPLX" 1616547 T MCMPLX (NIL) -8 NIL NIL NIL) (-704 1604758 1604904 1605105 "MCDEN" 1605470 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-703 1602648 1602918 1603298 "MCALCFN" 1604488 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-702 1601573 1601813 1602046 "MAYBE" 1602454 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-701 1599185 1599708 1600270 "MATSTOR" 1601044 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-700 1595142 1598557 1598805 "MATRIX" 1598970 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-699 1590908 1591615 1592351 "MATLIN" 1594499 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-698 1581014 1584200 1584277 "MATCAT" 1589157 NIL MATCAT (NIL T T T) -9 NIL 1590574 NIL) (-697 1577370 1578391 1579747 "MATCAT-" 1579752 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-696 1575964 1576117 1576450 "MATCAT2" 1577205 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-695 1574076 1574400 1574784 "MAPPKG3" 1575639 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-694 1573057 1573230 1573452 "MAPPKG2" 1573900 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-693 1571556 1571840 1572167 "MAPPKG1" 1572763 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-692 1570635 1570962 1571139 "MAPPAST" 1571399 T MAPPAST (NIL) -8 NIL NIL NIL) (-691 1570246 1570304 1570427 "MAPHACK3" 1570571 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-690 1569838 1569899 1570013 "MAPHACK2" 1570178 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-689 1569276 1569379 1569521 "MAPHACK1" 1569729 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-688 1567355 1567976 1568280 "MAGMA" 1569004 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-687 1566834 1567079 1567170 "MACROAST" 1567284 T MACROAST (NIL) -8 NIL NIL NIL) (-686 1563252 1565073 1565534 "M3D" 1566406 NIL M3D (NIL T) -8 NIL NIL NIL) (-685 1557327 1561591 1561632 "LZSTAGG" 1562414 NIL LZSTAGG (NIL T) -9 NIL 1562709 NIL) (-684 1553285 1554458 1555915 "LZSTAGG-" 1555920 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-683 1550372 1551176 1551663 "LWORD" 1552830 NIL LWORD (NIL T) -8 NIL NIL NIL) (-682 1549948 1550176 1550251 "LSTAST" 1550317 T LSTAST (NIL) -8 NIL NIL NIL) (-681 1543025 1549719 1549853 "LSQM" 1549858 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-680 1542249 1542388 1542616 "LSPP" 1542880 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-679 1540061 1540362 1540818 "LSMP" 1541938 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-678 1536840 1537514 1538244 "LSMP1" 1539363 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-677 1530686 1535977 1536018 "LSAGG" 1536080 NIL LSAGG (NIL T) -9 NIL 1536158 NIL) (-676 1527381 1528305 1529518 "LSAGG-" 1529523 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-675 1524980 1526525 1526774 "LPOLY" 1527176 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-674 1524562 1524647 1524770 "LPEFRAC" 1524889 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-673 1522883 1523656 1523909 "LO" 1524394 NIL LO (NIL T T T) -8 NIL NIL NIL) (-672 1522535 1522647 1522675 "LOGIC" 1522786 T LOGIC (NIL) -9 NIL 1522867 NIL) (-671 1522397 1522420 1522491 "LOGIC-" 1522496 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-670 1521590 1521730 1521923 "LODOOPS" 1522253 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-669 1519013 1521506 1521572 "LODO" 1521577 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-668 1517551 1517786 1518139 "LODOF" 1518760 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-667 1513755 1516186 1516227 "LODOCAT" 1516665 NIL LODOCAT (NIL T) -9 NIL 1516876 NIL) (-666 1513488 1513546 1513673 "LODOCAT-" 1513678 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-665 1510808 1513329 1513447 "LODO2" 1513452 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-664 1508243 1510745 1510790 "LODO1" 1510795 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-663 1507124 1507289 1507594 "LODEEF" 1508066 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-662 1502427 1505318 1505359 "LNAGG" 1506221 NIL LNAGG (NIL T) -9 NIL 1506656 NIL) (-661 1501574 1501788 1502130 "LNAGG-" 1502135 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-660 1497710 1498499 1499138 "LMOPS" 1500989 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-659 1497113 1497501 1497542 "LMODULE" 1497547 NIL LMODULE (NIL T) -9 NIL 1497573 NIL) (-658 1494311 1496758 1496881 "LMDICT" 1497023 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-657 1493717 1493938 1493979 "LLINSET" 1494170 NIL LLINSET (NIL T) -9 NIL 1494261 NIL) (-656 1493416 1493625 1493685 "LITERAL" 1493690 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-655 1486579 1492350 1492654 "LIST" 1493145 NIL LIST (NIL T) -8 NIL NIL NIL) (-654 1486104 1486178 1486317 "LIST3" 1486499 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-653 1485111 1485289 1485517 "LIST2" 1485922 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-652 1483245 1483557 1483956 "LIST2MAP" 1484758 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-651 1482841 1483078 1483119 "LINSET" 1483124 NIL LINSET (NIL T) -9 NIL 1483158 NIL) (-650 1481570 1482103 1482144 "LINEXP" 1482495 NIL LINEXP (NIL T) -9 NIL 1482686 NIL) (-649 1480147 1480407 1480718 "LINDEP" 1481322 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-648 1476914 1477633 1478410 "LIMITRF" 1479402 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-647 1475217 1475513 1475922 "LIMITPS" 1476609 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-646 1469645 1474728 1474956 "LIE" 1475038 NIL LIE (NIL T T) -8 NIL NIL NIL) (-645 1468593 1469062 1469102 "LIECAT" 1469242 NIL LIECAT (NIL T) -9 NIL 1469393 NIL) (-644 1468434 1468461 1468549 "LIECAT-" 1468554 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-643 1461021 1467974 1468130 "LIB" 1468298 T LIB (NIL) -8 NIL NIL NIL) (-642 1456656 1457539 1458474 "LGROBP" 1460138 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-641 1454654 1454928 1455278 "LF" 1456377 NIL LF (NIL T T) -7 NIL NIL NIL) (-640 1453494 1454186 1454214 "LFCAT" 1454421 T LFCAT (NIL) -9 NIL 1454560 NIL) (-639 1450396 1451026 1451714 "LEXTRIPK" 1452858 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-638 1447140 1447966 1448469 "LEXP" 1449976 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-637 1446616 1446861 1446953 "LETAST" 1447068 T LETAST (NIL) -8 NIL NIL NIL) (-636 1445014 1445327 1445728 "LEADCDET" 1446298 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-635 1444204 1444278 1444507 "LAZM3PK" 1444935 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-634 1439121 1442281 1442819 "LAUPOL" 1443716 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-633 1438700 1438744 1438905 "LAPLACE" 1439071 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-632 1436639 1437801 1438052 "LA" 1438533 NIL LA (NIL T T T) -8 NIL NIL NIL) (-631 1435633 1436217 1436258 "LALG" 1436320 NIL LALG (NIL T) -9 NIL 1436379 NIL) (-630 1435347 1435406 1435542 "LALG-" 1435547 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-629 1435182 1435206 1435247 "KVTFROM" 1435309 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-628 1434105 1434549 1434734 "KTVLOGIC" 1435017 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-627 1433940 1433964 1434005 "KRCFROM" 1434067 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-626 1432844 1433031 1433330 "KOVACIC" 1433740 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-625 1432679 1432703 1432744 "KONVERT" 1432806 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-624 1432514 1432538 1432579 "KOERCE" 1432641 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-623 1430345 1431107 1431484 "KERNEL" 1432170 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-622 1429841 1429922 1430054 "KERNEL2" 1430259 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-621 1423611 1428380 1428434 "KDAGG" 1428811 NIL KDAGG (NIL T T) -9 NIL 1429017 NIL) (-620 1423140 1423264 1423469 "KDAGG-" 1423474 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-619 1416288 1422801 1422956 "KAFILE" 1423018 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-618 1410716 1415799 1416027 "JORDAN" 1416109 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1410095 1410365 1410486 "JOINAST" 1410615 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1409941 1410000 1410055 "JAVACODE" 1410060 T JAVACODE (NIL) -8 NIL NIL NIL) (-615 1406193 1408146 1408200 "IXAGG" 1409129 NIL IXAGG (NIL T T) -9 NIL 1409588 NIL) (-614 1405112 1405418 1405837 "IXAGG-" 1405842 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1400642 1405034 1405093 "IVECTOR" 1405098 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-612 1399408 1399645 1399911 "ITUPLE" 1400409 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-611 1397910 1398087 1398382 "ITRIGMNP" 1399230 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-610 1396655 1396859 1397142 "ITFUN3" 1397686 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-609 1396287 1396344 1396453 "ITFUN2" 1396592 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-608 1395446 1395767 1395941 "ITFORM" 1396133 T ITFORM (NIL) -8 NIL NIL NIL) (-607 1393407 1394466 1394744 "ITAYLOR" 1395201 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-606 1382352 1387544 1388707 "ISUPS" 1392277 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-605 1381456 1381596 1381832 "ISUMP" 1382199 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-604 1376831 1381401 1381442 "ISTRING" 1381447 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-603 1376307 1376552 1376644 "ISAST" 1376759 T ISAST (NIL) -8 NIL NIL NIL) (-602 1375516 1375598 1375814 "IRURPK" 1376221 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-601 1374452 1374653 1374893 "IRSN" 1375296 T IRSN (NIL) -7 NIL NIL NIL) (-600 1372523 1372878 1373307 "IRRF2F" 1374090 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-599 1372270 1372308 1372384 "IRREDFFX" 1372479 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-598 1370885 1371144 1371443 "IROOT" 1372003 NIL IROOT (NIL T) -7 NIL NIL NIL) (-597 1367489 1368569 1369261 "IR" 1370225 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1366694 1366982 1367133 "IRFORM" 1367358 T IRFORM (NIL) -8 NIL NIL NIL) (-595 1364307 1364802 1365368 "IR2" 1366172 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-594 1363407 1363520 1363734 "IR2F" 1364190 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-593 1363198 1363232 1363292 "IPRNTPK" 1363367 T IPRNTPK (NIL) -7 NIL NIL NIL) (-592 1359779 1363087 1363156 "IPF" 1363161 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-591 1358106 1359704 1359761 "IPADIC" 1359766 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-590 1357418 1357666 1357796 "IP4ADDR" 1357996 T IP4ADDR (NIL) -8 NIL NIL NIL) (-589 1356792 1357047 1357179 "IOMODE" 1357306 T IOMODE (NIL) -8 NIL NIL NIL) (-588 1355865 1356389 1356516 "IOBFILE" 1356685 T IOBFILE (NIL) -8 NIL NIL NIL) (-587 1355353 1355769 1355797 "IOBCON" 1355802 T IOBCON (NIL) -9 NIL 1355823 NIL) (-586 1354864 1354922 1355105 "INVLAPLA" 1355289 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-585 1344512 1346866 1349252 "INTTR" 1352528 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-584 1340847 1341589 1342454 "INTTOOLS" 1343697 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-583 1340433 1340524 1340641 "INTSLPE" 1340750 T INTSLPE (NIL) -7 NIL NIL NIL) (-582 1338386 1340356 1340415 "INTRVL" 1340420 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-581 1335988 1336500 1337075 "INTRF" 1337871 NIL INTRF (NIL T) -7 NIL NIL NIL) (-580 1335399 1335496 1335638 "INTRET" 1335886 NIL INTRET (NIL T) -7 NIL NIL NIL) (-579 1333396 1333785 1334255 "INTRAT" 1335007 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-578 1330659 1331242 1331861 "INTPM" 1332881 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-577 1327404 1328003 1328741 "INTPAF" 1330045 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-576 1322583 1323545 1324596 "INTPACK" 1326373 T INTPACK (NIL) -7 NIL NIL NIL) (-575 1319481 1322380 1322489 "INT" 1322494 T INT (NIL) -8 NIL NIL NIL) (-574 1318733 1318885 1319093 "INTHERTR" 1319323 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-573 1318172 1318252 1318440 "INTHERAL" 1318647 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-572 1316018 1316461 1316918 "INTHEORY" 1317735 T INTHEORY (NIL) -7 NIL NIL NIL) (-571 1307424 1309045 1310817 "INTG0" 1314370 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-570 1287997 1292787 1297597 "INTFTBL" 1302634 T INTFTBL (NIL) -8 NIL NIL NIL) (-569 1287246 1287384 1287557 "INTFACT" 1287856 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-568 1284673 1285119 1285676 "INTEF" 1286800 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-567 1283040 1283779 1283807 "INTDOM" 1284108 T INTDOM (NIL) -9 NIL 1284315 NIL) (-566 1282409 1282583 1282825 "INTDOM-" 1282830 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-565 1278797 1280725 1280779 "INTCAT" 1281578 NIL INTCAT (NIL T) -9 NIL 1281899 NIL) (-564 1278269 1278372 1278500 "INTBIT" 1278689 T INTBIT (NIL) -7 NIL NIL NIL) (-563 1276968 1277122 1277429 "INTALG" 1278114 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-562 1276451 1276541 1276698 "INTAF" 1276872 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-561 1269794 1276261 1276401 "INTABL" 1276406 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-560 1269127 1269593 1269658 "INT8" 1269692 T INT8 (NIL) -8 NIL NIL 1269737) (-559 1268459 1268925 1268990 "INT64" 1269024 T INT64 (NIL) -8 NIL NIL 1269069) (-558 1267791 1268257 1268322 "INT32" 1268356 T INT32 (NIL) -8 NIL NIL 1268401) (-557 1267123 1267589 1267654 "INT16" 1267688 T INT16 (NIL) -8 NIL NIL 1267733) (-556 1261918 1264684 1264712 "INS" 1265646 T INS (NIL) -9 NIL 1266311 NIL) (-555 1259158 1259929 1260903 "INS-" 1260976 NIL INS- (NIL T) -8 NIL NIL NIL) (-554 1257933 1258160 1258458 "INPSIGN" 1258911 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-553 1257051 1257168 1257365 "INPRODPF" 1257813 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-552 1255945 1256062 1256299 "INPRODFF" 1256931 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-551 1254945 1255097 1255357 "INNMFACT" 1255781 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-550 1254142 1254239 1254427 "INMODGCD" 1254844 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-549 1252650 1252895 1253219 "INFSP" 1253887 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-548 1251834 1251951 1252134 "INFPROD0" 1252530 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-547 1248689 1249899 1250414 "INFORM" 1251327 T INFORM (NIL) -8 NIL NIL NIL) (-546 1248299 1248359 1248457 "INFORM1" 1248624 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-545 1247822 1247911 1248025 "INFINITY" 1248205 T INFINITY (NIL) -7 NIL NIL NIL) (-544 1246998 1247542 1247643 "INETCLTS" 1247741 T INETCLTS (NIL) -8 NIL NIL NIL) (-543 1245614 1245864 1246185 "INEP" 1246746 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-542 1244863 1245511 1245576 "INDE" 1245581 NIL INDE (NIL T) -8 NIL NIL NIL) (-541 1244427 1244495 1244612 "INCRMAPS" 1244790 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-540 1243245 1243696 1243902 "INBFILE" 1244241 T INBFILE (NIL) -8 NIL NIL NIL) (-539 1238544 1239481 1240425 "INBFF" 1242333 NIL INBFF (NIL T) -7 NIL NIL NIL) (-538 1237452 1237721 1237749 "INBCON" 1238262 T INBCON (NIL) -9 NIL 1238528 NIL) (-537 1236704 1236927 1237203 "INBCON-" 1237208 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-536 1236183 1236428 1236519 "INAST" 1236633 T INAST (NIL) -8 NIL NIL NIL) (-535 1235610 1235862 1235968 "IMPTAST" 1236097 T IMPTAST (NIL) -8 NIL NIL NIL) (-534 1232056 1235454 1235558 "IMATRIX" 1235563 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-533 1230764 1230887 1231203 "IMATQF" 1231912 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-532 1228984 1229211 1229548 "IMATLIN" 1230520 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-531 1223562 1228908 1228966 "ILIST" 1228971 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-530 1221467 1223422 1223535 "IIARRAY2" 1223540 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-529 1216865 1221378 1221442 "IFF" 1221447 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-528 1216212 1216482 1216598 "IFAST" 1216769 T IFAST (NIL) -8 NIL NIL NIL) (-527 1211207 1215504 1215692 "IFARRAY" 1216069 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-526 1210387 1211111 1211184 "IFAMON" 1211189 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-525 1209971 1210036 1210090 "IEVALAB" 1210297 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-524 1209646 1209714 1209874 "IEVALAB-" 1209879 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-523 1209277 1209560 1209623 "IDPO" 1209628 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-522 1208527 1209166 1209241 "IDPOAMS" 1209246 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-521 1207834 1208416 1208491 "IDPOAM" 1208496 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-520 1206893 1207169 1207222 "IDPC" 1207635 NIL IDPC (NIL T T) -9 NIL 1207784 NIL) (-519 1206362 1206785 1206858 "IDPAM" 1206863 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-518 1205738 1206254 1206327 "IDPAG" 1206332 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-517 1205383 1205574 1205649 "IDENT" 1205683 T IDENT (NIL) -8 NIL NIL NIL) (-516 1201638 1202486 1203381 "IDECOMP" 1204540 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-515 1194475 1195561 1196608 "IDEAL" 1200674 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-514 1193635 1193747 1193947 "ICDEN" 1194359 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-513 1192706 1193115 1193262 "ICARD" 1193508 T ICARD (NIL) -8 NIL NIL NIL) (-512 1190766 1191079 1191484 "IBPTOOLS" 1192383 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-511 1186373 1190386 1190499 "IBITS" 1190685 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-510 1183096 1183672 1184367 "IBATOOL" 1185790 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-509 1180875 1181337 1181870 "IBACHIN" 1182631 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-508 1178704 1180721 1180824 "IARRAY2" 1180829 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-507 1174810 1178630 1178687 "IARRAY1" 1178692 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-506 1168848 1173222 1173703 "IAN" 1174349 T IAN (NIL) -8 NIL NIL NIL) (-505 1168359 1168416 1168589 "IALGFACT" 1168785 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-504 1167887 1168000 1168028 "HYPCAT" 1168235 T HYPCAT (NIL) -9 NIL NIL NIL) (-503 1167425 1167542 1167728 "HYPCAT-" 1167733 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-502 1167020 1167220 1167303 "HOSTNAME" 1167362 T HOSTNAME (NIL) -8 NIL NIL NIL) (-501 1166865 1166902 1166943 "HOMOTOP" 1166948 NIL HOMOTOP (NIL T) -9 NIL 1166981 NIL) (-500 1163497 1164875 1164916 "HOAGG" 1165897 NIL HOAGG (NIL T) -9 NIL 1166576 NIL) (-499 1162091 1162490 1163016 "HOAGG-" 1163021 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-498 1156000 1161684 1161834 "HEXADEC" 1161961 T HEXADEC (NIL) -8 NIL NIL NIL) (-497 1154748 1154970 1155233 "HEUGCD" 1155777 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-496 1153824 1154585 1154715 "HELLFDIV" 1154720 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-495 1152003 1153601 1153689 "HEAP" 1153768 NIL HEAP (NIL T) -8 NIL NIL NIL) (-494 1151266 1151555 1151689 "HEADAST" 1151889 T HEADAST (NIL) -8 NIL NIL NIL) (-493 1145285 1151181 1151243 "HDP" 1151248 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-492 1139184 1144920 1145072 "HDMP" 1145186 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-491 1138508 1138648 1138812 "HB" 1139040 T HB (NIL) -7 NIL NIL NIL) (-490 1131894 1138354 1138458 "HASHTBL" 1138463 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-489 1131370 1131615 1131707 "HASAST" 1131822 T HASAST (NIL) -8 NIL NIL NIL) (-488 1129148 1130992 1131174 "HACKPI" 1131208 T HACKPI (NIL) -8 NIL NIL NIL) (-487 1124816 1129001 1129114 "GTSET" 1129119 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-486 1118231 1124694 1124792 "GSTBL" 1124797 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-485 1110509 1117262 1117527 "GSERIES" 1118022 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-484 1109650 1110067 1110095 "GROUP" 1110298 T GROUP (NIL) -9 NIL 1110432 NIL) (-483 1109016 1109175 1109426 "GROUP-" 1109431 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-482 1107383 1107704 1108091 "GROEBSOL" 1108693 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-481 1106297 1106585 1106636 "GRMOD" 1107165 NIL GRMOD (NIL T T) -9 NIL 1107333 NIL) (-480 1106065 1106101 1106229 "GRMOD-" 1106234 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-479 1101355 1102419 1103419 "GRIMAGE" 1105085 T GRIMAGE (NIL) -8 NIL NIL NIL) (-478 1099821 1100082 1100406 "GRDEF" 1101051 T GRDEF (NIL) -7 NIL NIL NIL) (-477 1099265 1099381 1099522 "GRAY" 1099700 T GRAY (NIL) -7 NIL NIL NIL) (-476 1098452 1098858 1098909 "GRALG" 1099062 NIL GRALG (NIL T T) -9 NIL 1099155 NIL) (-475 1098113 1098186 1098349 "GRALG-" 1098354 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-474 1094890 1097698 1097876 "GPOLSET" 1098020 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-473 1094244 1094301 1094559 "GOSPER" 1094827 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-472 1089976 1090682 1091208 "GMODPOL" 1093943 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-471 1088981 1089165 1089403 "GHENSEL" 1089788 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-470 1083137 1083980 1085000 "GENUPS" 1088065 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-469 1082834 1082885 1082974 "GENUFACT" 1083080 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-468 1082246 1082323 1082488 "GENPGCD" 1082752 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-467 1081720 1081755 1081968 "GENMFACT" 1082205 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-466 1080286 1080543 1080850 "GENEEZ" 1081463 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-465 1074345 1079897 1080059 "GDMP" 1080209 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-464 1063688 1068116 1069222 "GCNAALG" 1073328 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-463 1062015 1062877 1062905 "GCDDOM" 1063160 T GCDDOM (NIL) -9 NIL 1063317 NIL) (-462 1061485 1061612 1061827 "GCDDOM-" 1061832 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-461 1060157 1060342 1060646 "GB" 1061264 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1048773 1051103 1053495 "GBINTERN" 1057848 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-459 1046610 1046902 1047323 "GBF" 1048448 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-458 1045391 1045556 1045823 "GBEUCLID" 1046426 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-457 1044740 1044865 1045014 "GAUSSFAC" 1045262 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-456 1043107 1043409 1043723 "GALUTIL" 1044459 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-455 1041415 1041689 1042013 "GALPOLYU" 1042834 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-454 1038780 1039070 1039477 "GALFACTU" 1041112 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-453 1030586 1032085 1033693 "GALFACT" 1037212 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-452 1027974 1028632 1028660 "FVFUN" 1029816 T FVFUN (NIL) -9 NIL 1030536 NIL) (-451 1027240 1027422 1027450 "FVC" 1027741 T FVC (NIL) -9 NIL 1027924 NIL) (-450 1026883 1027065 1027133 "FUNDESC" 1027192 T FUNDESC (NIL) -8 NIL NIL NIL) (-449 1026498 1026680 1026761 "FUNCTION" 1026835 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-448 1024242 1024820 1025286 "FT" 1026052 T FT (NIL) -8 NIL NIL NIL) (-447 1023033 1023543 1023746 "FTEM" 1024059 T FTEM (NIL) -8 NIL NIL NIL) (-446 1021324 1021613 1022010 "FSUPFACT" 1022724 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-445 1019721 1020010 1020342 "FST" 1021012 T FST (NIL) -8 NIL NIL NIL) (-444 1018920 1019026 1019214 "FSRED" 1019603 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-443 1017619 1017875 1018222 "FSPRMELT" 1018635 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-442 1014925 1015363 1015849 "FSPECF" 1017182 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-441 996227 1004699 1004740 "FS" 1008624 NIL FS (NIL T) -9 NIL 1010913 NIL) (-440 984870 987863 991920 "FS-" 992220 NIL FS- (NIL T T) -8 NIL NIL NIL) (-439 984398 984452 984622 "FSINT" 984811 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-438 982690 983391 983694 "FSERIES" 984177 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-437 981732 981848 982072 "FSCINT" 982570 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-436 977940 980676 980717 "FSAGG" 981087 NIL FSAGG (NIL T) -9 NIL 981346 NIL) (-435 975702 976303 977099 "FSAGG-" 977194 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-434 974744 974887 975114 "FSAGG2" 975555 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-433 972422 972702 973250 "FS2UPS" 974462 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-432 972056 972099 972228 "FS2" 972373 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-431 970934 971105 971407 "FS2EXPXP" 971881 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-430 970360 970475 970627 "FRUTIL" 970814 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-429 961773 965855 967213 "FR" 969034 NIL FR (NIL T) -8 NIL NIL NIL) (-428 956787 959462 959502 "FRNAALG" 960822 NIL FRNAALG (NIL T) -9 NIL 961420 NIL) (-427 952460 953536 954811 "FRNAALG-" 955561 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-426 952098 952141 952268 "FRNAAF2" 952411 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-425 950473 950947 951243 "FRMOD" 951910 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-424 948216 948848 949166 "FRIDEAL" 950264 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-423 947407 947494 947785 "FRIDEAL2" 948123 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-422 946540 946954 946995 "FRETRCT" 947000 NIL FRETRCT (NIL T) -9 NIL 947176 NIL) (-421 945652 945883 946234 "FRETRCT-" 946239 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-420 942740 943950 944009 "FRAMALG" 944891 NIL FRAMALG (NIL T T) -9 NIL 945183 NIL) (-419 940874 941329 941959 "FRAMALG-" 942182 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-418 934704 940347 940624 "FRAC" 940629 NIL FRAC (NIL T) -8 NIL NIL NIL) (-417 934340 934397 934504 "FRAC2" 934641 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-416 933976 934033 934140 "FR2" 934277 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-415 928489 931382 931410 "FPS" 932529 T FPS (NIL) -9 NIL 933086 NIL) (-414 927938 928047 928211 "FPS-" 928357 NIL FPS- (NIL T) -8 NIL NIL NIL) (-413 925240 926909 926937 "FPC" 927162 T FPC (NIL) -9 NIL 927304 NIL) (-412 925033 925073 925170 "FPC-" 925175 NIL FPC- (NIL T) -8 NIL NIL NIL) (-411 923823 924521 924562 "FPATMAB" 924567 NIL FPATMAB (NIL T) -9 NIL 924719 NIL) (-410 921496 921999 922425 "FPARFRAC" 923460 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-409 916890 917388 918070 "FORTRAN" 920928 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-408 914606 915106 915645 "FORT" 916371 T FORT (NIL) -7 NIL NIL NIL) (-407 912282 912844 912872 "FORTFN" 913932 T FORTFN (NIL) -9 NIL 914556 NIL) (-406 912046 912096 912124 "FORTCAT" 912183 T FORTCAT (NIL) -9 NIL 912245 NIL) (-405 910152 910662 911052 "FORMULA" 911676 T FORMULA (NIL) -8 NIL NIL NIL) (-404 909940 909970 910039 "FORMULA1" 910116 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-403 909463 909515 909688 "FORDER" 909882 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-402 908559 908723 908916 "FOP" 909290 T FOP (NIL) -7 NIL NIL NIL) (-401 907140 907839 908013 "FNLA" 908441 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-400 905869 906284 906312 "FNCAT" 906772 T FNCAT (NIL) -9 NIL 907032 NIL) (-399 905408 905828 905856 "FNAME" 905861 T FNAME (NIL) -8 NIL NIL NIL) (-398 903971 904934 904962 "FMTC" 904967 T FMTC (NIL) -9 NIL 905003 NIL) (-397 902717 903907 903953 "FMONOID" 903958 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-396 899545 900713 900754 "FMONCAT" 901971 NIL FMONCAT (NIL T) -9 NIL 902576 NIL) (-395 898737 899287 899436 "FM" 899441 NIL FM (NIL T T) -8 NIL NIL NIL) (-394 896161 896807 896835 "FMFUN" 897979 T FMFUN (NIL) -9 NIL 898687 NIL) (-393 895430 895611 895639 "FMC" 895929 T FMC (NIL) -9 NIL 896111 NIL) (-392 892509 893369 893423 "FMCAT" 894618 NIL FMCAT (NIL T T) -9 NIL 895113 NIL) (-391 891375 892275 892375 "FM1" 892454 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-390 889149 889565 890059 "FLOATRP" 890926 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-389 882727 886878 887499 "FLOAT" 888548 T FLOAT (NIL) -8 NIL NIL NIL) (-388 880165 880665 881243 "FLOATCP" 882194 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-387 879012 879771 879812 "FLINEXP" 879817 NIL FLINEXP (NIL T) -9 NIL 879910 NIL) (-386 877944 878241 878649 "FLINEXP-" 878654 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-385 877020 877164 877388 "FLASORT" 877796 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-384 874136 875004 875056 "FLALG" 876283 NIL FLALG (NIL T T) -9 NIL 876750 NIL) (-383 867840 871592 871633 "FLAGG" 872895 NIL FLAGG (NIL T) -9 NIL 873547 NIL) (-382 866566 866905 867395 "FLAGG-" 867400 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-381 865608 865751 865978 "FLAGG2" 866419 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-380 862459 863467 863526 "FINRALG" 864654 NIL FINRALG (NIL T T) -9 NIL 865162 NIL) (-379 861619 861848 862187 "FINRALG-" 862192 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-378 860999 861238 861266 "FINITE" 861462 T FINITE (NIL) -9 NIL 861569 NIL) (-377 853356 855543 855583 "FINAALG" 859250 NIL FINAALG (NIL T) -9 NIL 860703 NIL) (-376 848688 849738 850882 "FINAALG-" 852261 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-375 848056 848443 848546 "FILE" 848618 NIL FILE (NIL T) -8 NIL NIL NIL) (-374 846714 847052 847106 "FILECAT" 847790 NIL FILECAT (NIL T T) -9 NIL 848006 NIL) (-373 844430 845958 845986 "FIELD" 846026 T FIELD (NIL) -9 NIL 846106 NIL) (-372 843050 843435 843946 "FIELD-" 843951 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-371 840900 841685 842032 "FGROUP" 842736 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-370 839990 840154 840374 "FGLMICPK" 840732 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-369 835822 839915 839972 "FFX" 839977 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-368 835423 835484 835619 "FFSLPE" 835755 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-367 831413 832195 832991 "FFPOLY" 834659 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-366 830917 830953 831162 "FFPOLY2" 831371 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-365 826763 830836 830899 "FFP" 830904 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-364 822161 826674 826738 "FF" 826743 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-363 817287 821504 821694 "FFNBX" 822015 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-362 812215 816422 816680 "FFNBP" 817141 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-361 806848 811499 811710 "FFNB" 812048 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-360 805680 805878 806193 "FFINTBAS" 806645 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-359 801706 803927 803955 "FFIELDC" 804575 T FFIELDC (NIL) -9 NIL 804951 NIL) (-358 800368 800739 801236 "FFIELDC-" 801241 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-357 799937 799983 800107 "FFHOM" 800310 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-356 797632 798119 798636 "FFF" 799452 NIL FFF (NIL T) -7 NIL NIL NIL) (-355 793250 797374 797475 "FFCGX" 797575 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-354 788872 792982 793089 "FFCGP" 793193 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-353 784055 788599 788707 "FFCG" 788808 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-352 763736 773731 773817 "FFCAT" 778982 NIL FFCAT (NIL T T T) -9 NIL 780433 NIL) (-351 758933 759981 761295 "FFCAT-" 762525 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-350 758344 758387 758622 "FFCAT2" 758884 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-349 747667 751316 752536 "FEXPR" 757196 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-348 746629 747064 747105 "FEVALAB" 747189 NIL FEVALAB (NIL T) -9 NIL 747450 NIL) (-347 745788 745998 746336 "FEVALAB-" 746341 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-346 744354 745171 745374 "FDIV" 745687 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 741374 742115 742230 "FDIVCAT" 743798 NIL FDIVCAT (NIL T T T T) -9 NIL 744235 NIL) (-344 741136 741163 741333 "FDIVCAT-" 741338 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-343 740356 740443 740720 "FDIV2" 741043 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-342 739330 739651 739853 "FCTRDATA" 740174 T FCTRDATA (NIL) -8 NIL NIL NIL) (-341 738016 738275 738564 "FCPAK1" 739061 T FCPAK1 (NIL) -7 NIL NIL NIL) (-340 737115 737516 737657 "FCOMP" 737907 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-339 720820 724265 727803 "FC" 733597 T FC (NIL) -8 NIL NIL NIL) (-338 713099 717127 717167 "FAXF" 718969 NIL FAXF (NIL T) -9 NIL 719661 NIL) (-337 710376 711033 711858 "FAXF-" 712323 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-336 705428 709752 709928 "FARRAY" 710233 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-335 700322 702389 702442 "FAMR" 703465 NIL FAMR (NIL T T) -9 NIL 703925 NIL) (-334 699212 699514 699949 "FAMR-" 699954 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-333 698381 699134 699187 "FAMONOID" 699192 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-332 696167 696877 696930 "FAMONC" 697871 NIL FAMONC (NIL T T) -9 NIL 698257 NIL) (-331 694831 695921 696058 "FAGROUP" 696063 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-330 692626 692945 693348 "FACUTIL" 694512 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-329 691725 691910 692132 "FACTFUNC" 692436 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-328 684147 691028 691227 "EXPUPXS" 691581 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-327 681630 682170 682756 "EXPRTUBE" 683581 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-326 677901 678493 679223 "EXPRODE" 680969 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-325 663620 676550 676979 "EXPR" 677505 NIL EXPR (NIL T) -8 NIL NIL NIL) (-324 658174 658761 659567 "EXPR2UPS" 662918 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-323 657806 657863 657972 "EXPR2" 658111 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-322 649059 656957 657248 "EXPEXPAN" 657642 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-321 648859 649016 649045 "EXIT" 649050 T EXIT (NIL) -8 NIL NIL NIL) (-320 648339 648583 648674 "EXITAST" 648788 T EXITAST (NIL) -8 NIL NIL NIL) (-319 647966 648028 648141 "EVALCYC" 648271 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-318 647507 647625 647666 "EVALAB" 647836 NIL EVALAB (NIL T) -9 NIL 647940 NIL) (-317 646988 647110 647331 "EVALAB-" 647336 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-316 644356 645658 645686 "EUCDOM" 646241 T EUCDOM (NIL) -9 NIL 646591 NIL) (-315 642761 643203 643793 "EUCDOM-" 643798 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-314 630300 633059 635809 "ESTOOLS" 640031 T ESTOOLS (NIL) -7 NIL NIL NIL) (-313 629932 629989 630098 "ESTOOLS2" 630237 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-312 629683 629725 629805 "ESTOOLS1" 629884 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-311 623720 625328 625356 "ES" 628124 T ES (NIL) -9 NIL 629534 NIL) (-310 618667 619954 621771 "ES-" 621935 NIL ES- (NIL T) -8 NIL NIL NIL) (-309 615041 615802 616582 "ESCONT" 617907 T ESCONT (NIL) -7 NIL NIL NIL) (-308 614786 614818 614900 "ESCONT1" 615003 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-307 614461 614511 614611 "ES2" 614730 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-306 614091 614149 614258 "ES1" 614397 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-305 613307 613436 613612 "ERROR" 613935 T ERROR (NIL) -7 NIL NIL NIL) (-304 606699 613166 613257 "EQTBL" 613262 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-303 599202 602013 603462 "EQ" 605283 NIL -3092 (NIL T) -8 NIL NIL NIL) (-302 598834 598891 599000 "EQ2" 599139 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-301 594125 595172 596265 "EP" 597773 NIL EP (NIL T) -7 NIL NIL NIL) (-300 592725 593016 593322 "ENV" 593839 T ENV (NIL) -8 NIL NIL NIL) (-299 591819 592373 592401 "ENTIRER" 592406 T ENTIRER (NIL) -9 NIL 592452 NIL) (-298 588513 590001 590362 "EMR" 591627 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-297 587643 587828 587882 "ELTAGG" 588262 NIL ELTAGG (NIL T T) -9 NIL 588473 NIL) (-296 587362 587424 587565 "ELTAGG-" 587570 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-295 587126 587155 587209 "ELTAB" 587293 NIL ELTAB (NIL T T) -9 NIL 587345 NIL) (-294 586252 586398 586597 "ELFUTS" 586977 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-293 585994 586050 586078 "ELEMFUN" 586183 T ELEMFUN (NIL) -9 NIL NIL NIL) (-292 585864 585885 585953 "ELEMFUN-" 585958 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-291 580678 583934 583975 "ELAGG" 584915 NIL ELAGG (NIL T) -9 NIL 585378 NIL) (-290 578963 579397 580060 "ELAGG-" 580065 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-289 578275 578412 578568 "ELABOR" 578827 T ELABOR (NIL) -8 NIL NIL NIL) (-288 576936 577215 577509 "ELABEXPR" 578001 T ELABEXPR (NIL) -8 NIL NIL NIL) (-287 569770 571573 572402 "EFUPXS" 576211 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-286 563218 565019 565830 "EFULS" 569045 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-285 560703 561061 561533 "EFSTRUC" 562850 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-284 550494 552060 553608 "EF" 559218 NIL EF (NIL T T) -7 NIL NIL NIL) (-283 549568 549979 550128 "EAB" 550365 T EAB (NIL) -8 NIL NIL NIL) (-282 548750 549527 549555 "E04UCFA" 549560 T E04UCFA (NIL) -8 NIL NIL NIL) (-281 547932 548709 548737 "E04NAFA" 548742 T E04NAFA (NIL) -8 NIL NIL NIL) (-280 547114 547891 547919 "E04MBFA" 547924 T E04MBFA (NIL) -8 NIL NIL NIL) (-279 546296 547073 547101 "E04JAFA" 547106 T E04JAFA (NIL) -8 NIL NIL NIL) (-278 545480 546255 546283 "E04GCFA" 546288 T E04GCFA (NIL) -8 NIL NIL NIL) (-277 544664 545439 545467 "E04FDFA" 545472 T E04FDFA (NIL) -8 NIL NIL NIL) (-276 543846 544623 544651 "E04DGFA" 544656 T E04DGFA (NIL) -8 NIL NIL NIL) (-275 538019 539371 540735 "E04AGNT" 542502 T E04AGNT (NIL) -7 NIL NIL NIL) (-274 536790 537333 537373 "DVARCAT" 537714 NIL DVARCAT (NIL T) -9 NIL 537877 NIL) (-273 535994 536206 536520 "DVARCAT-" 536525 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-272 529042 535793 535922 "DSMP" 535927 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-271 527465 528184 528225 "DSEXT" 528588 NIL DSEXT (NIL T) -9 NIL 528882 NIL) (-270 525750 526178 526844 "DSEXT-" 526849 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-269 520531 521695 522763 "DROPT" 524702 T DROPT (NIL) -8 NIL NIL NIL) (-268 520196 520255 520353 "DROPT1" 520466 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-267 515311 516437 517574 "DROPT0" 519079 T DROPT0 (NIL) -7 NIL NIL NIL) (-266 513656 513981 514367 "DRAWPT" 514945 T DRAWPT (NIL) -7 NIL NIL NIL) (-265 508243 509166 510245 "DRAW" 512630 NIL DRAW (NIL T) -7 NIL NIL NIL) (-264 507876 507929 508047 "DRAWHACK" 508184 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-263 506607 506876 507167 "DRAWCX" 507605 T DRAWCX (NIL) -7 NIL NIL NIL) (-262 506122 506191 506342 "DRAWCURV" 506533 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-261 496590 498552 500667 "DRAWCFUN" 504027 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-260 493354 495283 495324 "DQAGG" 495953 NIL DQAGG (NIL T) -9 NIL 496227 NIL) (-259 481006 487565 487648 "DPOLCAT" 489500 NIL DPOLCAT (NIL T T T T) -9 NIL 490045 NIL) (-258 475843 477191 479149 "DPOLCAT-" 479154 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-257 469425 475704 475802 "DPMO" 475807 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-256 462910 469205 469372 "DPMM" 469377 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-255 462480 462694 462783 "DOMTMPLT" 462841 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-254 461913 462282 462362 "DOMCTOR" 462420 T DOMCTOR (NIL) -8 NIL NIL NIL) (-253 461125 461393 461544 "DOMAIN" 461782 T DOMAIN (NIL) -8 NIL NIL NIL) (-252 455024 460760 460912 "DMP" 461026 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-251 454624 454680 454824 "DLP" 454962 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 448446 453951 454141 "DLIST" 454466 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 445243 447299 447340 "DLAGG" 447890 NIL DLAGG (NIL T) -9 NIL 448120 NIL) (-248 443919 444583 444611 "DIVRING" 444703 T DIVRING (NIL) -9 NIL 444786 NIL) (-247 443156 443346 443646 "DIVRING-" 443651 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 441258 441615 442021 "DISPLAY" 442770 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 435297 441172 441235 "DIRPROD" 441240 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 434145 434348 434613 "DIRPROD2" 435090 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 423073 428931 428984 "DIRPCAT" 429242 NIL DIRPCAT (NIL NIL T) -9 NIL 430117 NIL) (-242 420177 420881 421842 "DIRPCAT-" 422179 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 419464 419624 419810 "DIOSP" 420011 T DIOSP (NIL) -7 NIL NIL NIL) (-240 416119 418376 418417 "DIOPS" 418851 NIL DIOPS (NIL T) -9 NIL 419080 NIL) (-239 415668 415782 415973 "DIOPS-" 415978 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 414719 415347 415375 "DIFRING" 415380 T DIFRING (NIL) -9 NIL 415402 NIL) (-237 414391 414465 414493 "DIFFSPC" 414612 T DIFFSPC (NIL) -9 NIL 414687 NIL) (-236 414036 414114 414266 "DIFFSPC-" 414271 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 413192 413670 413710 "DIFFMOD" 413715 NIL DIFFMOD (NIL T) -9 NIL 413742 NIL) (-234 412900 412945 412986 "DIFFDOM" 413107 NIL DIFFDOM (NIL T) -9 NIL 413175 NIL) (-233 412753 412777 412861 "DIFFDOM-" 412866 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 410685 411957 411998 "DIFEXT" 412003 NIL DIFEXT (NIL T) -9 NIL 412156 NIL) (-231 407960 410217 410258 "DIAGG" 410263 NIL DIAGG (NIL T) -9 NIL 410283 NIL) (-230 407344 407501 407753 "DIAGG-" 407758 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 402761 406303 406580 "DHMATRIX" 407113 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 398373 399282 400292 "DFSFUN" 401771 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 393453 397304 397616 "DFLOAT" 398081 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 391716 391997 392386 "DFINTTLS" 393161 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 388745 389737 390137 "DERHAM" 391382 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 386546 388520 388609 "DEQUEUE" 388689 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 385800 385933 386116 "DEGRED" 386408 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 382230 382975 383821 "DEFINTRF" 385028 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 379785 380254 380846 "DEFINTEF" 381749 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 379135 379405 379520 "DEFAST" 379690 T DEFAST (NIL) -8 NIL NIL NIL) (-219 373044 378728 378878 "DECIMAL" 379005 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 370556 371014 371520 "DDFACT" 372588 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 370152 370195 370346 "DBLRESP" 370507 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 368020 368382 368743 "DBASE" 369918 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 367262 367500 367646 "DATAARY" 367919 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 366368 367221 367249 "D03FAFA" 367254 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 365475 366327 366355 "D03EEFA" 366360 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 363425 363891 364380 "D03AGNT" 365006 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 362714 363384 363412 "D02EJFA" 363417 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 362003 362673 362701 "D02CJFA" 362706 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 361292 361962 361990 "D02BHFA" 361995 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 360581 361251 361279 "D02BBFA" 361284 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 353778 355367 356973 "D02AGNT" 358995 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 351546 352069 352615 "D01WGTS" 353252 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 350613 351505 351533 "D01TRNS" 351538 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 349681 350572 350600 "D01GBFA" 350605 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 348749 349640 349668 "D01FCFA" 349673 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 347817 348708 348736 "D01ASFA" 348741 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 346885 347776 347804 "D01AQFA" 347809 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 345953 346844 346872 "D01APFA" 346877 T D01APFA (NIL) -8 NIL NIL NIL) (-199 345021 345912 345940 "D01ANFA" 345945 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 344089 344980 345008 "D01AMFA" 345013 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 343157 344048 344076 "D01ALFA" 344081 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 342225 343116 343144 "D01AKFA" 343149 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 341293 342184 342212 "D01AJFA" 342217 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 334588 336141 337702 "D01AGNT" 339752 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 333925 334053 334205 "CYCLOTOM" 334456 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 330658 331373 332100 "CYCLES" 333218 T CYCLES (NIL) -7 NIL NIL NIL) (-191 329970 330104 330275 "CVMP" 330519 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 327811 328069 328438 "CTRIGMNP" 329698 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 327247 327605 327678 "CTOR" 327758 T CTOR (NIL) -8 NIL NIL NIL) (-188 326756 326978 327079 "CTORKIND" 327166 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 326047 326363 326391 "CTORCAT" 326573 T CTORCAT (NIL) -9 NIL 326686 NIL) (-186 325645 325756 325915 "CTORCAT-" 325920 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 325107 325319 325427 "CTORCALL" 325569 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 324481 324580 324733 "CSTTOOLS" 325004 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 320280 320937 321695 "CRFP" 323793 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 319755 320001 320093 "CRCEAST" 320208 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 318802 318987 319215 "CRAPACK" 319559 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 318186 318287 318491 "CPMATCH" 318678 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 317911 317939 318045 "CPIMA" 318152 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 314259 314931 315650 "COORDSYS" 317246 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 313671 313792 313934 "CONTOUR" 314137 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 309562 311674 312166 "CONTFRAC" 313211 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 309442 309463 309491 "CONDUIT" 309528 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 308530 309084 309112 "COMRING" 309117 T COMRING (NIL) -9 NIL 309169 NIL) (-173 307584 307888 308072 "COMPPROP" 308366 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 307245 307280 307408 "COMPLPAT" 307543 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 296735 307054 307163 "COMPLEX" 307168 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 296371 296428 296535 "COMPLEX2" 296672 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 295710 295831 295991 "COMPILER" 296231 T COMPILER (NIL) -8 NIL NIL NIL) (-168 295428 295463 295561 "COMPFACT" 295669 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 277894 289132 289172 "COMPCAT" 290176 NIL COMPCAT (NIL T) -9 NIL 291524 NIL) (-166 267184 270173 273880 "COMPCAT-" 274236 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 266913 266941 267044 "COMMUPC" 267150 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 266707 266741 266800 "COMMONOP" 266874 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 266263 266458 266545 "COMM" 266640 T COMM (NIL) -8 NIL NIL NIL) (-162 265839 266067 266142 "COMMAAST" 266208 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 265088 265282 265310 "COMBOPC" 265648 T COMBOPC (NIL) -9 NIL 265823 NIL) (-160 263984 264194 264436 "COMBINAT" 264878 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 260441 261015 261642 "COMBF" 263406 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 259199 259557 259792 "COLOR" 260226 T COLOR (NIL) -8 NIL NIL NIL) (-157 258675 258920 259012 "COLONAST" 259127 T COLONAST (NIL) -8 NIL NIL NIL) (-156 258315 258362 258487 "CMPLXRT" 258622 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 257763 258015 258114 "CLLCTAST" 258236 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 253265 254293 255373 "CLIP" 256703 T CLIP (NIL) -7 NIL NIL NIL) (-153 251606 252366 252606 "CLIF" 253092 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 247781 249752 249793 "CLAGG" 250722 NIL CLAGG (NIL T) -9 NIL 251258 NIL) (-151 246203 246660 247243 "CLAGG-" 247248 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 245747 245832 245972 "CINTSLPE" 246112 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 243248 243719 244267 "CHVAR" 245275 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 242422 242976 243004 "CHARZ" 243009 T CHARZ (NIL) -9 NIL 243024 NIL) (-147 242176 242216 242294 "CHARPOL" 242376 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 241234 241821 241849 "CHARNZ" 241896 T CHARNZ (NIL) -9 NIL 241952 NIL) (-145 239140 239888 240241 "CHAR" 240901 T CHAR (NIL) -8 NIL NIL NIL) (-144 238866 238927 238955 "CFCAT" 239066 T CFCAT (NIL) -9 NIL NIL NIL) (-143 238107 238218 238401 "CDEN" 238750 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 234072 237260 237540 "CCLASS" 237847 T CCLASS (NIL) -8 NIL NIL NIL) (-141 233323 233480 233657 "CATEGORY" 233915 T -10 (NIL) -8 NIL NIL NIL) (-140 232896 233242 233290 "CATCTOR" 233295 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 232347 232599 232697 "CATAST" 232818 T CATAST (NIL) -8 NIL NIL NIL) (-138 231823 232068 232160 "CASEAST" 232275 T CASEAST (NIL) -8 NIL NIL NIL) (-137 226961 227980 228724 "CARTEN" 231135 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 226069 226217 226438 "CARTEN2" 226808 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 224385 225219 225476 "CARD" 225832 T CARD (NIL) -8 NIL NIL NIL) (-134 223961 224189 224264 "CAPSLAST" 224330 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 223465 223673 223701 "CACHSET" 223833 T CACHSET (NIL) -9 NIL 223911 NIL) (-132 222935 223257 223285 "CABMON" 223335 T CABMON (NIL) -9 NIL 223391 NIL) (-131 222408 222639 222749 "BYTEORD" 222845 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 221385 221937 222079 "BYTE" 222242 T BYTE (NIL) -8 NIL NIL 222364) (-129 216735 220890 221062 "BYTEBUF" 221233 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214244 216427 216534 "BTREE" 216661 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 211693 213892 214014 "BTOURN" 214154 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 209063 211163 211204 "BTCAT" 211272 NIL BTCAT (NIL T) -9 NIL 211349 NIL) (-125 208730 208810 208959 "BTCAT-" 208964 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 204109 207989 208017 "BTAGG" 208131 T BTAGG (NIL) -9 NIL 208241 NIL) (-123 203599 203724 203930 "BTAGG-" 203935 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 200594 202877 203092 "BSTREE" 203416 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 199732 199858 200042 "BRILL" 200450 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 196384 198458 198499 "BRAGG" 199148 NIL BRAGG (NIL T) -9 NIL 199406 NIL) (-119 194913 195319 195874 "BRAGG-" 195879 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 188037 194257 194442 "BPADICRT" 194760 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 186352 187974 188019 "BPADIC" 188024 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 186050 186080 186194 "BOUNDZRO" 186316 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 181278 182476 183388 "BOP" 185158 T BOP (NIL) -8 NIL NIL NIL) (-114 179059 179463 179938 "BOP1" 180836 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 178760 178821 178849 "BOOLE" 178960 T BOOLE (NIL) -9 NIL 179042 NIL) (-112 177585 178334 178483 "BOOLEAN" 178631 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 176864 177268 177322 "BMODULE" 177327 NIL BMODULE (NIL T T) -9 NIL 177392 NIL) (-110 172665 176662 176735 "BITS" 176811 T BITS (NIL) -8 NIL NIL NIL) (-109 172086 172205 172345 "BINDING" 172545 T BINDING (NIL) -8 NIL NIL NIL) (-108 165998 171681 171830 "BINARY" 171957 T BINARY (NIL) -8 NIL NIL NIL) (-107 163778 165253 165294 "BGAGG" 165554 NIL BGAGG (NIL T) -9 NIL 165691 NIL) (-106 163609 163641 163732 "BGAGG-" 163737 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 162680 162993 163198 "BFUNCT" 163424 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 161370 161548 161836 "BEZOUT" 162504 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 157839 160222 160552 "BBTREE" 161073 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 157573 157626 157654 "BASTYPE" 157773 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 157425 157454 157527 "BASTYPE-" 157532 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 156859 156935 157087 "BALFACT" 157336 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 155715 156274 156460 "AUTOMOR" 156704 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 155441 155446 155472 "ATTREG" 155477 T ATTREG (NIL) -9 NIL NIL NIL) (-97 153693 154138 154490 "ATTRBUT" 155107 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 153301 153521 153587 "ATTRAST" 153645 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 152837 152950 152976 "ATRIG" 153177 T ATRIG (NIL) -9 NIL NIL NIL) (-94 152646 152687 152774 "ATRIG-" 152779 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 152291 152477 152503 "ASTCAT" 152508 T ASTCAT (NIL) -9 NIL 152538 NIL) (-92 152018 152077 152196 "ASTCAT-" 152201 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 150167 151794 151882 "ASTACK" 151961 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 148672 148969 149334 "ASSOCEQ" 149849 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 147704 148331 148455 "ASP9" 148579 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 147467 147652 147691 "ASP8" 147696 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 146335 147072 147214 "ASP80" 147356 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 145233 145970 146102 "ASP7" 146234 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 144187 144910 145028 "ASP78" 145146 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 143156 143867 143984 "ASP77" 144101 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142068 142794 142925 "ASP74" 143056 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 140968 141703 141835 "ASP73" 141967 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140072 140794 140894 "ASP6" 140899 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139019 139749 139867 "ASP55" 139985 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 137968 138693 138812 "ASP50" 138931 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137056 137669 137779 "ASP4" 137889 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 136144 136757 136867 "ASP49" 136977 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 134928 135683 135851 "ASP42" 136033 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 133705 134461 134631 "ASP41" 134815 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 132655 133382 133500 "ASP35" 133618 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 132420 132603 132642 "ASP34" 132647 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 132157 132224 132300 "ASP33" 132375 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131051 131792 131924 "ASP31" 132056 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 130816 130999 131038 "ASP30" 131043 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 130551 130620 130696 "ASP29" 130771 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 130316 130499 130538 "ASP28" 130543 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130081 130264 130303 "ASP27" 130308 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 129165 129779 129890 "ASP24" 130001 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 128242 128967 129079 "ASP20" 129084 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 127330 127943 128053 "ASP1" 128163 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 126273 127004 127123 "ASP19" 127242 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126010 126077 126153 "ASP12" 126228 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 124862 125609 125753 "ASP10" 125897 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 122713 124706 124797 "ARRAY2" 124802 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 118478 122361 122475 "ARRAY1" 122630 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 117510 117683 117904 "ARRAY12" 118301 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 111822 113740 113815 "ARR2CAT" 116445 NIL ARR2CAT (NIL T T T) -9 NIL 117203 NIL) (-56 109256 110000 110954 "ARR2CAT-" 110959 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 108573 108883 109008 "ARITY" 109149 T ARITY (NIL) -8 NIL NIL NIL) (-54 107349 107501 107800 "APPRULE" 108409 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107000 107048 107167 "APPLYORE" 107295 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 106354 106593 106713 "ANY" 106898 T ANY (NIL) -8 NIL NIL NIL) (-51 105632 105755 105912 "ANY1" 106228 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 103162 104069 104396 "ANTISYM" 105356 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 102654 102869 102965 "ANON" 103084 T ANON (NIL) -8 NIL NIL NIL) (-48 96832 101193 101647 "AN" 102218 T AN (NIL) -8 NIL NIL NIL) (-47 92730 94118 94169 "AMR" 94917 NIL AMR (NIL T T) -9 NIL 95517 NIL) (-46 91842 92063 92426 "AMR-" 92431 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76281 91759 91820 "ALIST" 91825 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73086 75875 76044 "ALGSC" 76199 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 69642 70196 70803 "ALGPKG" 72526 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 68919 69020 69204 "ALGMFACT" 69528 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 64954 65533 66127 "ALGMANIP" 68503 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55373 64580 64730 "ALGFF" 64887 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54569 54700 54879 "ALGFACT" 55231 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53510 54110 54148 "ALGEBRA" 54153 NIL ALGEBRA (NIL T) -9 NIL 54194 NIL) (-37 53228 53287 53419 "ALGEBRA-" 53424 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35291 51200 51252 "ALAGG" 51388 NIL ALAGG (NIL T T) -9 NIL 51549 NIL) (-35 34827 34940 34966 "AHYP" 35167 T AHYP (NIL) -9 NIL NIL NIL) (-34 33758 34006 34032 "AGG" 34531 T AGG (NIL) -9 NIL 34810 NIL) (-33 33192 33354 33568 "AGG-" 33573 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30998 31421 31826 "AF" 32834 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30478 30723 30813 "ADDAST" 30926 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29746 30005 30161 "ACPLOT" 30340 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26678 26716 "ACFS" 27323 NIL ACFS (NIL T) -9 NIL 27562 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3248516 3248521 3248526 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3248501 3248506 3248511 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3248486 3248491 3248496 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3248471 3248476 3248481 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1314 3247614 3248346 3248423 "ZMOD" 3248428 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1313 3246668 3246832 3247055 "ZLINDEP" 3247446 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1312 3235968 3237736 3239708 "ZDSOLVE" 3244798 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1311 3235214 3235355 3235544 "YSTREAM" 3235814 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1310 3234642 3234888 3235001 "YDIAGRAM" 3235123 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1309 3232416 3233943 3234147 "XRPOLY" 3234485 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1308 3228969 3230287 3230862 "XPR" 3231888 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1307 3226690 3228300 3228504 "XPOLY" 3228800 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1306 3224343 3225711 3225766 "XPOLYC" 3226054 NIL XPOLYC (NIL T T) -9 NIL 3226167 NIL) (-1305 3220719 3222860 3223248 "XPBWPOLY" 3224001 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1304 3216414 3218709 3218751 "XF" 3219372 NIL XF (NIL T) -9 NIL 3219772 NIL) (-1303 3216035 3216123 3216292 "XF-" 3216297 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1302 3211231 3212520 3212575 "XFALG" 3214747 NIL XFALG (NIL T T) -9 NIL 3215536 NIL) (-1301 3210364 3210468 3210673 "XEXPPKG" 3211123 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1300 3208473 3210214 3210310 "XDPOLY" 3210315 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1299 3207280 3207880 3207923 "XALG" 3207928 NIL XALG (NIL T) -9 NIL 3208039 NIL) (-1298 3200722 3205257 3205751 "WUTSET" 3206872 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1297 3198978 3199774 3200097 "WP" 3200533 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1296 3198580 3198800 3198870 "WHILEAST" 3198930 T WHILEAST (NIL) -8 NIL NIL NIL) (-1295 3198052 3198297 3198391 "WHEREAST" 3198508 T WHEREAST (NIL) -8 NIL NIL NIL) (-1294 3196938 3197136 3197431 "WFFINTBS" 3197849 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1293 3194842 3195269 3195731 "WEIER" 3196510 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1292 3193888 3194338 3194380 "VSPACE" 3194516 NIL VSPACE (NIL T) -9 NIL 3194590 NIL) (-1291 3193726 3193753 3193844 "VSPACE-" 3193849 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1290 3193535 3193577 3193645 "VOID" 3193680 T VOID (NIL) -8 NIL NIL NIL) (-1289 3191671 3192030 3192436 "VIEW" 3193151 T VIEW (NIL) -7 NIL NIL NIL) (-1288 3188095 3188734 3189471 "VIEWDEF" 3190956 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1287 3177399 3179643 3181816 "VIEW3D" 3185944 T VIEW3D (NIL) -8 NIL NIL NIL) (-1286 3169650 3171310 3172889 "VIEW2D" 3175842 T VIEW2D (NIL) -8 NIL NIL NIL) (-1285 3165003 3169420 3169512 "VECTOR" 3169593 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1284 3163580 3163839 3164157 "VECTOR2" 3164733 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1283 3157022 3161331 3161374 "VECTCAT" 3162369 NIL VECTCAT (NIL T) -9 NIL 3162956 NIL) (-1282 3156036 3156290 3156680 "VECTCAT-" 3156685 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1281 3155490 3155687 3155807 "VARIABLE" 3155951 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1280 3155423 3155428 3155458 "UTYPE" 3155463 T UTYPE (NIL) -9 NIL NIL NIL) (-1279 3154253 3154407 3154669 "UTSODETL" 3155249 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1278 3151693 3152153 3152677 "UTSODE" 3153794 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1277 3143641 3149454 3149934 "UTS" 3151271 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1276 3134205 3139575 3139618 "UTSCAT" 3140730 NIL UTSCAT (NIL T) -9 NIL 3141488 NIL) (-1275 3131553 3132275 3133264 "UTSCAT-" 3133269 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1274 3131180 3131223 3131356 "UTS2" 3131504 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1273 3125406 3128018 3128061 "URAGG" 3130131 NIL URAGG (NIL T) -9 NIL 3130854 NIL) (-1272 3122345 3123208 3124331 "URAGG-" 3124336 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1271 3118054 3120980 3121445 "UPXSSING" 3122009 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1270 3110230 3117436 3117700 "UPXS" 3117848 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1269 3103303 3110134 3110206 "UPXSCONS" 3110211 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1268 3092710 3099506 3099568 "UPXSCCA" 3100142 NIL UPXSCCA (NIL T T) -9 NIL 3100375 NIL) (-1267 3092348 3092433 3092607 "UPXSCCA-" 3092612 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1266 3081607 3088176 3088219 "UPXSCAT" 3088867 NIL UPXSCAT (NIL T) -9 NIL 3089476 NIL) (-1265 3081037 3081116 3081295 "UPXS2" 3081522 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1264 3079691 3079944 3080295 "UPSQFREE" 3080780 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1263 3072899 3075959 3076014 "UPSCAT" 3077094 NIL UPSCAT (NIL T T) -9 NIL 3077859 NIL) (-1262 3072103 3072310 3072637 "UPSCAT-" 3072642 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1261 3057372 3065230 3065273 "UPOLYC" 3067374 NIL UPOLYC (NIL T) -9 NIL 3068595 NIL) (-1260 3048700 3051126 3054273 "UPOLYC-" 3054278 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1259 3048327 3048370 3048503 "UPOLYC2" 3048651 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1258 3040049 3048010 3048139 "UP" 3048246 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1257 3039388 3039495 3039659 "UPMP" 3039938 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1256 3038941 3039022 3039161 "UPDIVP" 3039301 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1255 3037509 3037758 3038074 "UPDECOMP" 3038690 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1254 3036740 3036852 3037038 "UPCDEN" 3037393 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1253 3036259 3036328 3036477 "UP2" 3036665 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1252 3034726 3035463 3035740 "UNISEG" 3036017 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1251 3033941 3034068 3034273 "UNISEG2" 3034569 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1250 3033001 3033181 3033407 "UNIFACT" 3033757 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1249 3016040 3032313 3032555 "ULS" 3032817 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3003903 3015944 3016016 "ULSCONS" 3016021 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1247 2984966 2997091 2997153 "ULSCCAT" 2997791 NIL ULSCCAT (NIL T T) -9 NIL 2998080 NIL) (-1246 2984016 2984261 2984649 "ULSCCAT-" 2984654 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1245 2973080 2979563 2979606 "ULSCAT" 2980469 NIL ULSCAT (NIL T) -9 NIL 2981200 NIL) (-1244 2972510 2972589 2972768 "ULS2" 2972995 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 2971629 2972139 2972246 "UINT8" 2972357 T UINT8 (NIL) -8 NIL NIL 2972442) (-1242 2970747 2971257 2971364 "UINT64" 2971475 T UINT64 (NIL) -8 NIL NIL 2971560) (-1241 2969865 2970375 2970482 "UINT32" 2970593 T UINT32 (NIL) -8 NIL NIL 2970678) (-1240 2968983 2969493 2969600 "UINT16" 2969711 T UINT16 (NIL) -8 NIL NIL 2969796) (-1239 2967286 2968243 2968273 "UFD" 2968485 T UFD (NIL) -9 NIL 2968599 NIL) (-1238 2967080 2967126 2967221 "UFD-" 2967226 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1237 2966162 2966345 2966561 "UDVO" 2966886 T UDVO (NIL) -7 NIL NIL NIL) (-1236 2963978 2964387 2964858 "UDPO" 2965726 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1235 2963911 2963916 2963946 "TYPE" 2963951 T TYPE (NIL) -9 NIL NIL NIL) (-1234 2963671 2963866 2963897 "TYPEAST" 2963902 T TYPEAST (NIL) -8 NIL NIL NIL) (-1233 2962642 2962844 2963084 "TWOFACT" 2963465 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1232 2961665 2962051 2962286 "TUPLE" 2962442 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1231 2959356 2959875 2960414 "TUBETOOL" 2961148 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1230 2958205 2958410 2958651 "TUBE" 2959149 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1229 2952934 2957177 2957460 "TS" 2957957 NIL TS (NIL T) -8 NIL NIL NIL) (-1228 2941574 2945693 2945790 "TSETCAT" 2951059 NIL TSETCAT (NIL T T T T) -9 NIL 2952590 NIL) (-1227 2936306 2937906 2939797 "TSETCAT-" 2939802 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1226 2930945 2931792 2932721 "TRMANIP" 2935442 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1225 2930386 2930449 2930612 "TRIMAT" 2930877 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1224 2928252 2928489 2928846 "TRIGMNIP" 2930135 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1223 2927772 2927885 2927915 "TRIGCAT" 2928128 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1222 2927441 2927520 2927661 "TRIGCAT-" 2927666 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1221 2924286 2926299 2926580 "TREE" 2927195 NIL TREE (NIL T) -8 NIL NIL NIL) (-1220 2923560 2924088 2924118 "TRANFUN" 2924153 T TRANFUN (NIL) -9 NIL 2924219 NIL) (-1219 2922839 2923030 2923310 "TRANFUN-" 2923315 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1218 2922643 2922675 2922736 "TOPSP" 2922800 T TOPSP (NIL) -7 NIL NIL NIL) (-1217 2921991 2922106 2922260 "TOOLSIGN" 2922524 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1216 2920625 2921168 2921407 "TEXTFILE" 2921774 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1215 2918537 2919078 2919507 "TEX" 2920218 T TEX (NIL) -8 NIL NIL NIL) (-1214 2918318 2918349 2918421 "TEX1" 2918500 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1213 2917966 2918029 2918119 "TEMUTL" 2918250 T TEMUTL (NIL) -7 NIL NIL NIL) (-1212 2916120 2916400 2916725 "TBCMPPK" 2917689 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1211 2907897 2914280 2914336 "TBAGG" 2914736 NIL TBAGG (NIL T T) -9 NIL 2914947 NIL) (-1210 2902967 2904455 2906209 "TBAGG-" 2906214 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1209 2902351 2902458 2902603 "TANEXP" 2902856 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1208 2901862 2902126 2902216 "TALGOP" 2902296 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1207 2895252 2901719 2901812 "TABLE" 2901817 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1206 2894664 2894763 2894901 "TABLEAU" 2895149 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1205 2889272 2890492 2891740 "TABLBUMP" 2893450 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1204 2888494 2888641 2888822 "SYSTEM" 2889113 T SYSTEM (NIL) -8 NIL NIL NIL) (-1203 2884953 2885652 2886435 "SYSSOLP" 2887745 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1202 2884751 2884908 2884939 "SYSPTR" 2884944 T SYSPTR (NIL) -8 NIL NIL NIL) (-1201 2883787 2884292 2884411 "SYSNNI" 2884597 NIL SYSNNI (NIL NIL) -8 NIL NIL 2884682) (-1200 2883086 2883545 2883624 "SYSINT" 2883684 NIL SYSINT (NIL NIL) -8 NIL NIL 2883729) (-1199 2879418 2880364 2881074 "SYNTAX" 2882398 T SYNTAX (NIL) -8 NIL NIL NIL) (-1198 2876576 2877178 2877810 "SYMTAB" 2878808 T SYMTAB (NIL) -8 NIL NIL NIL) (-1197 2871825 2872727 2873710 "SYMS" 2875615 T SYMS (NIL) -8 NIL NIL NIL) (-1196 2869060 2871283 2871513 "SYMPOLY" 2871630 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1195 2868577 2868652 2868775 "SYMFUNC" 2868972 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1194 2864597 2865889 2866702 "SYMBOL" 2867786 T SYMBOL (NIL) -8 NIL NIL NIL) (-1193 2858136 2859825 2861545 "SWITCH" 2862899 T SWITCH (NIL) -8 NIL NIL NIL) (-1192 2851480 2857092 2857386 "SUTS" 2857900 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1191 2843656 2850862 2851126 "SUPXS" 2851274 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1190 2835326 2843274 2843400 "SUP" 2843565 NIL SUP (NIL T) -8 NIL NIL NIL) (-1189 2834485 2834612 2834829 "SUPFRACF" 2835194 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1188 2834106 2834165 2834278 "SUP2" 2834420 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1187 2832554 2832828 2833184 "SUMRF" 2833805 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1186 2831889 2831955 2832147 "SUMFS" 2832475 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1185 2814963 2831201 2831443 "SULS" 2831705 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1184 2814565 2814785 2814855 "SUCHTAST" 2814915 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1183 2813860 2814090 2814230 "SUCH" 2814473 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1182 2807727 2808766 2809725 "SUBSPACE" 2812948 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1181 2807157 2807247 2807411 "SUBRESP" 2807615 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1180 2800525 2801822 2803133 "STTF" 2805893 NIL STTF (NIL T) -7 NIL NIL NIL) (-1179 2794698 2795818 2796965 "STTFNC" 2799425 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1178 2786011 2787880 2789674 "STTAYLOR" 2792939 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1177 2779141 2785875 2785958 "STRTBL" 2785963 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1176 2774505 2779096 2779127 "STRING" 2779132 T STRING (NIL) -8 NIL NIL NIL) (-1175 2769334 2773848 2773878 "STRICAT" 2773937 T STRICAT (NIL) -9 NIL 2773999 NIL) (-1174 2762087 2766953 2767564 "STREAM" 2768758 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1173 2761597 2761674 2761818 "STREAM3" 2762004 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1172 2760579 2760762 2760997 "STREAM2" 2761410 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1171 2760267 2760319 2760412 "STREAM1" 2760521 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1170 2759283 2759464 2759695 "STINPROD" 2760083 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1169 2758835 2759045 2759075 "STEP" 2759155 T STEP (NIL) -9 NIL 2759233 NIL) (-1168 2758022 2758324 2758472 "STEPAST" 2758709 T STEPAST (NIL) -8 NIL NIL NIL) (-1167 2751454 2757921 2757998 "STBL" 2758003 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1166 2746549 2750645 2750688 "STAGG" 2750841 NIL STAGG (NIL T) -9 NIL 2750930 NIL) (-1165 2744251 2744853 2745725 "STAGG-" 2745730 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1164 2742398 2744021 2744113 "STACK" 2744194 NIL STACK (NIL T) -8 NIL NIL NIL) (-1163 2735093 2740539 2740995 "SREGSET" 2742028 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1162 2727518 2728887 2730400 "SRDCMPK" 2733699 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1161 2720403 2724928 2724958 "SRAGG" 2726261 T SRAGG (NIL) -9 NIL 2726869 NIL) (-1160 2719420 2719675 2720054 "SRAGG-" 2720059 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1159 2713791 2718367 2718788 "SQMATRIX" 2719046 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1158 2707476 2710509 2711236 "SPLTREE" 2713136 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1157 2703439 2704132 2704778 "SPLNODE" 2706902 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1156 2702486 2702719 2702749 "SPFCAT" 2703193 T SPFCAT (NIL) -9 NIL NIL NIL) (-1155 2701223 2701433 2701697 "SPECOUT" 2702244 T SPECOUT (NIL) -7 NIL NIL NIL) (-1154 2692333 2694205 2694235 "SPADXPT" 2698911 T SPADXPT (NIL) -9 NIL 2701075 NIL) (-1153 2692094 2692134 2692203 "SPADPRSR" 2692286 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1152 2690143 2692049 2692080 "SPADAST" 2692085 T SPADAST (NIL) -8 NIL NIL NIL) (-1151 2682088 2683861 2683904 "SPACEC" 2688277 NIL SPACEC (NIL T) -9 NIL 2690093 NIL) (-1150 2680218 2682020 2682069 "SPACE3" 2682074 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1149 2678970 2679141 2679432 "SORTPAK" 2680023 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1148 2677062 2677365 2677777 "SOLVETRA" 2678634 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1147 2676112 2676334 2676595 "SOLVESER" 2676835 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1146 2671416 2672304 2673299 "SOLVERAD" 2675164 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1145 2667231 2667840 2668569 "SOLVEFOR" 2670783 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1144 2661501 2666580 2666677 "SNTSCAT" 2666682 NIL SNTSCAT (NIL T T T T) -9 NIL 2666752 NIL) (-1143 2655607 2659824 2660215 "SMTS" 2661191 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1142 2650203 2655495 2655572 "SMP" 2655577 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1141 2648362 2648663 2649061 "SMITH" 2649900 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1140 2640653 2644941 2645044 "SMATCAT" 2646395 NIL SMATCAT (NIL NIL T T T) -9 NIL 2646945 NIL) (-1139 2637371 2638256 2639514 "SMATCAT-" 2639519 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1138 2635037 2636607 2636650 "SKAGG" 2636911 NIL SKAGG (NIL T) -9 NIL 2637046 NIL) (-1137 2631313 2634510 2634694 "SINT" 2634846 T SINT (NIL) -8 NIL NIL 2635008) (-1136 2631085 2631123 2631189 "SIMPAN" 2631269 T SIMPAN (NIL) -7 NIL NIL NIL) (-1135 2630364 2630620 2630760 "SIG" 2630967 T SIG (NIL) -8 NIL NIL NIL) (-1134 2629202 2629423 2629698 "SIGNRF" 2630123 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1133 2628035 2628186 2628470 "SIGNEF" 2629031 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1132 2627341 2627618 2627742 "SIGAST" 2627933 T SIGAST (NIL) -8 NIL NIL NIL) (-1131 2625031 2625485 2625991 "SHP" 2626882 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1130 2619036 2624932 2625008 "SHDP" 2625013 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1129 2618609 2618801 2618831 "SGROUP" 2618924 T SGROUP (NIL) -9 NIL 2618986 NIL) (-1128 2618467 2618493 2618566 "SGROUP-" 2618571 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1127 2615258 2615956 2616679 "SGCF" 2617766 T SGCF (NIL) -7 NIL NIL NIL) (-1126 2609626 2614705 2614802 "SFRTCAT" 2614807 NIL SFRTCAT (NIL T T T T) -9 NIL 2614846 NIL) (-1125 2603047 2604065 2605201 "SFRGCD" 2608609 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1124 2596173 2597246 2598432 "SFQCMPK" 2601980 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1123 2595793 2595882 2595993 "SFORT" 2596114 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1122 2594911 2595633 2595754 "SEXOF" 2595759 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1121 2594018 2594792 2594860 "SEX" 2594865 T SEX (NIL) -8 NIL NIL NIL) (-1120 2589799 2590514 2590609 "SEXCAT" 2593231 NIL SEXCAT (NIL T T T T T) -9 NIL 2593791 NIL) (-1119 2586952 2589733 2589781 "SET" 2589786 NIL SET (NIL T) -8 NIL NIL NIL) (-1118 2585176 2585665 2585970 "SETMN" 2586693 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1117 2584672 2584824 2584854 "SETCAT" 2585030 T SETCAT (NIL) -9 NIL 2585140 NIL) (-1116 2584364 2584442 2584572 "SETCAT-" 2584577 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1115 2580725 2582825 2582868 "SETAGG" 2583738 NIL SETAGG (NIL T) -9 NIL 2584078 NIL) (-1114 2580183 2580299 2580536 "SETAGG-" 2580541 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1113 2579626 2579879 2579980 "SEQAST" 2580104 T SEQAST (NIL) -8 NIL NIL NIL) (-1112 2578825 2579119 2579180 "SEGXCAT" 2579466 NIL SEGXCAT (NIL T T) -9 NIL 2579586 NIL) (-1111 2577831 2578491 2578673 "SEG" 2578678 NIL SEG (NIL T) -8 NIL NIL NIL) (-1110 2576810 2577024 2577067 "SEGCAT" 2577589 NIL SEGCAT (NIL T) -9 NIL 2577810 NIL) (-1109 2575742 2576173 2576381 "SEGBIND" 2576637 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1108 2575363 2575422 2575535 "SEGBIND2" 2575677 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1107 2574936 2575164 2575241 "SEGAST" 2575308 T SEGAST (NIL) -8 NIL NIL NIL) (-1106 2574155 2574281 2574485 "SEG2" 2574780 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1105 2573526 2574090 2574137 "SDVAR" 2574142 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1104 2565964 2573296 2573426 "SDPOL" 2573431 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1103 2564557 2564823 2565142 "SCPKG" 2565679 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1102 2563721 2563893 2564085 "SCOPE" 2564387 T SCOPE (NIL) -8 NIL NIL NIL) (-1101 2562941 2563075 2563254 "SCACHE" 2563576 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1100 2562587 2562773 2562803 "SASTCAT" 2562808 T SASTCAT (NIL) -9 NIL 2562821 NIL) (-1099 2562074 2562422 2562498 "SAOS" 2562533 T SAOS (NIL) -8 NIL NIL NIL) (-1098 2561639 2561674 2561847 "SAERFFC" 2562033 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1097 2555489 2561536 2561616 "SAE" 2561621 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1096 2555082 2555117 2555276 "SAEFACT" 2555448 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1095 2553403 2553717 2554118 "RURPK" 2554748 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1094 2552040 2552346 2552651 "RULESET" 2553237 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1093 2549263 2549793 2550251 "RULE" 2551721 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1092 2548875 2549057 2549140 "RULECOLD" 2549215 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1091 2548665 2548693 2548764 "RTVALUE" 2548826 T RTVALUE (NIL) -8 NIL NIL NIL) (-1090 2548136 2548382 2548476 "RSTRCAST" 2548593 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1089 2542984 2543779 2544699 "RSETGCD" 2547335 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1088 2532214 2537293 2537390 "RSETCAT" 2541509 NIL RSETCAT (NIL T T T T) -9 NIL 2542606 NIL) (-1087 2530141 2530680 2531504 "RSETCAT-" 2531509 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1086 2522527 2523903 2525423 "RSDCMPK" 2528740 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1085 2520506 2520973 2521047 "RRCC" 2522133 NIL RRCC (NIL T T) -9 NIL 2522477 NIL) (-1084 2519857 2520031 2520310 "RRCC-" 2520315 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1083 2519300 2519553 2519654 "RPTAST" 2519778 T RPTAST (NIL) -8 NIL NIL NIL) (-1082 2492963 2502412 2502479 "RPOLCAT" 2513145 NIL RPOLCAT (NIL T T T) -9 NIL 2516305 NIL) (-1081 2484461 2486801 2489923 "RPOLCAT-" 2489928 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1080 2475392 2482672 2483154 "ROUTINE" 2484001 T ROUTINE (NIL) -8 NIL NIL NIL) (-1079 2472139 2475018 2475158 "ROMAN" 2475274 T ROMAN (NIL) -8 NIL NIL NIL) (-1078 2470383 2470999 2471259 "ROIRC" 2471944 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1077 2466615 2468899 2468929 "RNS" 2469233 T RNS (NIL) -9 NIL 2469507 NIL) (-1076 2465124 2465507 2466041 "RNS-" 2466116 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1075 2464527 2464935 2464965 "RNG" 2464970 T RNG (NIL) -9 NIL 2464991 NIL) (-1074 2463530 2463892 2464094 "RNGBIND" 2464378 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1073 2462929 2463317 2463360 "RMODULE" 2463365 NIL RMODULE (NIL T) -9 NIL 2463392 NIL) (-1072 2461765 2461859 2462195 "RMCAT2" 2462830 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1071 2458615 2461111 2461408 "RMATRIX" 2461527 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1070 2451442 2453702 2453817 "RMATCAT" 2457176 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2458158 NIL) (-1069 2450817 2450964 2451271 "RMATCAT-" 2451276 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1068 2450218 2450439 2450482 "RLINSET" 2450676 NIL RLINSET (NIL T) -9 NIL 2450767 NIL) (-1067 2449785 2449860 2449988 "RINTERP" 2450137 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1066 2448843 2449397 2449427 "RING" 2449483 T RING (NIL) -9 NIL 2449575 NIL) (-1065 2448635 2448679 2448776 "RING-" 2448781 NIL RING- (NIL T) -8 NIL NIL NIL) (-1064 2447476 2447713 2447971 "RIDIST" 2448399 T RIDIST (NIL) -7 NIL NIL NIL) (-1063 2438765 2446944 2447150 "RGCHAIN" 2447324 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1062 2438115 2438521 2438562 "RGBCSPC" 2438620 NIL RGBCSPC (NIL T) -9 NIL 2438672 NIL) (-1061 2437273 2437654 2437695 "RGBCMDL" 2437927 NIL RGBCMDL (NIL T) -9 NIL 2438041 NIL) (-1060 2434267 2434881 2435551 "RF" 2436637 NIL RF (NIL T) -7 NIL NIL NIL) (-1059 2433913 2433976 2434079 "RFFACTOR" 2434198 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1058 2433638 2433673 2433770 "RFFACT" 2433872 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1057 2431755 2432119 2432501 "RFDIST" 2433278 T RFDIST (NIL) -7 NIL NIL NIL) (-1056 2431208 2431300 2431463 "RETSOL" 2431657 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1055 2430844 2430924 2430967 "RETRACT" 2431100 NIL RETRACT (NIL T) -9 NIL 2431187 NIL) (-1054 2430693 2430718 2430805 "RETRACT-" 2430810 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1053 2430295 2430515 2430585 "RETAST" 2430645 T RETAST (NIL) -8 NIL NIL NIL) (-1052 2423033 2429948 2430075 "RESULT" 2430190 T RESULT (NIL) -8 NIL NIL NIL) (-1051 2421624 2422302 2422501 "RESRING" 2422936 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1050 2421260 2421309 2421407 "RESLATC" 2421561 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1049 2420965 2421000 2421107 "REPSQ" 2421219 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1048 2418387 2418967 2419569 "REP" 2420385 T REP (NIL) -7 NIL NIL NIL) (-1047 2418084 2418119 2418230 "REPDB" 2418346 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1046 2411984 2413373 2414596 "REP2" 2416896 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1045 2408361 2409042 2409850 "REP1" 2411211 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1044 2401057 2406502 2406958 "REGSET" 2407991 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1043 2399822 2400205 2400455 "REF" 2400842 NIL REF (NIL T) -8 NIL NIL NIL) (-1042 2399199 2399302 2399469 "REDORDER" 2399706 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1041 2395167 2398412 2398639 "RECLOS" 2399027 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1040 2394219 2394400 2394615 "REALSOLV" 2394974 T REALSOLV (NIL) -7 NIL NIL NIL) (-1039 2394065 2394106 2394136 "REAL" 2394141 T REAL (NIL) -9 NIL 2394176 NIL) (-1038 2390548 2391350 2392234 "REAL0Q" 2393230 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1037 2386149 2387137 2388198 "REAL0" 2389529 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1036 2385620 2385866 2385960 "RDUCEAST" 2386077 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1035 2385025 2385097 2385304 "RDIV" 2385542 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1034 2384093 2384267 2384480 "RDIST" 2384847 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1033 2382690 2382977 2383349 "RDETRS" 2383801 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1032 2380502 2380956 2381494 "RDETR" 2382232 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1031 2379127 2379405 2379802 "RDEEFS" 2380218 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1030 2377636 2377942 2378367 "RDEEF" 2378815 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1029 2371697 2374617 2374647 "RCFIELD" 2375942 T RCFIELD (NIL) -9 NIL 2376673 NIL) (-1028 2369761 2370265 2370961 "RCFIELD-" 2371036 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1027 2366030 2367862 2367905 "RCAGG" 2368989 NIL RCAGG (NIL T) -9 NIL 2369454 NIL) (-1026 2365658 2365752 2365915 "RCAGG-" 2365920 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1025 2364993 2365105 2365270 "RATRET" 2365542 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1024 2364546 2364613 2364734 "RATFACT" 2364921 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1023 2363854 2363974 2364126 "RANDSRC" 2364416 T RANDSRC (NIL) -7 NIL NIL NIL) (-1022 2363588 2363632 2363705 "RADUTIL" 2363803 T RADUTIL (NIL) -7 NIL NIL NIL) (-1021 2356609 2362419 2362730 "RADIX" 2363311 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1020 2347277 2356451 2356581 "RADFF" 2356586 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1019 2346924 2346999 2347029 "RADCAT" 2347189 T RADCAT (NIL) -9 NIL NIL NIL) (-1018 2346706 2346754 2346854 "RADCAT-" 2346859 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1017 2344804 2346476 2346568 "QUEUE" 2346649 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1016 2341252 2344737 2344785 "QUAT" 2344790 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1015 2340883 2340926 2341057 "QUATCT2" 2341203 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2333896 2337333 2337375 "QUATCAT" 2338166 NIL QUATCAT (NIL T) -9 NIL 2338932 NIL) (-1013 2330035 2331072 2332462 "QUATCAT-" 2332558 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1012 2327500 2329111 2329154 "QUAGG" 2329535 NIL QUAGG (NIL T) -9 NIL 2329710 NIL) (-1011 2327102 2327322 2327392 "QQUTAST" 2327452 T QQUTAST (NIL) -8 NIL NIL NIL) (-1010 2326115 2326615 2326780 "QFORM" 2326983 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1009 2316689 2322017 2322059 "QFCAT" 2322727 NIL QFCAT (NIL T) -9 NIL 2323728 NIL) (-1008 2312034 2313297 2314971 "QFCAT-" 2315067 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1007 2311665 2311708 2311839 "QFCAT2" 2311985 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1006 2311120 2311230 2311362 "QEQUAT" 2311555 T QEQUAT (NIL) -8 NIL NIL NIL) (-1005 2304246 2305319 2306505 "QCMPACK" 2310053 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1004 2301784 2302232 2302662 "QALGSET" 2303901 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1003 2301019 2301195 2301431 "QALGSET2" 2301602 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1002 2299704 2299928 2300247 "PWFFINTB" 2300792 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1001 2297879 2298047 2298403 "PUSHVAR" 2299518 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1000 2293768 2294822 2294865 "PTRANFN" 2296776 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-999 2292170 2292461 2292783 "PTPACK" 2293479 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-998 2291802 2291859 2291968 "PTFUNC2" 2292107 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-997 2286247 2290644 2290685 "PTCAT" 2290981 NIL PTCAT (NIL T) -9 NIL 2291134 NIL) (-996 2285905 2285940 2286064 "PSQFR" 2286206 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-995 2284500 2284798 2285132 "PSEUDLIN" 2285603 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-994 2271263 2273634 2275958 "PSETPK" 2282260 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-993 2264281 2267021 2267117 "PSETCAT" 2270138 NIL PSETCAT (NIL T T T T) -9 NIL 2270952 NIL) (-992 2262117 2262751 2263572 "PSETCAT-" 2263577 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-991 2261466 2261631 2261659 "PSCURVE" 2261927 T PSCURVE (NIL) -9 NIL 2262094 NIL) (-990 2257464 2258980 2259045 "PSCAT" 2259889 NIL PSCAT (NIL T T T) -9 NIL 2260129 NIL) (-989 2256527 2256743 2257143 "PSCAT-" 2257148 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-988 2254886 2255596 2255859 "PRTITION" 2256284 T PRTITION (NIL) -8 NIL NIL NIL) (-987 2254361 2254607 2254699 "PRTDAST" 2254814 T PRTDAST (NIL) -8 NIL NIL NIL) (-986 2243451 2245665 2247853 "PRS" 2252223 NIL PRS (NIL T T) -7 NIL NIL NIL) (-985 2241262 2242801 2242841 "PRQAGG" 2243024 NIL PRQAGG (NIL T) -9 NIL 2243126 NIL) (-984 2240598 2240903 2240931 "PROPLOG" 2241070 T PROPLOG (NIL) -9 NIL 2241185 NIL) (-983 2240202 2240259 2240382 "PROPFUN2" 2240521 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-982 2239517 2239638 2239810 "PROPFUN1" 2240063 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-981 2237698 2238264 2238561 "PROPFRML" 2239253 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-980 2237167 2237274 2237402 "PROPERTY" 2237590 T PROPERTY (NIL) -8 NIL NIL NIL) (-979 2231225 2235333 2236153 "PRODUCT" 2236393 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-978 2228503 2230683 2230917 "PR" 2231036 NIL PR (NIL T T) -8 NIL NIL NIL) (-977 2228299 2228331 2228390 "PRINT" 2228464 T PRINT (NIL) -7 NIL NIL NIL) (-976 2227639 2227756 2227908 "PRIMES" 2228179 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-975 2225704 2226105 2226571 "PRIMELT" 2227218 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-974 2225433 2225482 2225510 "PRIMCAT" 2225634 T PRIMCAT (NIL) -9 NIL NIL NIL) (-973 2221548 2225371 2225416 "PRIMARR" 2225421 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-972 2220555 2220733 2220961 "PRIMARR2" 2221366 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-971 2220198 2220254 2220365 "PREASSOC" 2220493 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-970 2219673 2219806 2219834 "PPCURVE" 2220039 T PPCURVE (NIL) -9 NIL 2220175 NIL) (-969 2219268 2219468 2219551 "PORTNUM" 2219610 T PORTNUM (NIL) -8 NIL NIL NIL) (-968 2216627 2217026 2217618 "POLYROOT" 2218849 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-967 2210720 2216231 2216391 "POLY" 2216500 NIL POLY (NIL T) -8 NIL NIL NIL) (-966 2210103 2210161 2210395 "POLYLIFT" 2210656 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-965 2206378 2206827 2207456 "POLYCATQ" 2209648 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-964 2192907 2198125 2198190 "POLYCAT" 2201704 NIL POLYCAT (NIL T T T) -9 NIL 2203582 NIL) (-963 2186134 2188058 2190522 "POLYCAT-" 2190527 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-962 2185721 2185789 2185909 "POLY2UP" 2186060 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-961 2185353 2185410 2185519 "POLY2" 2185658 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-960 2184038 2184277 2184553 "POLUTIL" 2185127 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-959 2182393 2182670 2183001 "POLTOPOL" 2183760 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-958 2177858 2182329 2182375 "POINT" 2182380 NIL POINT (NIL T) -8 NIL NIL NIL) (-957 2176045 2176402 2176777 "PNTHEORY" 2177503 T PNTHEORY (NIL) -7 NIL NIL NIL) (-956 2174503 2174800 2175199 "PMTOOLS" 2175743 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-955 2174096 2174174 2174291 "PMSYM" 2174419 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-954 2173604 2173673 2173848 "PMQFCAT" 2174021 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-953 2172959 2173069 2173225 "PMPRED" 2173481 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-952 2172352 2172438 2172600 "PMPREDFS" 2172860 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-951 2171016 2171224 2171602 "PMPLCAT" 2172114 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-950 2170548 2170627 2170779 "PMLSAGG" 2170931 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-949 2170021 2170097 2170279 "PMKERNEL" 2170466 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-948 2169638 2169713 2169826 "PMINS" 2169940 NIL PMINS (NIL T) -7 NIL NIL NIL) (-947 2169080 2169149 2169358 "PMFS" 2169563 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-946 2168308 2168426 2168631 "PMDOWN" 2168957 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-945 2167475 2167633 2167814 "PMASS" 2168147 T PMASS (NIL) -7 NIL NIL NIL) (-944 2166748 2166858 2167021 "PMASSFS" 2167362 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-943 2166403 2166471 2166565 "PLOTTOOL" 2166674 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-942 2161010 2162214 2163362 "PLOT" 2165275 T PLOT (NIL) -8 NIL NIL NIL) (-941 2156814 2157858 2158779 "PLOT3D" 2160109 T PLOT3D (NIL) -8 NIL NIL NIL) (-940 2155726 2155903 2156138 "PLOT1" 2156618 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-939 2131117 2135792 2140643 "PLEQN" 2150992 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-938 2130435 2130557 2130737 "PINTERP" 2130982 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-937 2130128 2130175 2130278 "PINTERPA" 2130382 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-936 2129344 2129892 2129979 "PI" 2130019 T PI (NIL) -8 NIL NIL 2130086) (-935 2127641 2128616 2128644 "PID" 2128826 T PID (NIL) -9 NIL 2128960 NIL) (-934 2127392 2127429 2127504 "PICOERCE" 2127598 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-933 2126712 2126851 2127027 "PGROEB" 2127248 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-932 2122299 2123113 2124018 "PGE" 2125827 T PGE (NIL) -7 NIL NIL NIL) (-931 2120422 2120669 2121035 "PGCD" 2122016 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-930 2119760 2119863 2120024 "PFRPAC" 2120306 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-929 2116400 2118308 2118661 "PFR" 2119439 NIL PFR (NIL T) -8 NIL NIL NIL) (-928 2114789 2115033 2115358 "PFOTOOLS" 2116147 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-927 2113322 2113561 2113912 "PFOQ" 2114546 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-926 2111823 2112035 2112391 "PFO" 2113106 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-925 2108376 2111712 2111781 "PF" 2111786 NIL PF (NIL NIL) -8 NIL NIL NIL) (-924 2105710 2106981 2107009 "PFECAT" 2107594 T PFECAT (NIL) -9 NIL 2107978 NIL) (-923 2105155 2105309 2105523 "PFECAT-" 2105528 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-922 2103758 2104010 2104311 "PFBRU" 2104904 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-921 2101624 2101976 2102408 "PFBR" 2103409 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-920 2097670 2099136 2099783 "PERM" 2101010 NIL PERM (NIL T) -8 NIL NIL NIL) (-919 2092904 2093877 2094747 "PERMGRP" 2096833 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-918 2091023 2091983 2092024 "PERMCAT" 2092424 NIL PERMCAT (NIL T) -9 NIL 2092722 NIL) (-917 2090676 2090717 2090841 "PERMAN" 2090976 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-916 2088164 2090341 2090463 "PENDTREE" 2090587 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-915 2087093 2087308 2087349 "PDSPC" 2087882 NIL PDSPC (NIL T) -9 NIL 2088127 NIL) (-914 2086196 2086414 2086776 "PDSPC-" 2086781 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-913 2085078 2085846 2085887 "PDRING" 2085892 NIL PDRING (NIL T) -9 NIL 2085920 NIL) (-912 2082293 2083071 2083739 "PDEPROB" 2084430 T PDEPROB (NIL) -8 NIL NIL NIL) (-911 2079838 2080342 2080897 "PDEPACK" 2081758 T PDEPACK (NIL) -7 NIL NIL NIL) (-910 2078750 2078940 2079191 "PDECOMP" 2079637 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-909 2076329 2077172 2077200 "PDECAT" 2077987 T PDECAT (NIL) -9 NIL 2078700 NIL) (-908 2075958 2076013 2076067 "PDDOM" 2076232 NIL PDDOM (NIL T T) -9 NIL 2076312 NIL) (-907 2075777 2075807 2075914 "PDDOM-" 2075919 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-906 2075528 2075561 2075651 "PCOMP" 2075738 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-905 2073706 2074329 2074626 "PBWLB" 2075257 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-904 2066179 2067779 2069117 "PATTERN" 2072389 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-903 2065811 2065868 2065977 "PATTERN2" 2066116 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-902 2063568 2063956 2064413 "PATTERN1" 2065400 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-901 2060936 2061517 2061998 "PATRES" 2063133 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-900 2060500 2060567 2060699 "PATRES2" 2060863 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-899 2058383 2058788 2059195 "PATMATCH" 2060167 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-898 2057893 2058102 2058143 "PATMAB" 2058250 NIL PATMAB (NIL T) -9 NIL 2058333 NIL) (-897 2056411 2056747 2057005 "PATLRES" 2057698 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-896 2055957 2056080 2056121 "PATAB" 2056126 NIL PATAB (NIL T) -9 NIL 2056298 NIL) (-895 2054139 2054534 2054957 "PARTPERM" 2055554 T PARTPERM (NIL) -7 NIL NIL NIL) (-894 2053760 2053823 2053925 "PARSURF" 2054070 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-893 2053392 2053449 2053558 "PARSU2" 2053697 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-892 2053156 2053196 2053263 "PARSER" 2053345 T PARSER (NIL) -7 NIL NIL NIL) (-891 2052777 2052840 2052942 "PARSCURV" 2053087 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-890 2052409 2052466 2052575 "PARSC2" 2052714 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-889 2052048 2052106 2052203 "PARPCURV" 2052345 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-888 2051680 2051737 2051846 "PARPC2" 2051985 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-887 2050741 2051053 2051235 "PARAMAST" 2051518 T PARAMAST (NIL) -8 NIL NIL NIL) (-886 2050261 2050347 2050466 "PAN2EXPR" 2050642 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-885 2049038 2049382 2049610 "PALETTE" 2050053 T PALETTE (NIL) -8 NIL NIL NIL) (-884 2047431 2048043 2048403 "PAIR" 2048724 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-883 2041210 2046688 2046883 "PADICRC" 2047285 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-882 2034334 2040554 2040739 "PADICRAT" 2041057 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-881 2032649 2034271 2034316 "PADIC" 2034321 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-880 2029759 2031323 2031363 "PADICCT" 2031944 NIL PADICCT (NIL NIL) -9 NIL 2032226 NIL) (-879 2028716 2028916 2029184 "PADEPAC" 2029546 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-878 2027928 2028061 2028267 "PADE" 2028578 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-877 2026315 2027136 2027416 "OWP" 2027732 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-876 2025808 2026021 2026118 "OVERSET" 2026238 T OVERSET (NIL) -8 NIL NIL NIL) (-875 2024854 2025413 2025585 "OVAR" 2025676 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-874 2024118 2024239 2024400 "OUT" 2024713 T OUT (NIL) -7 NIL NIL NIL) (-873 2012990 2015227 2017427 "OUTFORM" 2021938 T OUTFORM (NIL) -8 NIL NIL NIL) (-872 2012326 2012587 2012714 "OUTBFILE" 2012883 T OUTBFILE (NIL) -8 NIL NIL NIL) (-871 2011633 2011798 2011826 "OUTBCON" 2012144 T OUTBCON (NIL) -9 NIL 2012310 NIL) (-870 2011234 2011346 2011503 "OUTBCON-" 2011508 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-869 2010614 2010963 2011052 "OSI" 2011165 T OSI (NIL) -8 NIL NIL NIL) (-868 2010144 2010482 2010510 "OSGROUP" 2010515 T OSGROUP (NIL) -9 NIL 2010537 NIL) (-867 2008889 2009116 2009401 "ORTHPOL" 2009891 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-866 2006440 2008724 2008845 "OREUP" 2008850 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-865 2003843 2006131 2006258 "ORESUP" 2006382 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-864 2001371 2001871 2002432 "OREPCTO" 2003332 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-863 1995057 1997258 1997299 "OREPCAT" 1999647 NIL OREPCAT (NIL T) -9 NIL 2000751 NIL) (-862 1992204 1992986 1994044 "OREPCAT-" 1994049 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-861 1991355 1991653 1991681 "ORDSET" 1991990 T ORDSET (NIL) -9 NIL 1992154 NIL) (-860 1990786 1990934 1991158 "ORDSET-" 1991163 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-859 1989351 1990142 1990170 "ORDRING" 1990372 T ORDRING (NIL) -9 NIL 1990497 NIL) (-858 1988996 1989090 1989234 "ORDRING-" 1989239 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-857 1988376 1988839 1988867 "ORDMON" 1988872 T ORDMON (NIL) -9 NIL 1988893 NIL) (-856 1987538 1987685 1987880 "ORDFUNS" 1988225 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-855 1986876 1987295 1987323 "ORDFIN" 1987388 T ORDFIN (NIL) -9 NIL 1987462 NIL) (-854 1983435 1985462 1985871 "ORDCOMP" 1986500 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-853 1982701 1982828 1983014 "ORDCOMP2" 1983295 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-852 1979282 1980192 1981006 "OPTPROB" 1981907 T OPTPROB (NIL) -8 NIL NIL NIL) (-851 1976084 1976723 1977427 "OPTPACK" 1978598 T OPTPACK (NIL) -7 NIL NIL NIL) (-850 1973771 1974537 1974565 "OPTCAT" 1975384 T OPTCAT (NIL) -9 NIL 1976034 NIL) (-849 1973155 1973448 1973553 "OPSIG" 1973686 T OPSIG (NIL) -8 NIL NIL NIL) (-848 1972923 1972962 1973028 "OPQUERY" 1973109 T OPQUERY (NIL) -7 NIL NIL NIL) (-847 1970054 1971234 1971738 "OP" 1972452 NIL OP (NIL T) -8 NIL NIL NIL) (-846 1969428 1969654 1969695 "OPERCAT" 1969907 NIL OPERCAT (NIL T) -9 NIL 1970004 NIL) (-845 1969183 1969239 1969356 "OPERCAT-" 1969361 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-844 1965996 1967980 1968349 "ONECOMP" 1968847 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-843 1965301 1965416 1965590 "ONECOMP2" 1965868 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1964720 1964826 1964956 "OMSERVER" 1965191 T OMSERVER (NIL) -7 NIL NIL NIL) (-841 1961582 1964160 1964200 "OMSAGG" 1964261 NIL OMSAGG (NIL T) -9 NIL 1964325 NIL) (-840 1960205 1960468 1960750 "OMPKG" 1961320 T OMPKG (NIL) -7 NIL NIL NIL) (-839 1959635 1959738 1959766 "OM" 1960065 T OM (NIL) -9 NIL NIL NIL) (-838 1958182 1959184 1959353 "OMLO" 1959516 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-837 1957142 1957289 1957509 "OMEXPR" 1958008 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-836 1956433 1956688 1956824 "OMERR" 1957026 T OMERR (NIL) -8 NIL NIL NIL) (-835 1955584 1955854 1956014 "OMERRK" 1956293 T OMERRK (NIL) -8 NIL NIL NIL) (-834 1955035 1955261 1955369 "OMENC" 1955496 T OMENC (NIL) -8 NIL NIL NIL) (-833 1948930 1950115 1951286 "OMDEV" 1953884 T OMDEV (NIL) -8 NIL NIL NIL) (-832 1947999 1948170 1948364 "OMCONN" 1948756 T OMCONN (NIL) -8 NIL NIL NIL) (-831 1946520 1947496 1947524 "OINTDOM" 1947529 T OINTDOM (NIL) -9 NIL 1947550 NIL) (-830 1943858 1945208 1945545 "OFMONOID" 1946215 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-829 1943230 1943795 1943840 "ODVAR" 1943845 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-828 1940653 1942975 1943130 "ODR" 1943135 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-827 1933145 1940429 1940555 "ODPOL" 1940560 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-826 1927120 1933017 1933122 "ODP" 1933127 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-825 1925886 1926101 1926376 "ODETOOLS" 1926894 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-824 1922853 1923511 1924227 "ODESYS" 1925219 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-823 1917735 1918643 1919668 "ODERTRIC" 1921928 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-822 1917161 1917243 1917437 "ODERED" 1917647 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-821 1914049 1914597 1915274 "ODERAT" 1916584 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-820 1911008 1911473 1912070 "ODEPRRIC" 1913578 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-819 1908951 1909547 1910033 "ODEPROB" 1910542 T ODEPROB (NIL) -8 NIL NIL NIL) (-818 1905471 1905956 1906603 "ODEPRIM" 1908430 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-817 1904720 1904822 1905082 "ODEPAL" 1905363 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-816 1900882 1901673 1902537 "ODEPACK" 1903876 T ODEPACK (NIL) -7 NIL NIL NIL) (-815 1899943 1900050 1900272 "ODEINT" 1900771 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-814 1894044 1895469 1896916 "ODEIFTBL" 1898516 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-813 1889442 1890228 1891180 "ODEEF" 1893203 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-812 1888791 1888880 1889103 "ODECONST" 1889347 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-811 1886916 1887577 1887605 "ODECAT" 1888210 T ODECAT (NIL) -9 NIL 1888741 NIL) (-810 1883771 1886621 1886743 "OCT" 1886826 NIL OCT (NIL T) -8 NIL NIL NIL) (-809 1883409 1883452 1883579 "OCTCT2" 1883722 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-808 1878020 1880455 1880495 "OC" 1881592 NIL OC (NIL T) -9 NIL 1882450 NIL) (-807 1875247 1875995 1876985 "OC-" 1877079 NIL OC- (NIL T T) -8 NIL NIL NIL) (-806 1874599 1875067 1875095 "OCAMON" 1875100 T OCAMON (NIL) -9 NIL 1875121 NIL) (-805 1874130 1874471 1874499 "OASGP" 1874504 T OASGP (NIL) -9 NIL 1874524 NIL) (-804 1873391 1873880 1873908 "OAMONS" 1873948 T OAMONS (NIL) -9 NIL 1873991 NIL) (-803 1872805 1873238 1873266 "OAMON" 1873271 T OAMON (NIL) -9 NIL 1873291 NIL) (-802 1872063 1872581 1872609 "OAGROUP" 1872614 T OAGROUP (NIL) -9 NIL 1872634 NIL) (-801 1871753 1871803 1871891 "NUMTUBE" 1872007 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-800 1865326 1866844 1868380 "NUMQUAD" 1870237 T NUMQUAD (NIL) -7 NIL NIL NIL) (-799 1861082 1862070 1863095 "NUMODE" 1864321 T NUMODE (NIL) -7 NIL NIL NIL) (-798 1858437 1859317 1859345 "NUMINT" 1860268 T NUMINT (NIL) -9 NIL 1861032 NIL) (-797 1857385 1857582 1857800 "NUMFMT" 1858239 T NUMFMT (NIL) -7 NIL NIL NIL) (-796 1843744 1846689 1849221 "NUMERIC" 1854892 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-795 1838114 1843193 1843288 "NTSCAT" 1843293 NIL NTSCAT (NIL T T T T) -9 NIL 1843332 NIL) (-794 1837308 1837473 1837666 "NTPOLFN" 1837953 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-793 1825296 1834133 1834945 "NSUP" 1836529 NIL NSUP (NIL T) -8 NIL NIL NIL) (-792 1824928 1824985 1825094 "NSUP2" 1825233 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-791 1815065 1824702 1824835 "NSMP" 1824840 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-790 1813497 1813798 1814155 "NREP" 1814753 NIL NREP (NIL T) -7 NIL NIL NIL) (-789 1812088 1812340 1812698 "NPCOEF" 1813240 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-788 1811154 1811269 1811485 "NORMRETR" 1811969 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-787 1809195 1809485 1809894 "NORMPK" 1810862 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-786 1808880 1808908 1809032 "NORMMA" 1809161 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-785 1808680 1808837 1808866 "NONE" 1808871 T NONE (NIL) -8 NIL NIL NIL) (-784 1808469 1808498 1808567 "NONE1" 1808644 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-783 1807966 1808028 1808207 "NODE1" 1808401 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-782 1806247 1807098 1807353 "NNI" 1807700 T NNI (NIL) -8 NIL NIL 1807935) (-781 1804667 1804980 1805344 "NLINSOL" 1805915 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-780 1800908 1801903 1802802 "NIPROB" 1803788 T NIPROB (NIL) -8 NIL NIL NIL) (-779 1799665 1799899 1800201 "NFINTBAS" 1800670 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-778 1798839 1799315 1799356 "NETCLT" 1799528 NIL NETCLT (NIL T) -9 NIL 1799610 NIL) (-777 1797547 1797778 1798059 "NCODIV" 1798607 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-776 1797309 1797346 1797421 "NCNTFRAC" 1797504 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-775 1795489 1795853 1796273 "NCEP" 1796934 NIL NCEP (NIL T) -7 NIL NIL NIL) (-774 1794340 1795113 1795141 "NASRING" 1795251 T NASRING (NIL) -9 NIL 1795331 NIL) (-773 1794135 1794179 1794273 "NASRING-" 1794278 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-772 1793242 1793767 1793795 "NARNG" 1793912 T NARNG (NIL) -9 NIL 1794003 NIL) (-771 1792934 1793001 1793135 "NARNG-" 1793140 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-770 1791813 1792020 1792255 "NAGSP" 1792719 T NAGSP (NIL) -7 NIL NIL NIL) (-769 1783085 1784769 1786442 "NAGS" 1790160 T NAGS (NIL) -7 NIL NIL NIL) (-768 1781633 1781941 1782272 "NAGF07" 1782774 T NAGF07 (NIL) -7 NIL NIL NIL) (-767 1776171 1777462 1778769 "NAGF04" 1780346 T NAGF04 (NIL) -7 NIL NIL NIL) (-766 1769139 1770753 1772386 "NAGF02" 1774558 T NAGF02 (NIL) -7 NIL NIL NIL) (-765 1764363 1765463 1766580 "NAGF01" 1768042 T NAGF01 (NIL) -7 NIL NIL NIL) (-764 1757991 1759557 1761142 "NAGE04" 1762798 T NAGE04 (NIL) -7 NIL NIL NIL) (-763 1749160 1751281 1753411 "NAGE02" 1755881 T NAGE02 (NIL) -7 NIL NIL NIL) (-762 1745113 1746060 1747024 "NAGE01" 1748216 T NAGE01 (NIL) -7 NIL NIL NIL) (-761 1742908 1743442 1744000 "NAGD03" 1744575 T NAGD03 (NIL) -7 NIL NIL NIL) (-760 1734658 1736586 1738540 "NAGD02" 1740974 T NAGD02 (NIL) -7 NIL NIL NIL) (-759 1728469 1729894 1731334 "NAGD01" 1733238 T NAGD01 (NIL) -7 NIL NIL NIL) (-758 1724678 1725500 1726337 "NAGC06" 1727652 T NAGC06 (NIL) -7 NIL NIL NIL) (-757 1723143 1723475 1723831 "NAGC05" 1724342 T NAGC05 (NIL) -7 NIL NIL NIL) (-756 1722519 1722638 1722782 "NAGC02" 1723019 T NAGC02 (NIL) -7 NIL NIL NIL) (-755 1721478 1722061 1722101 "NAALG" 1722180 NIL NAALG (NIL T) -9 NIL 1722241 NIL) (-754 1721313 1721342 1721432 "NAALG-" 1721437 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-753 1715263 1716371 1717558 "MULTSQFR" 1720209 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-752 1714582 1714657 1714841 "MULTFACT" 1715175 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-751 1707253 1711167 1711220 "MTSCAT" 1712290 NIL MTSCAT (NIL T T) -9 NIL 1712805 NIL) (-750 1706965 1707019 1707111 "MTHING" 1707193 NIL MTHING (NIL T) -7 NIL NIL NIL) (-749 1706757 1706790 1706850 "MSYSCMD" 1706925 T MSYSCMD (NIL) -7 NIL NIL NIL) (-748 1702839 1705512 1705832 "MSET" 1706470 NIL MSET (NIL T) -8 NIL NIL NIL) (-747 1699908 1702400 1702441 "MSETAGG" 1702446 NIL MSETAGG (NIL T) -9 NIL 1702480 NIL) (-746 1695750 1697287 1698032 "MRING" 1699208 NIL MRING (NIL T T) -8 NIL NIL NIL) (-745 1695316 1695383 1695514 "MRF2" 1695677 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-744 1694934 1694969 1695113 "MRATFAC" 1695275 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-743 1692546 1692841 1693272 "MPRFF" 1694639 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-742 1686754 1692400 1692497 "MPOLY" 1692502 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-741 1686244 1686279 1686487 "MPCPF" 1686713 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-740 1685758 1685801 1685985 "MPC3" 1686195 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1684953 1685034 1685255 "MPC2" 1685673 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-738 1683254 1683591 1683981 "MONOTOOL" 1684613 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-737 1682479 1682796 1682824 "MONOID" 1683043 T MONOID (NIL) -9 NIL 1683190 NIL) (-736 1682025 1682144 1682325 "MONOID-" 1682330 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-735 1671760 1677803 1677862 "MONOGEN" 1678536 NIL MONOGEN (NIL T T) -9 NIL 1678992 NIL) (-734 1668978 1669713 1670713 "MONOGEN-" 1670832 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-733 1667811 1668257 1668285 "MONADWU" 1668677 T MONADWU (NIL) -9 NIL 1668915 NIL) (-732 1667183 1667342 1667590 "MONADWU-" 1667595 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-731 1666542 1666786 1666814 "MONAD" 1667021 T MONAD (NIL) -9 NIL 1667133 NIL) (-730 1666227 1666305 1666437 "MONAD-" 1666442 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-729 1664516 1665140 1665419 "MOEBIUS" 1665980 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-728 1663794 1664198 1664238 "MODULE" 1664243 NIL MODULE (NIL T) -9 NIL 1664282 NIL) (-727 1663362 1663458 1663648 "MODULE-" 1663653 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-726 1661042 1661726 1662053 "MODRING" 1663186 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-725 1657986 1659147 1659668 "MODOP" 1660571 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-724 1656574 1657053 1657330 "MODMONOM" 1657849 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-723 1646529 1654865 1655279 "MODMON" 1656211 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-722 1643685 1645373 1645649 "MODFIELD" 1646404 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-721 1642662 1642966 1643156 "MMLFORM" 1643515 T MMLFORM (NIL) -8 NIL NIL NIL) (-720 1642188 1642231 1642410 "MMAP" 1642613 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-719 1640267 1641034 1641075 "MLO" 1641498 NIL MLO (NIL T) -9 NIL 1641740 NIL) (-718 1637633 1638149 1638751 "MLIFT" 1639748 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-717 1637024 1637108 1637262 "MKUCFUNC" 1637544 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-716 1636623 1636693 1636816 "MKRECORD" 1636947 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-715 1635670 1635832 1636060 "MKFUNC" 1636434 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-714 1635058 1635162 1635318 "MKFLCFN" 1635553 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-713 1634335 1634437 1634622 "MKBCFUNC" 1634951 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-712 1631010 1633889 1634025 "MINT" 1634219 T MINT (NIL) -8 NIL NIL NIL) (-711 1629822 1630065 1630342 "MHROWRED" 1630765 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-710 1625202 1628357 1628762 "MFLOAT" 1629437 T MFLOAT (NIL) -8 NIL NIL NIL) (-709 1624559 1624635 1624806 "MFINFACT" 1625114 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-708 1620874 1621722 1622606 "MESH" 1623695 T MESH (NIL) -7 NIL NIL NIL) (-707 1619264 1619576 1619929 "MDDFACT" 1620561 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-706 1616059 1618423 1618464 "MDAGG" 1618719 NIL MDAGG (NIL T) -9 NIL 1618862 NIL) (-705 1604946 1615352 1615559 "MCMPLX" 1615872 T MCMPLX (NIL) -8 NIL NIL NIL) (-704 1604083 1604229 1604430 "MCDEN" 1604795 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-703 1601973 1602243 1602623 "MCALCFN" 1603813 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-702 1600898 1601138 1601371 "MAYBE" 1601779 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-701 1598510 1599033 1599595 "MATSTOR" 1600369 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-700 1594467 1597882 1598130 "MATRIX" 1598295 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-699 1590233 1590940 1591676 "MATLIN" 1593824 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-698 1580339 1583525 1583602 "MATCAT" 1588482 NIL MATCAT (NIL T T T) -9 NIL 1589899 NIL) (-697 1576695 1577716 1579072 "MATCAT-" 1579077 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-696 1575289 1575442 1575775 "MATCAT2" 1576530 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-695 1573401 1573725 1574109 "MAPPKG3" 1574964 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-694 1572382 1572555 1572777 "MAPPKG2" 1573225 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-693 1570881 1571165 1571492 "MAPPKG1" 1572088 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-692 1569960 1570287 1570464 "MAPPAST" 1570724 T MAPPAST (NIL) -8 NIL NIL NIL) (-691 1569571 1569629 1569752 "MAPHACK3" 1569896 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-690 1569163 1569224 1569338 "MAPHACK2" 1569503 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-689 1568601 1568704 1568846 "MAPHACK1" 1569054 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-688 1566680 1567301 1567605 "MAGMA" 1568329 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-687 1566159 1566404 1566495 "MACROAST" 1566609 T MACROAST (NIL) -8 NIL NIL NIL) (-686 1562577 1564398 1564859 "M3D" 1565731 NIL M3D (NIL T) -8 NIL NIL NIL) (-685 1556652 1560916 1560957 "LZSTAGG" 1561739 NIL LZSTAGG (NIL T) -9 NIL 1562034 NIL) (-684 1552610 1553783 1555240 "LZSTAGG-" 1555245 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-683 1549697 1550501 1550988 "LWORD" 1552155 NIL LWORD (NIL T) -8 NIL NIL NIL) (-682 1549273 1549501 1549576 "LSTAST" 1549642 T LSTAST (NIL) -8 NIL NIL NIL) (-681 1542350 1549044 1549178 "LSQM" 1549183 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-680 1541574 1541713 1541941 "LSPP" 1542205 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-679 1539386 1539687 1540143 "LSMP" 1541263 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-678 1536165 1536839 1537569 "LSMP1" 1538688 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-677 1530011 1535302 1535343 "LSAGG" 1535405 NIL LSAGG (NIL T) -9 NIL 1535483 NIL) (-676 1526706 1527630 1528843 "LSAGG-" 1528848 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-675 1524305 1525850 1526099 "LPOLY" 1526501 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-674 1523887 1523972 1524095 "LPEFRAC" 1524214 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-673 1522208 1522981 1523234 "LO" 1523719 NIL LO (NIL T T T) -8 NIL NIL NIL) (-672 1521860 1521972 1522000 "LOGIC" 1522111 T LOGIC (NIL) -9 NIL 1522192 NIL) (-671 1521722 1521745 1521816 "LOGIC-" 1521821 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-670 1520915 1521055 1521248 "LODOOPS" 1521578 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-669 1518338 1520831 1520897 "LODO" 1520902 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-668 1516876 1517111 1517464 "LODOF" 1518085 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-667 1513080 1515511 1515552 "LODOCAT" 1515990 NIL LODOCAT (NIL T) -9 NIL 1516201 NIL) (-666 1512813 1512871 1512998 "LODOCAT-" 1513003 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-665 1510133 1512654 1512772 "LODO2" 1512777 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-664 1507568 1510070 1510115 "LODO1" 1510120 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-663 1506449 1506614 1506919 "LODEEF" 1507391 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-662 1501752 1504643 1504684 "LNAGG" 1505546 NIL LNAGG (NIL T) -9 NIL 1505981 NIL) (-661 1500899 1501113 1501455 "LNAGG-" 1501460 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-660 1497035 1497824 1498463 "LMOPS" 1500314 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-659 1496438 1496826 1496867 "LMODULE" 1496872 NIL LMODULE (NIL T) -9 NIL 1496898 NIL) (-658 1493636 1496083 1496206 "LMDICT" 1496348 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-657 1493042 1493263 1493304 "LLINSET" 1493495 NIL LLINSET (NIL T) -9 NIL 1493586 NIL) (-656 1492741 1492950 1493010 "LITERAL" 1493015 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-655 1485904 1491675 1491979 "LIST" 1492470 NIL LIST (NIL T) -8 NIL NIL NIL) (-654 1485429 1485503 1485642 "LIST3" 1485824 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-653 1484436 1484614 1484842 "LIST2" 1485247 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-652 1482570 1482882 1483281 "LIST2MAP" 1484083 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-651 1482166 1482403 1482444 "LINSET" 1482449 NIL LINSET (NIL T) -9 NIL 1482483 NIL) (-650 1480895 1481428 1481469 "LINEXP" 1481820 NIL LINEXP (NIL T) -9 NIL 1482011 NIL) (-649 1479472 1479732 1480043 "LINDEP" 1480647 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-648 1476239 1476958 1477735 "LIMITRF" 1478727 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-647 1474542 1474838 1475247 "LIMITPS" 1475934 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-646 1468970 1474053 1474281 "LIE" 1474363 NIL LIE (NIL T T) -8 NIL NIL NIL) (-645 1467918 1468387 1468427 "LIECAT" 1468567 NIL LIECAT (NIL T) -9 NIL 1468718 NIL) (-644 1467759 1467786 1467874 "LIECAT-" 1467879 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-643 1460346 1467299 1467455 "LIB" 1467623 T LIB (NIL) -8 NIL NIL NIL) (-642 1455981 1456864 1457799 "LGROBP" 1459463 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-641 1453979 1454253 1454603 "LF" 1455702 NIL LF (NIL T T) -7 NIL NIL NIL) (-640 1452819 1453511 1453539 "LFCAT" 1453746 T LFCAT (NIL) -9 NIL 1453885 NIL) (-639 1449721 1450351 1451039 "LEXTRIPK" 1452183 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-638 1446465 1447291 1447794 "LEXP" 1449301 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-637 1445941 1446186 1446278 "LETAST" 1446393 T LETAST (NIL) -8 NIL NIL NIL) (-636 1444339 1444652 1445053 "LEADCDET" 1445623 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-635 1443529 1443603 1443832 "LAZM3PK" 1444260 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-634 1438446 1441606 1442144 "LAUPOL" 1443041 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-633 1438025 1438069 1438230 "LAPLACE" 1438396 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-632 1435964 1437126 1437377 "LA" 1437858 NIL LA (NIL T T T) -8 NIL NIL NIL) (-631 1434958 1435542 1435583 "LALG" 1435645 NIL LALG (NIL T) -9 NIL 1435704 NIL) (-630 1434672 1434731 1434867 "LALG-" 1434872 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-629 1434507 1434531 1434572 "KVTFROM" 1434634 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-628 1433430 1433874 1434059 "KTVLOGIC" 1434342 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-627 1433265 1433289 1433330 "KRCFROM" 1433392 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-626 1432169 1432356 1432655 "KOVACIC" 1433065 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-625 1432004 1432028 1432069 "KONVERT" 1432131 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-624 1431839 1431863 1431904 "KOERCE" 1431966 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-623 1429670 1430432 1430809 "KERNEL" 1431495 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-622 1429166 1429247 1429379 "KERNEL2" 1429584 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-621 1422936 1427705 1427759 "KDAGG" 1428136 NIL KDAGG (NIL T T) -9 NIL 1428342 NIL) (-620 1422465 1422589 1422794 "KDAGG-" 1422799 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-619 1415613 1422126 1422281 "KAFILE" 1422343 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-618 1410041 1415124 1415352 "JORDAN" 1415434 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-617 1409420 1409690 1409811 "JOINAST" 1409940 T JOINAST (NIL) -8 NIL NIL NIL) (-616 1409266 1409325 1409380 "JAVACODE" 1409385 T JAVACODE (NIL) -8 NIL NIL NIL) (-615 1405518 1407471 1407525 "IXAGG" 1408454 NIL IXAGG (NIL T T) -9 NIL 1408913 NIL) (-614 1404437 1404743 1405162 "IXAGG-" 1405167 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1399967 1404359 1404418 "IVECTOR" 1404423 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-612 1398733 1398970 1399236 "ITUPLE" 1399734 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-611 1397235 1397412 1397707 "ITRIGMNP" 1398555 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-610 1395980 1396184 1396467 "ITFUN3" 1397011 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-609 1395612 1395669 1395778 "ITFUN2" 1395917 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-608 1394771 1395092 1395266 "ITFORM" 1395458 T ITFORM (NIL) -8 NIL NIL NIL) (-607 1392732 1393791 1394069 "ITAYLOR" 1394526 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-606 1381677 1386869 1388032 "ISUPS" 1391602 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-605 1380781 1380921 1381157 "ISUMP" 1381524 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-604 1376156 1380726 1380767 "ISTRING" 1380772 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-603 1375632 1375877 1375969 "ISAST" 1376084 T ISAST (NIL) -8 NIL NIL NIL) (-602 1374841 1374923 1375139 "IRURPK" 1375546 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-601 1373777 1373978 1374218 "IRSN" 1374621 T IRSN (NIL) -7 NIL NIL NIL) (-600 1371848 1372203 1372632 "IRRF2F" 1373415 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-599 1371595 1371633 1371709 "IRREDFFX" 1371804 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-598 1370210 1370469 1370768 "IROOT" 1371328 NIL IROOT (NIL T) -7 NIL NIL NIL) (-597 1366814 1367894 1368586 "IR" 1369550 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1366019 1366307 1366458 "IRFORM" 1366683 T IRFORM (NIL) -8 NIL NIL NIL) (-595 1363632 1364127 1364693 "IR2" 1365497 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-594 1362732 1362845 1363059 "IR2F" 1363515 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-593 1362523 1362557 1362617 "IPRNTPK" 1362692 T IPRNTPK (NIL) -7 NIL NIL NIL) (-592 1359104 1362412 1362481 "IPF" 1362486 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-591 1357431 1359029 1359086 "IPADIC" 1359091 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-590 1356743 1356991 1357121 "IP4ADDR" 1357321 T IP4ADDR (NIL) -8 NIL NIL NIL) (-589 1356117 1356372 1356504 "IOMODE" 1356631 T IOMODE (NIL) -8 NIL NIL NIL) (-588 1355190 1355714 1355841 "IOBFILE" 1356010 T IOBFILE (NIL) -8 NIL NIL NIL) (-587 1354678 1355094 1355122 "IOBCON" 1355127 T IOBCON (NIL) -9 NIL 1355148 NIL) (-586 1354189 1354247 1354430 "INVLAPLA" 1354614 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-585 1343837 1346191 1348577 "INTTR" 1351853 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-584 1340172 1340914 1341779 "INTTOOLS" 1343022 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-583 1339758 1339849 1339966 "INTSLPE" 1340075 T INTSLPE (NIL) -7 NIL NIL NIL) (-582 1337711 1339681 1339740 "INTRVL" 1339745 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-581 1335313 1335825 1336400 "INTRF" 1337196 NIL INTRF (NIL T) -7 NIL NIL NIL) (-580 1334724 1334821 1334963 "INTRET" 1335211 NIL INTRET (NIL T) -7 NIL NIL NIL) (-579 1332721 1333110 1333580 "INTRAT" 1334332 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-578 1329984 1330567 1331186 "INTPM" 1332206 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-577 1326729 1327328 1328066 "INTPAF" 1329370 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-576 1321908 1322870 1323921 "INTPACK" 1325698 T INTPACK (NIL) -7 NIL NIL NIL) (-575 1318806 1321705 1321814 "INT" 1321819 T INT (NIL) -8 NIL NIL NIL) (-574 1318058 1318210 1318418 "INTHERTR" 1318648 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-573 1317497 1317577 1317765 "INTHERAL" 1317972 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-572 1315343 1315786 1316243 "INTHEORY" 1317060 T INTHEORY (NIL) -7 NIL NIL NIL) (-571 1306749 1308370 1310142 "INTG0" 1313695 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-570 1287322 1292112 1296922 "INTFTBL" 1301959 T INTFTBL (NIL) -8 NIL NIL NIL) (-569 1286571 1286709 1286882 "INTFACT" 1287181 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-568 1283998 1284444 1285001 "INTEF" 1286125 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-567 1282365 1283104 1283132 "INTDOM" 1283433 T INTDOM (NIL) -9 NIL 1283640 NIL) (-566 1281734 1281908 1282150 "INTDOM-" 1282155 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-565 1278122 1280050 1280104 "INTCAT" 1280903 NIL INTCAT (NIL T) -9 NIL 1281224 NIL) (-564 1277594 1277697 1277825 "INTBIT" 1278014 T INTBIT (NIL) -7 NIL NIL NIL) (-563 1276293 1276447 1276754 "INTALG" 1277439 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-562 1275776 1275866 1276023 "INTAF" 1276197 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-561 1269119 1275586 1275726 "INTABL" 1275731 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-560 1268452 1268918 1268983 "INT8" 1269017 T INT8 (NIL) -8 NIL NIL 1269062) (-559 1267784 1268250 1268315 "INT64" 1268349 T INT64 (NIL) -8 NIL NIL 1268394) (-558 1267116 1267582 1267647 "INT32" 1267681 T INT32 (NIL) -8 NIL NIL 1267726) (-557 1266448 1266914 1266979 "INT16" 1267013 T INT16 (NIL) -8 NIL NIL 1267058) (-556 1261243 1264009 1264037 "INS" 1264971 T INS (NIL) -9 NIL 1265636 NIL) (-555 1258483 1259254 1260228 "INS-" 1260301 NIL INS- (NIL T) -8 NIL NIL NIL) (-554 1257258 1257485 1257783 "INPSIGN" 1258236 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-553 1256376 1256493 1256690 "INPRODPF" 1257138 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-552 1255270 1255387 1255624 "INPRODFF" 1256256 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-551 1254270 1254422 1254682 "INNMFACT" 1255106 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-550 1253467 1253564 1253752 "INMODGCD" 1254169 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-549 1251975 1252220 1252544 "INFSP" 1253212 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-548 1251159 1251276 1251459 "INFPROD0" 1251855 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-547 1248014 1249224 1249739 "INFORM" 1250652 T INFORM (NIL) -8 NIL NIL NIL) (-546 1247624 1247684 1247782 "INFORM1" 1247949 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-545 1247147 1247236 1247350 "INFINITY" 1247530 T INFINITY (NIL) -7 NIL NIL NIL) (-544 1246323 1246867 1246968 "INETCLTS" 1247066 T INETCLTS (NIL) -8 NIL NIL NIL) (-543 1244939 1245189 1245510 "INEP" 1246071 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-542 1244188 1244836 1244901 "INDE" 1244906 NIL INDE (NIL T) -8 NIL NIL NIL) (-541 1243752 1243820 1243937 "INCRMAPS" 1244115 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-540 1242570 1243021 1243227 "INBFILE" 1243566 T INBFILE (NIL) -8 NIL NIL NIL) (-539 1237869 1238806 1239750 "INBFF" 1241658 NIL INBFF (NIL T) -7 NIL NIL NIL) (-538 1236777 1237046 1237074 "INBCON" 1237587 T INBCON (NIL) -9 NIL 1237853 NIL) (-537 1236029 1236252 1236528 "INBCON-" 1236533 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-536 1235508 1235753 1235844 "INAST" 1235958 T INAST (NIL) -8 NIL NIL NIL) (-535 1234935 1235187 1235293 "IMPTAST" 1235422 T IMPTAST (NIL) -8 NIL NIL NIL) (-534 1231381 1234779 1234883 "IMATRIX" 1234888 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-533 1230089 1230212 1230528 "IMATQF" 1231237 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-532 1228309 1228536 1228873 "IMATLIN" 1229845 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-531 1222887 1228233 1228291 "ILIST" 1228296 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-530 1220792 1222747 1222860 "IIARRAY2" 1222865 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-529 1216190 1220703 1220767 "IFF" 1220772 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-528 1215537 1215807 1215923 "IFAST" 1216094 T IFAST (NIL) -8 NIL NIL NIL) (-527 1210532 1214829 1215017 "IFARRAY" 1215394 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-526 1209712 1210436 1210509 "IFAMON" 1210514 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-525 1209296 1209361 1209415 "IEVALAB" 1209622 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-524 1208971 1209039 1209199 "IEVALAB-" 1209204 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-523 1208602 1208885 1208948 "IDPO" 1208953 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-522 1207852 1208491 1208566 "IDPOAMS" 1208571 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-521 1207159 1207741 1207816 "IDPOAM" 1207821 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-520 1206218 1206494 1206547 "IDPC" 1206960 NIL IDPC (NIL T T) -9 NIL 1207109 NIL) (-519 1205687 1206110 1206183 "IDPAM" 1206188 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-518 1205063 1205579 1205652 "IDPAG" 1205657 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-517 1204708 1204899 1204974 "IDENT" 1205008 T IDENT (NIL) -8 NIL NIL NIL) (-516 1200963 1201811 1202706 "IDECOMP" 1203865 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-515 1193800 1194886 1195933 "IDEAL" 1199999 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-514 1192960 1193072 1193272 "ICDEN" 1193684 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-513 1192031 1192440 1192587 "ICARD" 1192833 T ICARD (NIL) -8 NIL NIL NIL) (-512 1190091 1190404 1190809 "IBPTOOLS" 1191708 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-511 1185698 1189711 1189824 "IBITS" 1190010 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-510 1182421 1182997 1183692 "IBATOOL" 1185115 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-509 1180200 1180662 1181195 "IBACHIN" 1181956 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-508 1178029 1180046 1180149 "IARRAY2" 1180154 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-507 1174135 1177955 1178012 "IARRAY1" 1178017 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-506 1168173 1172547 1173028 "IAN" 1173674 T IAN (NIL) -8 NIL NIL NIL) (-505 1167684 1167741 1167914 "IALGFACT" 1168110 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-504 1167212 1167325 1167353 "HYPCAT" 1167560 T HYPCAT (NIL) -9 NIL NIL NIL) (-503 1166750 1166867 1167053 "HYPCAT-" 1167058 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-502 1166345 1166545 1166628 "HOSTNAME" 1166687 T HOSTNAME (NIL) -8 NIL NIL NIL) (-501 1166190 1166227 1166268 "HOMOTOP" 1166273 NIL HOMOTOP (NIL T) -9 NIL 1166306 NIL) (-500 1162822 1164200 1164241 "HOAGG" 1165222 NIL HOAGG (NIL T) -9 NIL 1165901 NIL) (-499 1161416 1161815 1162341 "HOAGG-" 1162346 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-498 1155325 1161009 1161159 "HEXADEC" 1161286 T HEXADEC (NIL) -8 NIL NIL NIL) (-497 1154073 1154295 1154558 "HEUGCD" 1155102 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-496 1153149 1153910 1154040 "HELLFDIV" 1154045 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-495 1151328 1152926 1153014 "HEAP" 1153093 NIL HEAP (NIL T) -8 NIL NIL NIL) (-494 1150591 1150880 1151014 "HEADAST" 1151214 T HEADAST (NIL) -8 NIL NIL NIL) (-493 1144610 1150506 1150568 "HDP" 1150573 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-492 1138509 1144245 1144397 "HDMP" 1144511 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-491 1137833 1137973 1138137 "HB" 1138365 T HB (NIL) -7 NIL NIL NIL) (-490 1131219 1137679 1137783 "HASHTBL" 1137788 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-489 1130695 1130940 1131032 "HASAST" 1131147 T HASAST (NIL) -8 NIL NIL NIL) (-488 1128473 1130317 1130499 "HACKPI" 1130533 T HACKPI (NIL) -8 NIL NIL NIL) (-487 1124141 1128326 1128439 "GTSET" 1128444 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-486 1117556 1124019 1124117 "GSTBL" 1124122 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-485 1109943 1116721 1116977 "GSERIES" 1117356 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-484 1109084 1109501 1109529 "GROUP" 1109732 T GROUP (NIL) -9 NIL 1109866 NIL) (-483 1108450 1108609 1108860 "GROUP-" 1108865 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-482 1106817 1107138 1107525 "GROEBSOL" 1108127 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-481 1105731 1106019 1106070 "GRMOD" 1106599 NIL GRMOD (NIL T T) -9 NIL 1106767 NIL) (-480 1105499 1105535 1105663 "GRMOD-" 1105668 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-479 1100789 1101853 1102853 "GRIMAGE" 1104519 T GRIMAGE (NIL) -8 NIL NIL NIL) (-478 1099255 1099516 1099840 "GRDEF" 1100485 T GRDEF (NIL) -7 NIL NIL NIL) (-477 1098699 1098815 1098956 "GRAY" 1099134 T GRAY (NIL) -7 NIL NIL NIL) (-476 1097886 1098292 1098343 "GRALG" 1098496 NIL GRALG (NIL T T) -9 NIL 1098589 NIL) (-475 1097547 1097620 1097783 "GRALG-" 1097788 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-474 1094324 1097132 1097310 "GPOLSET" 1097454 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-473 1093678 1093735 1093993 "GOSPER" 1094261 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-472 1089410 1090116 1090642 "GMODPOL" 1093377 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-471 1088415 1088599 1088837 "GHENSEL" 1089222 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-470 1082571 1083414 1084434 "GENUPS" 1087499 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-469 1082268 1082319 1082408 "GENUFACT" 1082514 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-468 1081680 1081757 1081922 "GENPGCD" 1082186 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-467 1081154 1081189 1081402 "GENMFACT" 1081639 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-466 1079720 1079977 1080284 "GENEEZ" 1080897 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-465 1073779 1079331 1079493 "GDMP" 1079643 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-464 1063122 1067550 1068656 "GCNAALG" 1072762 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-463 1061449 1062311 1062339 "GCDDOM" 1062594 T GCDDOM (NIL) -9 NIL 1062751 NIL) (-462 1060919 1061046 1061261 "GCDDOM-" 1061266 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-461 1059591 1059776 1060080 "GB" 1060698 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1048207 1050537 1052929 "GBINTERN" 1057282 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-459 1046044 1046336 1046757 "GBF" 1047882 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-458 1044825 1044990 1045257 "GBEUCLID" 1045860 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-457 1044174 1044299 1044448 "GAUSSFAC" 1044696 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-456 1042541 1042843 1043157 "GALUTIL" 1043893 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-455 1040849 1041123 1041447 "GALPOLYU" 1042268 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-454 1038214 1038504 1038911 "GALFACTU" 1040546 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-453 1030020 1031519 1033127 "GALFACT" 1036646 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-452 1027408 1028066 1028094 "FVFUN" 1029250 T FVFUN (NIL) -9 NIL 1029970 NIL) (-451 1026674 1026856 1026884 "FVC" 1027175 T FVC (NIL) -9 NIL 1027358 NIL) (-450 1026317 1026499 1026567 "FUNDESC" 1026626 T FUNDESC (NIL) -8 NIL NIL NIL) (-449 1025932 1026114 1026195 "FUNCTION" 1026269 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-448 1023676 1024254 1024720 "FT" 1025486 T FT (NIL) -8 NIL NIL NIL) (-447 1022467 1022977 1023180 "FTEM" 1023493 T FTEM (NIL) -8 NIL NIL NIL) (-446 1020758 1021047 1021444 "FSUPFACT" 1022158 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-445 1019155 1019444 1019776 "FST" 1020446 T FST (NIL) -8 NIL NIL NIL) (-444 1018354 1018460 1018648 "FSRED" 1019037 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-443 1017053 1017309 1017656 "FSPRMELT" 1018069 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-442 1014359 1014797 1015283 "FSPECF" 1016616 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-441 995661 1004133 1004174 "FS" 1008058 NIL FS (NIL T) -9 NIL 1010347 NIL) (-440 984304 987297 991354 "FS-" 991654 NIL FS- (NIL T T) -8 NIL NIL NIL) (-439 983832 983886 984056 "FSINT" 984245 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-438 982124 982825 983128 "FSERIES" 983611 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-437 981166 981282 981506 "FSCINT" 982004 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-436 977374 980110 980151 "FSAGG" 980521 NIL FSAGG (NIL T) -9 NIL 980780 NIL) (-435 975136 975737 976533 "FSAGG-" 976628 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-434 974178 974321 974548 "FSAGG2" 974989 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-433 971856 972136 972684 "FS2UPS" 973896 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-432 971490 971533 971662 "FS2" 971807 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-431 970368 970539 970841 "FS2EXPXP" 971315 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-430 969794 969909 970061 "FRUTIL" 970248 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-429 961207 965289 966647 "FR" 968468 NIL FR (NIL T) -8 NIL NIL NIL) (-428 956221 958896 958936 "FRNAALG" 960256 NIL FRNAALG (NIL T) -9 NIL 960854 NIL) (-427 951894 952970 954245 "FRNAALG-" 954995 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-426 951532 951575 951702 "FRNAAF2" 951845 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-425 949907 950381 950677 "FRMOD" 951344 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-424 947650 948282 948600 "FRIDEAL" 949698 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-423 946841 946928 947219 "FRIDEAL2" 947557 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-422 945974 946388 946429 "FRETRCT" 946434 NIL FRETRCT (NIL T) -9 NIL 946610 NIL) (-421 945086 945317 945668 "FRETRCT-" 945673 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-420 942174 943384 943443 "FRAMALG" 944325 NIL FRAMALG (NIL T T) -9 NIL 944617 NIL) (-419 940308 940763 941393 "FRAMALG-" 941616 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-418 934138 939781 940058 "FRAC" 940063 NIL FRAC (NIL T) -8 NIL NIL NIL) (-417 933774 933831 933938 "FRAC2" 934075 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-416 933410 933467 933574 "FR2" 933711 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-415 927923 930816 930844 "FPS" 931963 T FPS (NIL) -9 NIL 932520 NIL) (-414 927372 927481 927645 "FPS-" 927791 NIL FPS- (NIL T) -8 NIL NIL NIL) (-413 924674 926343 926371 "FPC" 926596 T FPC (NIL) -9 NIL 926738 NIL) (-412 924467 924507 924604 "FPC-" 924609 NIL FPC- (NIL T) -8 NIL NIL NIL) (-411 923257 923955 923996 "FPATMAB" 924001 NIL FPATMAB (NIL T) -9 NIL 924153 NIL) (-410 921496 921999 922346 "FPARFRAC" 922973 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-409 916890 917388 918070 "FORTRAN" 920928 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-408 914606 915106 915645 "FORT" 916371 T FORT (NIL) -7 NIL NIL NIL) (-407 912282 912844 912872 "FORTFN" 913932 T FORTFN (NIL) -9 NIL 914556 NIL) (-406 912046 912096 912124 "FORTCAT" 912183 T FORTCAT (NIL) -9 NIL 912245 NIL) (-405 910152 910662 911052 "FORMULA" 911676 T FORMULA (NIL) -8 NIL NIL NIL) (-404 909940 909970 910039 "FORMULA1" 910116 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-403 909463 909515 909688 "FORDER" 909882 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-402 908559 908723 908916 "FOP" 909290 T FOP (NIL) -7 NIL NIL NIL) (-401 907140 907839 908013 "FNLA" 908441 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-400 905869 906284 906312 "FNCAT" 906772 T FNCAT (NIL) -9 NIL 907032 NIL) (-399 905408 905828 905856 "FNAME" 905861 T FNAME (NIL) -8 NIL NIL NIL) (-398 903971 904934 904962 "FMTC" 904967 T FMTC (NIL) -9 NIL 905003 NIL) (-397 902717 903907 903953 "FMONOID" 903958 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-396 899545 900713 900754 "FMONCAT" 901971 NIL FMONCAT (NIL T) -9 NIL 902576 NIL) (-395 898737 899287 899436 "FM" 899441 NIL FM (NIL T T) -8 NIL NIL NIL) (-394 896161 896807 896835 "FMFUN" 897979 T FMFUN (NIL) -9 NIL 898687 NIL) (-393 895430 895611 895639 "FMC" 895929 T FMC (NIL) -9 NIL 896111 NIL) (-392 892509 893369 893423 "FMCAT" 894618 NIL FMCAT (NIL T T) -9 NIL 895113 NIL) (-391 891375 892275 892375 "FM1" 892454 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-390 889149 889565 890059 "FLOATRP" 890926 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-389 882727 886878 887499 "FLOAT" 888548 T FLOAT (NIL) -8 NIL NIL NIL) (-388 880165 880665 881243 "FLOATCP" 882194 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-387 879012 879771 879812 "FLINEXP" 879817 NIL FLINEXP (NIL T) -9 NIL 879910 NIL) (-386 877944 878241 878649 "FLINEXP-" 878654 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-385 877020 877164 877388 "FLASORT" 877796 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-384 874136 875004 875056 "FLALG" 876283 NIL FLALG (NIL T T) -9 NIL 876750 NIL) (-383 867840 871592 871633 "FLAGG" 872895 NIL FLAGG (NIL T) -9 NIL 873547 NIL) (-382 866566 866905 867395 "FLAGG-" 867400 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-381 865608 865751 865978 "FLAGG2" 866419 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-380 862459 863467 863526 "FINRALG" 864654 NIL FINRALG (NIL T T) -9 NIL 865162 NIL) (-379 861619 861848 862187 "FINRALG-" 862192 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-378 860999 861238 861266 "FINITE" 861462 T FINITE (NIL) -9 NIL 861569 NIL) (-377 853356 855543 855583 "FINAALG" 859250 NIL FINAALG (NIL T) -9 NIL 860703 NIL) (-376 848688 849738 850882 "FINAALG-" 852261 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-375 848056 848443 848546 "FILE" 848618 NIL FILE (NIL T) -8 NIL NIL NIL) (-374 846714 847052 847106 "FILECAT" 847790 NIL FILECAT (NIL T T) -9 NIL 848006 NIL) (-373 844430 845958 845986 "FIELD" 846026 T FIELD (NIL) -9 NIL 846106 NIL) (-372 843050 843435 843946 "FIELD-" 843951 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-371 840900 841685 842032 "FGROUP" 842736 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-370 839990 840154 840374 "FGLMICPK" 840732 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-369 835822 839915 839972 "FFX" 839977 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-368 835423 835484 835619 "FFSLPE" 835755 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-367 831413 832195 832991 "FFPOLY" 834659 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-366 830917 830953 831162 "FFPOLY2" 831371 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-365 826763 830836 830899 "FFP" 830904 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-364 822161 826674 826738 "FF" 826743 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-363 817287 821504 821694 "FFNBX" 822015 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-362 812215 816422 816680 "FFNBP" 817141 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-361 806848 811499 811710 "FFNB" 812048 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-360 805680 805878 806193 "FFINTBAS" 806645 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-359 801706 803927 803955 "FFIELDC" 804575 T FFIELDC (NIL) -9 NIL 804951 NIL) (-358 800368 800739 801236 "FFIELDC-" 801241 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-357 799937 799983 800107 "FFHOM" 800310 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-356 797632 798119 798636 "FFF" 799452 NIL FFF (NIL T) -7 NIL NIL NIL) (-355 793250 797374 797475 "FFCGX" 797575 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-354 788872 792982 793089 "FFCGP" 793193 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-353 784055 788599 788707 "FFCG" 788808 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-352 763736 773731 773817 "FFCAT" 778982 NIL FFCAT (NIL T T T) -9 NIL 780433 NIL) (-351 758933 759981 761295 "FFCAT-" 762525 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-350 758344 758387 758622 "FFCAT2" 758884 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-349 747667 751316 752536 "FEXPR" 757196 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-348 746629 747064 747105 "FEVALAB" 747189 NIL FEVALAB (NIL T) -9 NIL 747450 NIL) (-347 745788 745998 746336 "FEVALAB-" 746341 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-346 744354 745171 745374 "FDIV" 745687 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 741374 742115 742230 "FDIVCAT" 743798 NIL FDIVCAT (NIL T T T T) -9 NIL 744235 NIL) (-344 741136 741163 741333 "FDIVCAT-" 741338 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-343 740356 740443 740720 "FDIV2" 741043 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-342 739330 739651 739853 "FCTRDATA" 740174 T FCTRDATA (NIL) -8 NIL NIL NIL) (-341 738016 738275 738564 "FCPAK1" 739061 T FCPAK1 (NIL) -7 NIL NIL NIL) (-340 737115 737516 737657 "FCOMP" 737907 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-339 720820 724265 727803 "FC" 733597 T FC (NIL) -8 NIL NIL NIL) (-338 713099 717127 717167 "FAXF" 718969 NIL FAXF (NIL T) -9 NIL 719661 NIL) (-337 710376 711033 711858 "FAXF-" 712323 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-336 705428 709752 709928 "FARRAY" 710233 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-335 700322 702389 702442 "FAMR" 703465 NIL FAMR (NIL T T) -9 NIL 703925 NIL) (-334 699212 699514 699949 "FAMR-" 699954 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-333 698381 699134 699187 "FAMONOID" 699192 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-332 696167 696877 696930 "FAMONC" 697871 NIL FAMONC (NIL T T) -9 NIL 698257 NIL) (-331 694831 695921 696058 "FAGROUP" 696063 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-330 692626 692945 693348 "FACUTIL" 694512 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-329 691725 691910 692132 "FACTFUNC" 692436 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-328 684147 691028 691227 "EXPUPXS" 691581 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-327 681630 682170 682756 "EXPRTUBE" 683581 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-326 677901 678493 679223 "EXPRODE" 680969 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-325 663620 676550 676979 "EXPR" 677505 NIL EXPR (NIL T) -8 NIL NIL NIL) (-324 658174 658761 659567 "EXPR2UPS" 662918 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-323 657806 657863 657972 "EXPR2" 658111 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-322 649059 656957 657248 "EXPEXPAN" 657642 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-321 648859 649016 649045 "EXIT" 649050 T EXIT (NIL) -8 NIL NIL NIL) (-320 648339 648583 648674 "EXITAST" 648788 T EXITAST (NIL) -8 NIL NIL NIL) (-319 647966 648028 648141 "EVALCYC" 648271 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-318 647507 647625 647666 "EVALAB" 647836 NIL EVALAB (NIL T) -9 NIL 647940 NIL) (-317 646988 647110 647331 "EVALAB-" 647336 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-316 644356 645658 645686 "EUCDOM" 646241 T EUCDOM (NIL) -9 NIL 646591 NIL) (-315 642761 643203 643793 "EUCDOM-" 643798 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-314 630300 633059 635809 "ESTOOLS" 640031 T ESTOOLS (NIL) -7 NIL NIL NIL) (-313 629932 629989 630098 "ESTOOLS2" 630237 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-312 629683 629725 629805 "ESTOOLS1" 629884 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-311 623720 625328 625356 "ES" 628124 T ES (NIL) -9 NIL 629534 NIL) (-310 618667 619954 621771 "ES-" 621935 NIL ES- (NIL T) -8 NIL NIL NIL) (-309 615041 615802 616582 "ESCONT" 617907 T ESCONT (NIL) -7 NIL NIL NIL) (-308 614786 614818 614900 "ESCONT1" 615003 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-307 614461 614511 614611 "ES2" 614730 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-306 614091 614149 614258 "ES1" 614397 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-305 613307 613436 613612 "ERROR" 613935 T ERROR (NIL) -7 NIL NIL NIL) (-304 606699 613166 613257 "EQTBL" 613262 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-303 599202 602013 603462 "EQ" 605283 NIL -3091 (NIL T) -8 NIL NIL NIL) (-302 598834 598891 599000 "EQ2" 599139 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-301 594125 595172 596265 "EP" 597773 NIL EP (NIL T) -7 NIL NIL NIL) (-300 592725 593016 593322 "ENV" 593839 T ENV (NIL) -8 NIL NIL NIL) (-299 591819 592373 592401 "ENTIRER" 592406 T ENTIRER (NIL) -9 NIL 592452 NIL) (-298 588513 590001 590362 "EMR" 591627 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-297 587643 587828 587882 "ELTAGG" 588262 NIL ELTAGG (NIL T T) -9 NIL 588473 NIL) (-296 587362 587424 587565 "ELTAGG-" 587570 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-295 587126 587155 587209 "ELTAB" 587293 NIL ELTAB (NIL T T) -9 NIL 587345 NIL) (-294 586252 586398 586597 "ELFUTS" 586977 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-293 585994 586050 586078 "ELEMFUN" 586183 T ELEMFUN (NIL) -9 NIL NIL NIL) (-292 585864 585885 585953 "ELEMFUN-" 585958 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-291 580678 583934 583975 "ELAGG" 584915 NIL ELAGG (NIL T) -9 NIL 585378 NIL) (-290 578963 579397 580060 "ELAGG-" 580065 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-289 578275 578412 578568 "ELABOR" 578827 T ELABOR (NIL) -8 NIL NIL NIL) (-288 576936 577215 577509 "ELABEXPR" 578001 T ELABEXPR (NIL) -8 NIL NIL NIL) (-287 569770 571573 572402 "EFUPXS" 576211 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-286 563218 565019 565830 "EFULS" 569045 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-285 560703 561061 561533 "EFSTRUC" 562850 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-284 550494 552060 553608 "EF" 559218 NIL EF (NIL T T) -7 NIL NIL NIL) (-283 549568 549979 550128 "EAB" 550365 T EAB (NIL) -8 NIL NIL NIL) (-282 548750 549527 549555 "E04UCFA" 549560 T E04UCFA (NIL) -8 NIL NIL NIL) (-281 547932 548709 548737 "E04NAFA" 548742 T E04NAFA (NIL) -8 NIL NIL NIL) (-280 547114 547891 547919 "E04MBFA" 547924 T E04MBFA (NIL) -8 NIL NIL NIL) (-279 546296 547073 547101 "E04JAFA" 547106 T E04JAFA (NIL) -8 NIL NIL NIL) (-278 545480 546255 546283 "E04GCFA" 546288 T E04GCFA (NIL) -8 NIL NIL NIL) (-277 544664 545439 545467 "E04FDFA" 545472 T E04FDFA (NIL) -8 NIL NIL NIL) (-276 543846 544623 544651 "E04DGFA" 544656 T E04DGFA (NIL) -8 NIL NIL NIL) (-275 538019 539371 540735 "E04AGNT" 542502 T E04AGNT (NIL) -7 NIL NIL NIL) (-274 536790 537333 537373 "DVARCAT" 537714 NIL DVARCAT (NIL T) -9 NIL 537877 NIL) (-273 535994 536206 536520 "DVARCAT-" 536525 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-272 529042 535793 535922 "DSMP" 535927 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-271 527465 528184 528225 "DSEXT" 528588 NIL DSEXT (NIL T) -9 NIL 528882 NIL) (-270 525750 526178 526844 "DSEXT-" 526849 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-269 520531 521695 522763 "DROPT" 524702 T DROPT (NIL) -8 NIL NIL NIL) (-268 520196 520255 520353 "DROPT1" 520466 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-267 515311 516437 517574 "DROPT0" 519079 T DROPT0 (NIL) -7 NIL NIL NIL) (-266 513656 513981 514367 "DRAWPT" 514945 T DRAWPT (NIL) -7 NIL NIL NIL) (-265 508243 509166 510245 "DRAW" 512630 NIL DRAW (NIL T) -7 NIL NIL NIL) (-264 507876 507929 508047 "DRAWHACK" 508184 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-263 506607 506876 507167 "DRAWCX" 507605 T DRAWCX (NIL) -7 NIL NIL NIL) (-262 506122 506191 506342 "DRAWCURV" 506533 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-261 496590 498552 500667 "DRAWCFUN" 504027 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-260 493354 495283 495324 "DQAGG" 495953 NIL DQAGG (NIL T) -9 NIL 496227 NIL) (-259 481006 487565 487648 "DPOLCAT" 489500 NIL DPOLCAT (NIL T T T T) -9 NIL 490045 NIL) (-258 475843 477191 479149 "DPOLCAT-" 479154 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-257 469425 475704 475802 "DPMO" 475807 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-256 462910 469205 469372 "DPMM" 469377 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-255 462480 462694 462783 "DOMTMPLT" 462841 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-254 461913 462282 462362 "DOMCTOR" 462420 T DOMCTOR (NIL) -8 NIL NIL NIL) (-253 461125 461393 461544 "DOMAIN" 461782 T DOMAIN (NIL) -8 NIL NIL NIL) (-252 455024 460760 460912 "DMP" 461026 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-251 454624 454680 454824 "DLP" 454962 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 448446 453951 454141 "DLIST" 454466 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 445243 447299 447340 "DLAGG" 447890 NIL DLAGG (NIL T) -9 NIL 448120 NIL) (-248 443919 444583 444611 "DIVRING" 444703 T DIVRING (NIL) -9 NIL 444786 NIL) (-247 443156 443346 443646 "DIVRING-" 443651 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 441258 441615 442021 "DISPLAY" 442770 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 435297 441172 441235 "DIRPROD" 441240 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 434145 434348 434613 "DIRPROD2" 435090 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 423073 428931 428984 "DIRPCAT" 429242 NIL DIRPCAT (NIL NIL T) -9 NIL 430117 NIL) (-242 420177 420881 421842 "DIRPCAT-" 422179 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 419464 419624 419810 "DIOSP" 420011 T DIOSP (NIL) -7 NIL NIL NIL) (-240 416119 418376 418417 "DIOPS" 418851 NIL DIOPS (NIL T) -9 NIL 419080 NIL) (-239 415668 415782 415973 "DIOPS-" 415978 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 414719 415347 415375 "DIFRING" 415380 T DIFRING (NIL) -9 NIL 415402 NIL) (-237 414391 414465 414493 "DIFFSPC" 414612 T DIFFSPC (NIL) -9 NIL 414687 NIL) (-236 414036 414114 414266 "DIFFSPC-" 414271 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 413192 413670 413710 "DIFFMOD" 413715 NIL DIFFMOD (NIL T) -9 NIL 413742 NIL) (-234 412900 412945 412986 "DIFFDOM" 413107 NIL DIFFDOM (NIL T) -9 NIL 413175 NIL) (-233 412753 412777 412861 "DIFFDOM-" 412866 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 410685 411957 411998 "DIFEXT" 412003 NIL DIFEXT (NIL T) -9 NIL 412156 NIL) (-231 407960 410217 410258 "DIAGG" 410263 NIL DIAGG (NIL T) -9 NIL 410283 NIL) (-230 407344 407501 407753 "DIAGG-" 407758 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 402761 406303 406580 "DHMATRIX" 407113 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 398373 399282 400292 "DFSFUN" 401771 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 393453 397304 397616 "DFLOAT" 398081 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 391716 391997 392386 "DFINTTLS" 393161 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 388745 389737 390137 "DERHAM" 391382 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 386546 388520 388609 "DEQUEUE" 388689 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 385800 385933 386116 "DEGRED" 386408 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 382230 382975 383821 "DEFINTRF" 385028 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 379785 380254 380846 "DEFINTEF" 381749 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 379135 379405 379520 "DEFAST" 379690 T DEFAST (NIL) -8 NIL NIL NIL) (-219 373044 378728 378878 "DECIMAL" 379005 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 370556 371014 371520 "DDFACT" 372588 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 370152 370195 370346 "DBLRESP" 370507 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 368020 368382 368743 "DBASE" 369918 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 367262 367500 367646 "DATAARY" 367919 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 366368 367221 367249 "D03FAFA" 367254 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 365475 366327 366355 "D03EEFA" 366360 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 363425 363891 364380 "D03AGNT" 365006 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 362714 363384 363412 "D02EJFA" 363417 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 362003 362673 362701 "D02CJFA" 362706 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 361292 361962 361990 "D02BHFA" 361995 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 360581 361251 361279 "D02BBFA" 361284 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 353778 355367 356973 "D02AGNT" 358995 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 351546 352069 352615 "D01WGTS" 353252 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 350613 351505 351533 "D01TRNS" 351538 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 349681 350572 350600 "D01GBFA" 350605 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 348749 349640 349668 "D01FCFA" 349673 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 347817 348708 348736 "D01ASFA" 348741 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 346885 347776 347804 "D01AQFA" 347809 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 345953 346844 346872 "D01APFA" 346877 T D01APFA (NIL) -8 NIL NIL NIL) (-199 345021 345912 345940 "D01ANFA" 345945 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 344089 344980 345008 "D01AMFA" 345013 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 343157 344048 344076 "D01ALFA" 344081 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 342225 343116 343144 "D01AKFA" 343149 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 341293 342184 342212 "D01AJFA" 342217 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 334588 336141 337702 "D01AGNT" 339752 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 333925 334053 334205 "CYCLOTOM" 334456 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 330658 331373 332100 "CYCLES" 333218 T CYCLES (NIL) -7 NIL NIL NIL) (-191 329970 330104 330275 "CVMP" 330519 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 327811 328069 328438 "CTRIGMNP" 329698 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 327247 327605 327678 "CTOR" 327758 T CTOR (NIL) -8 NIL NIL NIL) (-188 326756 326978 327079 "CTORKIND" 327166 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 326047 326363 326391 "CTORCAT" 326573 T CTORCAT (NIL) -9 NIL 326686 NIL) (-186 325645 325756 325915 "CTORCAT-" 325920 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 325107 325319 325427 "CTORCALL" 325569 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 324481 324580 324733 "CSTTOOLS" 325004 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 320280 320937 321695 "CRFP" 323793 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 319755 320001 320093 "CRCEAST" 320208 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 318802 318987 319215 "CRAPACK" 319559 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 318186 318287 318491 "CPMATCH" 318678 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 317911 317939 318045 "CPIMA" 318152 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 314259 314931 315650 "COORDSYS" 317246 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 313671 313792 313934 "CONTOUR" 314137 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 309562 311674 312166 "CONTFRAC" 313211 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 309442 309463 309491 "CONDUIT" 309528 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 308530 309084 309112 "COMRING" 309117 T COMRING (NIL) -9 NIL 309169 NIL) (-173 307584 307888 308072 "COMPPROP" 308366 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 307245 307280 307408 "COMPLPAT" 307543 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 296735 307054 307163 "COMPLEX" 307168 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 296371 296428 296535 "COMPLEX2" 296672 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 295710 295831 295991 "COMPILER" 296231 T COMPILER (NIL) -8 NIL NIL NIL) (-168 295428 295463 295561 "COMPFACT" 295669 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 277894 289132 289172 "COMPCAT" 290176 NIL COMPCAT (NIL T) -9 NIL 291524 NIL) (-166 267184 270173 273880 "COMPCAT-" 274236 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 266913 266941 267044 "COMMUPC" 267150 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 266707 266741 266800 "COMMONOP" 266874 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 266263 266458 266545 "COMM" 266640 T COMM (NIL) -8 NIL NIL NIL) (-162 265839 266067 266142 "COMMAAST" 266208 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 265088 265282 265310 "COMBOPC" 265648 T COMBOPC (NIL) -9 NIL 265823 NIL) (-160 263984 264194 264436 "COMBINAT" 264878 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 260441 261015 261642 "COMBF" 263406 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 259199 259557 259792 "COLOR" 260226 T COLOR (NIL) -8 NIL NIL NIL) (-157 258675 258920 259012 "COLONAST" 259127 T COLONAST (NIL) -8 NIL NIL NIL) (-156 258315 258362 258487 "CMPLXRT" 258622 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 257763 258015 258114 "CLLCTAST" 258236 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 253265 254293 255373 "CLIP" 256703 T CLIP (NIL) -7 NIL NIL NIL) (-153 251606 252366 252606 "CLIF" 253092 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 247781 249752 249793 "CLAGG" 250722 NIL CLAGG (NIL T) -9 NIL 251258 NIL) (-151 246203 246660 247243 "CLAGG-" 247248 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 245747 245832 245972 "CINTSLPE" 246112 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 243248 243719 244267 "CHVAR" 245275 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 242422 242976 243004 "CHARZ" 243009 T CHARZ (NIL) -9 NIL 243024 NIL) (-147 242176 242216 242294 "CHARPOL" 242376 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 241234 241821 241849 "CHARNZ" 241896 T CHARNZ (NIL) -9 NIL 241952 NIL) (-145 239140 239888 240241 "CHAR" 240901 T CHAR (NIL) -8 NIL NIL NIL) (-144 238866 238927 238955 "CFCAT" 239066 T CFCAT (NIL) -9 NIL NIL NIL) (-143 238107 238218 238401 "CDEN" 238750 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 234072 237260 237540 "CCLASS" 237847 T CCLASS (NIL) -8 NIL NIL NIL) (-141 233323 233480 233657 "CATEGORY" 233915 T -10 (NIL) -8 NIL NIL NIL) (-140 232896 233242 233290 "CATCTOR" 233295 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 232347 232599 232697 "CATAST" 232818 T CATAST (NIL) -8 NIL NIL NIL) (-138 231823 232068 232160 "CASEAST" 232275 T CASEAST (NIL) -8 NIL NIL NIL) (-137 226961 227980 228724 "CARTEN" 231135 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 226069 226217 226438 "CARTEN2" 226808 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 224385 225219 225476 "CARD" 225832 T CARD (NIL) -8 NIL NIL NIL) (-134 223961 224189 224264 "CAPSLAST" 224330 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 223465 223673 223701 "CACHSET" 223833 T CACHSET (NIL) -9 NIL 223911 NIL) (-132 222935 223257 223285 "CABMON" 223335 T CABMON (NIL) -9 NIL 223391 NIL) (-131 222408 222639 222749 "BYTEORD" 222845 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 221385 221937 222079 "BYTE" 222242 T BYTE (NIL) -8 NIL NIL 222364) (-129 216735 220890 221062 "BYTEBUF" 221233 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 214244 216427 216534 "BTREE" 216661 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 211693 213892 214014 "BTOURN" 214154 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 209063 211163 211204 "BTCAT" 211272 NIL BTCAT (NIL T) -9 NIL 211349 NIL) (-125 208730 208810 208959 "BTCAT-" 208964 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 204109 207989 208017 "BTAGG" 208131 T BTAGG (NIL) -9 NIL 208241 NIL) (-123 203599 203724 203930 "BTAGG-" 203935 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 200594 202877 203092 "BSTREE" 203416 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 199732 199858 200042 "BRILL" 200450 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 196384 198458 198499 "BRAGG" 199148 NIL BRAGG (NIL T) -9 NIL 199406 NIL) (-119 194913 195319 195874 "BRAGG-" 195879 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 188037 194257 194442 "BPADICRT" 194760 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 186352 187974 188019 "BPADIC" 188024 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 186050 186080 186194 "BOUNDZRO" 186316 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 181278 182476 183388 "BOP" 185158 T BOP (NIL) -8 NIL NIL NIL) (-114 179059 179463 179938 "BOP1" 180836 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 178760 178821 178849 "BOOLE" 178960 T BOOLE (NIL) -9 NIL 179042 NIL) (-112 177585 178334 178483 "BOOLEAN" 178631 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 176864 177268 177322 "BMODULE" 177327 NIL BMODULE (NIL T T) -9 NIL 177392 NIL) (-110 172665 176662 176735 "BITS" 176811 T BITS (NIL) -8 NIL NIL NIL) (-109 172086 172205 172345 "BINDING" 172545 T BINDING (NIL) -8 NIL NIL NIL) (-108 165998 171681 171830 "BINARY" 171957 T BINARY (NIL) -8 NIL NIL NIL) (-107 163778 165253 165294 "BGAGG" 165554 NIL BGAGG (NIL T) -9 NIL 165691 NIL) (-106 163609 163641 163732 "BGAGG-" 163737 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 162680 162993 163198 "BFUNCT" 163424 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 161370 161548 161836 "BEZOUT" 162504 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 157839 160222 160552 "BBTREE" 161073 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 157573 157626 157654 "BASTYPE" 157773 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 157425 157454 157527 "BASTYPE-" 157532 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 156859 156935 157087 "BALFACT" 157336 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 155715 156274 156460 "AUTOMOR" 156704 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 155441 155446 155472 "ATTREG" 155477 T ATTREG (NIL) -9 NIL NIL NIL) (-97 153693 154138 154490 "ATTRBUT" 155107 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 153301 153521 153587 "ATTRAST" 153645 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 152837 152950 152976 "ATRIG" 153177 T ATRIG (NIL) -9 NIL NIL NIL) (-94 152646 152687 152774 "ATRIG-" 152779 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 152291 152477 152503 "ASTCAT" 152508 T ASTCAT (NIL) -9 NIL 152538 NIL) (-92 152018 152077 152196 "ASTCAT-" 152201 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 150167 151794 151882 "ASTACK" 151961 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 148672 148969 149334 "ASSOCEQ" 149849 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 147704 148331 148455 "ASP9" 148579 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 147467 147652 147691 "ASP8" 147696 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 146335 147072 147214 "ASP80" 147356 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 145233 145970 146102 "ASP7" 146234 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 144187 144910 145028 "ASP78" 145146 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 143156 143867 143984 "ASP77" 144101 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 142068 142794 142925 "ASP74" 143056 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 140968 141703 141835 "ASP73" 141967 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 140072 140794 140894 "ASP6" 140899 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139019 139749 139867 "ASP55" 139985 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 137968 138693 138812 "ASP50" 138931 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 137056 137669 137779 "ASP4" 137889 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 136144 136757 136867 "ASP49" 136977 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 134928 135683 135851 "ASP42" 136033 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 133705 134461 134631 "ASP41" 134815 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 132655 133382 133500 "ASP35" 133618 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 132420 132603 132642 "ASP34" 132647 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 132157 132224 132300 "ASP33" 132375 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 131051 131792 131924 "ASP31" 132056 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 130816 130999 131038 "ASP30" 131043 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 130551 130620 130696 "ASP29" 130771 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 130316 130499 130538 "ASP28" 130543 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 130081 130264 130303 "ASP27" 130308 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 129165 129779 129890 "ASP24" 130001 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 128242 128967 129079 "ASP20" 129084 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 127330 127943 128053 "ASP1" 128163 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 126273 127004 127123 "ASP19" 127242 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126010 126077 126153 "ASP12" 126228 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 124862 125609 125753 "ASP10" 125897 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 122713 124706 124797 "ARRAY2" 124802 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 118478 122361 122475 "ARRAY1" 122630 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 117510 117683 117904 "ARRAY12" 118301 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 111822 113740 113815 "ARR2CAT" 116445 NIL ARR2CAT (NIL T T T) -9 NIL 117203 NIL) (-56 109256 110000 110954 "ARR2CAT-" 110959 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 108573 108883 109008 "ARITY" 109149 T ARITY (NIL) -8 NIL NIL NIL) (-54 107349 107501 107800 "APPRULE" 108409 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107000 107048 107167 "APPLYORE" 107295 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 106354 106593 106713 "ANY" 106898 T ANY (NIL) -8 NIL NIL NIL) (-51 105632 105755 105912 "ANY1" 106228 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 103162 104069 104396 "ANTISYM" 105356 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 102654 102869 102965 "ANON" 103084 T ANON (NIL) -8 NIL NIL NIL) (-48 96832 101193 101647 "AN" 102218 T AN (NIL) -8 NIL NIL NIL) (-47 92730 94118 94169 "AMR" 94917 NIL AMR (NIL T T) -9 NIL 95517 NIL) (-46 91842 92063 92426 "AMR-" 92431 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 76281 91759 91820 "ALIST" 91825 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73086 75875 76044 "ALGSC" 76199 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 69642 70196 70803 "ALGPKG" 72526 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 68919 69020 69204 "ALGMFACT" 69528 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 64954 65533 66127 "ALGMANIP" 68503 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55373 64580 64730 "ALGFF" 64887 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54569 54700 54879 "ALGFACT" 55231 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53510 54110 54148 "ALGEBRA" 54153 NIL ALGEBRA (NIL T) -9 NIL 54194 NIL) (-37 53228 53287 53419 "ALGEBRA-" 53424 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35291 51200 51252 "ALAGG" 51388 NIL ALAGG (NIL T T) -9 NIL 51549 NIL) (-35 34827 34940 34966 "AHYP" 35167 T AHYP (NIL) -9 NIL NIL NIL) (-34 33758 34006 34032 "AGG" 34531 T AGG (NIL) -9 NIL 34810 NIL) (-33 33192 33354 33568 "AGG-" 33573 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30998 31421 31826 "AF" 32834 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30478 30723 30813 "ADDAST" 30926 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29746 30005 30161 "ACPLOT" 30340 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18670 26678 26716 "ACFS" 27323 NIL ACFS (NIL T) -9 NIL 27562 NIL) (-28 16697 17187 17949 "ACFS-" 17954 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12815 14744 14770 "ACF" 15649 T ACF (NIL) -9 NIL 16062 NIL) (-26 11519 11853 12346 "ACF-" 12351 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11091 11286 11312 "ABELSG" 11404 T ABELSG (NIL) -9 NIL 11469 NIL) (-24 10958 10983 11049 "ABELSG-" 11054 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10301 10588 10614 "ABELMON" 10784 T ABELMON (NIL) -9 NIL 10896 NIL) (-22 9965 10049 10187 "ABELMON-" 10192 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9313 9685 9711 "ABELGRP" 9783 T ABELGRP (NIL) -9 NIL 9858 NIL) (-20 8776 8905 9121 "ABELGRP-" 9126 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8085 8124 "A1AGG" 8129 NIL A1AGG (NIL T) -9 NIL 8169 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
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(-12 (-5 *2 (-1 (-958 *3) (-958 *3))) (-5 *1 (-178 *3)) - (-4 *3 (-13 (-373) (-1220) (-1019)))))) + (-12 (-5 *3 (-1285 *4)) (-4 *4 (-359)) (-5 *2 (-1190 *4)) + (-5 *1 (-539 *4))))) +(((*1 *1 *2 *3 *1) + (-12 (-5 *2 (-904 *4)) (-4 *4 (-1117)) (-5 *1 (-901 *4 *3)) + (-4 *3 (-1117))))) (((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1066)) (-4 *3 (-803)))) ((*1 *1 *1) (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1066)) (-14 *3 (-655 (-1194))))) @@ -356,10 +202,10 @@ (-12 (-4 *1 (-392 *2 *3)) (-4 *2 (-1066)) (-4 *3 (-1117)))) ((*1 *1 *1) (-12 (-14 *2 (-655 (-1194))) (-4 *3 (-174)) - (-4 *5 (-243 (-2871 *2) (-782))) + (-4 *5 (-243 (-2869 *2) (-782))) (-14 *6 - (-1 (-112) (-2 (|:| -4317 *4) (|:| -2398 *5)) - (-2 (|:| -4317 *4) (|:| -2398 *5)))) + (-1 (-112) (-2 (|:| -4317 *4) (|:| -1658 *5)) + (-2 (|:| -4317 *4) (|:| -1658 *5)))) (-5 *1 (-472 *2 *3 *4 *5 *6 *7)) (-4 *4 (-861)) (-4 *7 (-964 *3 *5 (-875 *2))))) ((*1 *1 *1) (-12 (-4 *1 (-520 *2 *3)) (-4 *2 (-1117)) (-4 *3 (-861)))) @@ -375,36 +221,22 @@ 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(-5 *1 (-346 *3 *4 *5 *6)) + (-4 *6 (-352 *3 *4 *5))))) +(((*1 *1 *2 *3 *4) + (-12 (-5 *3 (-575)) (-5 *4 (-3 "nil" "sqfr" "irred" "prime")) + (-5 *1 (-429 *2)) (-4 *2 (-567))))) (((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-376 *3 *4)) - (-4 *3 (-377 *4)))) - ((*1 *2) (-12 (-4 *1 (-377 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) -(((*1 *2 *2) - (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) - (-4 *2 (-13 (-441 *3) (-1019)))))) + (-12 (-4 *3 (-567)) (-5 *2 (-655 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-428 *3))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-655 (-623 *5))) (-5 *3 (-1194)) (-4 *5 (-441 *4)) + (-4 *4 (-1117)) (-5 *1 (-584 *4 *5))))) (((*1 *2 *3) - (-12 (-5 *3 (-1176)) (-5 *2 (-655 (-702 (-289)))) (-5 *1 (-169))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-1117)) (-5 *2 (-112))))) + (-12 (-5 *2 (-1 (-958 *3) (-958 *3))) (-5 *1 (-178 *3)) + (-4 *3 (-13 (-373) (-1220) (-1019)))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1235)))) ((*1 *1 *2) (-12 (-5 *2 (-967 (-389))) (-5 *1 (-349 *3 *4 *5)) @@ -460,11 +292,11 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) - (|:| -3437 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) + (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-325 (-227))) - (|:| -3437 (-655 (-1111 (-854 (-227))))) + (|:| -1974 (-655 (-1111 (-854 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-780)))) ((*1 *2 *1) @@ -480,13 +312,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-325 (-227))) (|:| -3474 (-655 (-227))) + (-2 (|:| |fn| (-325 (-227))) (|:| -3472 (-655 (-227))) (|:| |lb| (-655 (-854 (-227)))) (|:| |cf| (-655 (-325 (-227)))) (|:| |ub| (-655 (-854 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-655 (-325 (-227)))) - (|:| -3474 (-655 (-227))))))) + (|:| -3472 (-655 (-227))))))) (-5 *1 (-852)))) ((*1 *2 *1) (-12 @@ -505,26 +337,26 @@ (-4 *4 (-804)) (-4 *5 (-861)) (-4 *1 (-993 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1055 *2)) (-4 *2 (-1235)))) ((*1 *1 *2) - (-3765 + 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(-14 *3 (-655 (-1194))))) @@ -603,10 +591,10 @@ ((*1 *2 *1) (-12 (-4 *1 (-392 *2 *3)) (-4 *3 (-1117)) (-4 *2 (-1066)))) ((*1 *2 *1) - (-12 (-14 *3 (-655 (-1194))) (-4 *5 (-243 (-2871 *3) (-782))) + (-12 (-14 *3 (-655 (-1194))) (-4 *5 (-243 (-2869 *3) (-782))) (-14 *6 - (-1 (-112) (-2 (|:| -4317 *4) (|:| -2398 *5)) - (-2 (|:| -4317 *4) (|:| -2398 *5)))) + (-1 (-112) (-2 (|:| -4317 *4) (|:| -1658 *5)) + (-2 (|:| -4317 *4) (|:| -1658 *5)))) (-4 *2 (-174)) (-5 *1 (-472 *3 *2 *4 *5 *6 *7)) (-4 *4 (-861)) (-4 *7 (-964 *2 *5 (-875 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-520 *2 *3)) (-4 *3 (-861)) (-4 *2 (-1117)))) @@ -623,30 +611,32 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1082 *3 *4 *2)) (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *2 (-861))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-700 *6)) (-5 *5 (-1 (-429 (-1190 *6)) (-1190 *6))) - (-4 *6 (-373)) - (-5 *2 - (-655 - (-2 (|:| |outval| *7) (|:| |outmult| (-575)) - (|:| |outvect| (-655 (-700 *7)))))) - (-5 *1 (-543 *6 *7 *4)) (-4 *7 (-373)) (-4 *4 (-13 (-373) 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(|:| -4317 *5) (|:| -2398 *6)) - (-2 (|:| -4317 *5) (|:| -2398 *6)))) + (-1 (-112) (-2 (|:| -4317 *5) (|:| -1658 *6)) + (-2 (|:| -4317 *5) (|:| -1658 *6)))) (-5 *2 (-724 *5 *6 *7)) (-5 *1 (-472 *3 *4 *5 *6 *7 *8)) (-4 *5 (-861)) (-4 *8 (-964 *4 *6 (-875 *3))))) ((*1 *2 *1) @@ -707,67 +700,63 @@ ((*1 *1 *1) (-12 (-4 *1 (-990 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-803)) (-4 *4 (-861))))) -(((*1 *2 *3 *4 *4 *2 *2 *2 *2) - (-12 (-5 *2 (-575)) - (-5 *3 - (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-782)) (|:| |poli| *4) - (|:| |polj| *4))) - (-4 *6 (-804)) (-4 *4 (-964 *5 *6 *7)) (-4 *5 (-463)) (-4 *7 (-861)) - (-5 *1 (-460 *5 *6 *7 *4))))) -(((*1 *2) (-12 (-4 *1 (-377 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) -(((*1 *2 *3) - (-12 (-4 *4 (-359)) (-5 *2 (-112)) (-5 *1 (-218 *4 *3)) - (-4 *3 (-1261 *4))))) -(((*1 *1 *1 *1) +(((*1 *1 *1) (-12 (-4 *1 (-1082 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-804)) - (-4 *4 (-861)))) - ((*1 *2 *2 *1) - (-12 (-4 *1 (-1228 *3 *4 *5 *2)) (-4 *3 (-567)) (-4 *4 (-804)) - (-4 *5 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+(((*1 *2 *3) + (-12 (-5 *3 (-575)) (|has| *1 (-6 -4451)) (-4 *1 (-415)) + (-5 *2 (-936))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-575)) (-5 *2 (-1052)) (-5 *1 (-769))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-782)) (-4 *2 (-567)) (-5 *1 (-986 *2 *4)) - (-4 *4 (-1261 *2))))) + (-12 (-5 *3 (-1194)) (-5 *4 (-967 (-575))) (-5 *2 (-339)) + (-5 *1 (-341))))) +(((*1 *2 *1) (-12 (-4 *1 (-400)) (-5 *2 (-1176))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-316) (-148))) (-4 *5 (-804)) (-4 *6 (-861)) - (-4 *7 (-964 *4 *5 *6)) (-5 *2 (-655 (-655 *7))) - (-5 *1 (-459 *4 *5 *6 *7)) (-5 *3 (-655 *7)))) + (-12 (-4 *4 (-463)) (-4 *4 (-567)) (-4 *5 (-804)) (-4 *6 (-861)) + (-5 *2 (-655 *3)) (-5 *1 (-994 *4 *5 *6 *3)) + (-4 *3 (-1082 *4 *5 *6))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-958 *5)) (-4 *5 (-1066)) (-5 *2 (-782)) + (-5 *1 (-1182 *4 *5)) (-14 *4 (-936)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-655 (-782))) (-5 *3 (-782)) (-5 *1 (-1182 *4 *5)) + (-14 *4 (-936)) (-4 *5 (-1066)))) + ((*1 *1 *1 *2 *3) + (-12 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(-4 *3 (-1082 *4 *5 *6)) (-5 *2 (-112))))) + (-12 (-5 *3 (-1 (-655 *5) (-655 *5))) (-5 *4 (-575)) + (-5 *2 (-655 *5)) (-5 *1 (-693 *5)) (-4 *5 (-1117))))) (((*1 *2 *3) - (-12 (-5 *3 (-655 (-575))) (-5 *2 (-919 (-575))) (-5 *1 (-932)))) - ((*1 *2 *3) (-12 (-5 *3 (-988)) (-5 *2 (-919 (-575))) (-5 *1 (-932))))) + (-12 (-14 *4 (-655 (-1194))) (-14 *5 (-782)) + (-5 *2 + (-655 + (-515 (-418 (-575)) (-245 *5 (-782)) (-875 *4) + (-252 *4 (-418 (-575)))))) + (-5 *1 (-516 *4 *5)) + (-5 *3 + (-515 (-418 (-575)) (-245 *5 (-782)) (-875 *4) + (-252 *4 (-418 (-575)))))))) +(((*1 *2 *2) + (-12 (-4 *3 (-567)) (-5 *1 (-442 *3 *2)) (-4 *2 (-441 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1176)) (-5 *2 (-1290)) (-5 *1 (-1287))))) +(((*1 *2 *3) + (-12 (-5 *3 (-655 *7)) (-4 *7 (-964 *4 *5 *6)) (-4 *4 (-463)) + (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-1290)) + (-5 *1 (-460 *4 *5 *6 *7))))) (((*1 *2 *1) (-12 (-4 *1 (-335 *2 *3)) (-4 *3 (-803)) (-4 *2 (-1066)))) ((*1 *2 *1) (-12 (-4 *1 (-441 *2)) (-4 *2 (-1117))))) (((*1 *2 *3 *4) @@ -777,94 +766,104 @@ (((*1 *1 *2 *3) (-12 (-5 *1 (-884 *2 *3)) (-4 *2 (-1235)) (-4 *3 (-1235))))) (((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-453 *3)) (-4 *3 (-1261 (-575)))))) -(((*1 *2 *1) - (-12 (-5 *2 (-176 (-418 (-575)))) (-5 *1 (-118 *3)) (-14 *3 (-575)))) - ((*1 *1 *2 *3 *3) - (-12 (-5 *3 (-1174 *2)) (-4 *2 (-316)) (-5 *1 (-176 *2)))) - ((*1 *1 *2) (-12 (-5 *2 (-418 *3)) (-4 *3 (-316)) (-5 *1 (-176 *3)))) - ((*1 *2 *3) - (-12 (-5 *2 (-176 (-575))) (-5 *1 (-776 *3)) (-4 *3 (-415)))) - ((*1 *2 *1) - (-12 (-5 *2 (-176 (-418 (-575)))) (-5 *1 (-882 *3)) (-14 *3 (-575)))) - ((*1 *2 *1) - (-12 (-14 *3 (-575)) (-5 *2 (-176 (-418 (-575)))) - (-5 *1 (-883 *3 *4)) (-4 *4 (-880 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1190 *4)) (-4 *4 (-359)) (-5 *2 (-973 (-1137))) - (-5 *1 (-356 *4))))) -(((*1 *2 *3) - (-12 (-5 *3 (-623 *5)) (-4 *5 (-441 *4)) (-4 *4 (-1055 (-575))) - (-4 *4 (-567)) (-5 *2 (-1190 *5)) (-5 *1 (-32 *4 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-623 *1)) (-4 *1 (-1066)) (-4 *1 (-311)) - (-5 *2 (-1190 *1))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-158)) (-5 *2 (-1290)) (-5 *1 (-1287))))) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-376 *3 *4)) + (-4 *3 (-377 *4)))) + ((*1 *2) (-12 (-4 *1 (-377 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) +(((*1 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-556)))) + ((*1 *1 *2) (-12 (-5 *2 (-655 (-936))) (-5 *1 (-988))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *4 (-112)) (-4 *6 (-13 (-463) (-1055 (-575)) (-650 (-575)))) + (-4 *3 (-13 (-27) (-1220) (-441 *6) (-10 -8 (-15 -2882 ($ *7))))) + (-4 *7 (-859)) + (-4 *8 + (-13 (-1263 *3 *7) (-373) (-1220) + (-10 -8 (-15 -2382 ($ $)) (-15 -4388 ($ $))))) + (-5 *2 + (-3 (|:| |%series| *8) + (|:| |%problem| (-2 (|:| |func| (-1176)) (|:| |prob| (-1176)))))) + (-5 *1 (-433 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1176)) (-4 *9 (-1000 *8)) + (-14 *10 (-1194))))) +(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *5 *6 *5 *4 *7 *3) + (-12 (-5 *4 (-700 (-575))) (-5 *5 (-112)) (-5 *7 (-700 (-227))) + (-5 *3 (-575)) (-5 *6 (-227)) (-5 *2 (-1052)) (-5 *1 (-765))))) (((*1 *2 *1) (-12 (-4 *1 (-335 *3 *4)) (-4 *3 (-1066)) (-4 *4 (-803)) (-5 *2 (-112)))) ((*1 *2 *1) (-12 (-4 *1 (-441 *3)) (-4 *3 (-1117)) (-5 *2 (-112))))) -(((*1 *2 *2) - (-12 (-4 *3 (-463)) (-5 *1 (-1226 *3 *2)) - (-4 *2 (-13 (-441 *3) (-1220)))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -1754 *3) (|:| |gap| (-782)) (|:| -2829 (-793 *3)) - (|:| -1635 (-793 *3)))) - (-5 *1 (-793 *3)) (-4 *3 (-1066)))) - ((*1 *2 *1 *1 *3) - (-12 (-4 *4 (-1066)) (-4 *5 (-804)) (-4 *3 (-861)) - (-5 *2 - (-2 (|:| -1754 *1) (|:| |gap| (-782)) (|:| -2829 *1) - (|:| -1635 *1))) - (-4 *1 (-1082 *4 *5 *3)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) - (-5 *2 - (-2 (|:| -1754 *1) (|:| |gap| (-782)) (|:| -2829 *1) - (|:| -1635 *1))) - (-4 *1 (-1082 *3 *4 *5))))) +(((*1 *2 *2) (-12 (-5 *2 (-575)) (-5 *1 (-263))))) (((*1 *2 *1) - (-12 (-5 *2 (-702 (-884 (-981 *3) (-981 *3)))) (-5 *1 (-981 *3)) - (-4 *3 (-1117))))) -(((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-528))))) -(((*1 *1) (-5 *1 (-142)))) + (-12 (-4 *1 (-1120 *3 *4 *5 *6 *7)) (-4 *3 (-1117)) (-4 *4 (-1117)) + (-4 *5 (-1117)) (-4 *6 (-1117)) (-4 *7 (-1117)) (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-5 *3 (-252 *4 *5)) (-14 *4 (-655 (-1194))) (-4 *5 (-1066)) - (-5 *2 (-492 *4 *5)) (-5 *1 (-959 *4 *5))))) -(((*1 *1 *1) - (-12 (-5 *1 (-225 *2 *3)) (-4 *2 (-13 (-1066) (-861))) - (-14 *3 (-655 (-1194)))))) -(((*1 *2 *1) (-12 (-4 *1 (-335 *3 *2)) (-4 *3 (-1066)) (-4 *2 (-803)))) - ((*1 *2 *1) (-12 (-4 *1 (-719 *3)) (-4 *3 (-1066)) (-5 *2 (-782)))) - ((*1 *2 *1) (-12 (-4 *1 (-863 *3)) (-4 *3 (-1066)) (-5 *2 (-782)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-655 *6)) (-4 *1 (-964 *4 *5 *6)) (-4 *4 (-1066)) - (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-655 (-782))))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-964 *4 *5 *3)) (-4 *4 (-1066)) (-4 *5 (-804)) - (-4 *3 (-861)) (-5 *2 (-782))))) + (-12 + (-5 *3 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1174 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1974 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *2 (-1052)) (-5 *1 (-314))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-575)) (-5 *2 (-1052)) (-5 *1 (-769))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |pde| (-655 (-325 (-227)))) + (|:| |constraints| + (-655 + (-2 (|:| |start| (-227)) (|:| |finish| (-227)) + (|:| |grid| (-782)) (|:| |boundaryType| (-575)) + (|:| |dStart| (-700 (-227))) (|:| |dFinish| (-700 (-227)))))) + (|:| |f| (-655 (-655 (-325 (-227))))) (|:| |st| (-1176)) + (|:| |tol| (-227)))) + (-5 *2 (-112)) (-5 *1 (-212))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) + (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (-5 *2 (-575)) (-5 *1 (-206))))) (((*1 *2 *1) (-12 (-4 *1 (-377 *2)) (-4 *2 (-174))))) -(((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-52)) (-5 *1 (-842))))) +(((*1 *2 *3) + (-12 (-5 *3 (-252 *4 *5)) (-14 *4 (-655 (-1194))) (-4 *5 (-1066)) + (-5 *2 (-967 *5)) (-5 *1 (-959 *4 *5))))) +(((*1 *2 *3 *4 *3) + (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1261 *5)) (-4 *5 (-373)) + (-5 *2 (-2 (|:| -2063 (-418 *6)) (|:| |coeff| (-418 *6)))) + (-5 *1 (-585 *5 *6)) (-5 *3 (-418 *6))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-332 *2 *3)) (-4 *2 (-1117)) (-4 *3 (-132)) + (-4 *3 (-803))))) +(((*1 *2 *2) + (-12 + (-5 *2 + (-655 + (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-782)) (|:| |poli| *6) + (|:| |polj| *6)))) + (-4 *4 (-804)) (-4 *6 (-964 *3 *4 *5)) (-4 *3 (-463)) (-4 *5 (-861)) + (-5 *1 (-460 *3 *4 *5 *6))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-655 (-1194))) (-5 *1 (-547))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-463)) (-4 *5 (-804)) (-4 *6 (-861)) - (-4 *7 (-1082 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1005 *4 *5 *6 *7 *3)) (-4 *3 (-1088 *4 *5 *6 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-655 *3)) (-4 *3 (-1088 *5 *6 *7 *8)) (-4 *5 (-463)) - (-4 *6 (-804)) (-4 *7 (-861)) (-4 *8 (-1082 *5 *6 *7)) - (-5 *2 (-112)) (-5 *1 (-1005 *5 *6 *7 *8 *3)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-463)) (-4 *5 (-804)) (-4 *6 (-861)) - (-4 *7 (-1082 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1124 *4 *5 *6 *7 *3)) (-4 *3 (-1088 *4 *5 *6 *7)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-655 *3)) (-4 *3 (-1088 *5 *6 *7 *8)) (-4 *5 (-463)) - (-4 *6 (-804)) (-4 *7 (-861)) (-4 *8 (-1082 *5 *6 *7)) - (-5 *2 (-112)) (-5 *1 (-1124 *5 *6 *7 *8 *3))))) +(((*1 *2 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-373) (-10 -8 (-15 ** ($ $ (-418 (-575))))))) + (-5 *1 (-1145 *3 *2)) (-4 *3 (-1261 *2))))) (((*1 *1 *1) (-4 *1 (-248))) ((*1 *1 *1) (-12 (-4 *2 (-174)) (-5 *1 (-298 *2 *3 *4 *5 *6 *7)) @@ -872,7 +871,7 @@ (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) ((*1 *1 *1) - (-3765 (-12 (-5 *1 (-303 *2)) (-4 *2 (-373)) (-4 *2 (-1235))) + (-3763 (-12 (-5 *1 (-303 *2)) (-4 *2 (-373)) (-4 *2 (-1235))) (-12 (-5 *1 (-303 *2)) (-4 *2 (-484)) (-4 *2 (-1235))))) ((*1 *1 *1) (-4 *1 (-484))) ((*1 *2 *2) (-12 (-5 *2 (-1285 *3)) (-4 *3 (-359)) (-5 *1 (-539 *3)))) @@ -881,60 +880,48 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *1) (-12 (-4 *1 (-808 *2)) (-4 *2 (-174)) (-4 *2 (-373))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-655 (-655 *8))) (-5 *3 (-655 *8)) - (-4 *8 (-964 *5 *7 *6)) (-4 *5 (-13 (-316) (-148))) - (-4 *6 (-13 (-861) (-625 (-1194)))) (-4 *7 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(-12 (-5 *3 (-700 (-171 (-418 (-575))))) - (-5 *2 - (-655 - (-2 (|:| |outval| (-171 *4)) (|:| |outmult| (-575)) - (|:| |outvect| (-655 (-700 (-171 *4))))))) - (-5 *1 (-775 *4)) (-4 *4 (-13 (-373) (-859)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1190 *6)) (-4 *6 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) - (-5 *2 (-1190 *7)) (-5 *1 (-330 *4 *5 *6 *7)) - (-4 *7 (-964 *6 *4 *5))))) + (-12 (-5 *2 (-655 (-936))) (-5 *1 (-1118 *3 *4)) (-14 *3 (-936)) + (-14 *4 (-936))))) (((*1 *2 *3) - (-12 (-5 *3 (-655 (-967 *4))) (-4 *4 (-463)) (-5 *2 (-112)) - (-5 *1 (-370 *4 *5)) (-14 *5 (-655 (-1194))))) - ((*1 *2 *3) - (-12 (-5 *3 (-655 (-791 *4 (-875 *5)))) (-4 *4 (-463)) - (-14 *5 (-655 (-1194))) (-5 *2 (-112)) (-5 *1 (-639 *4 *5))))) + (-12 (-5 *2 (-655 (-1190 (-575)))) (-5 *1 (-193)) (-5 *3 (-575))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-373) (-10 -8 (-15 ** ($ $ (-418 (-575))))))) - (-5 *2 (-655 *4)) (-5 *1 (-1145 *3 *4)) (-4 *3 (-1261 *4)))) - ((*1 *2 *3 *3 *3) - (-12 (-4 *3 (-13 (-373) (-10 -8 (-15 ** ($ $ 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+(((*1 *1 *1 *2) (-12 (-5 *2 (-1194)) (-5 *1 (-1080))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1176)) (-5 *2 (-1290)) (-5 *1 (-1287))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1285 *5)) (-4 *5 (-13 (-1066) (-650 *4))) - (-4 *4 (-567)) (-5 *2 (-1285 *4)) (-5 *1 (-649 *4 *5))))) + (-12 (-4 *4 (-359)) (-5 *2 (-973 (-1190 *4))) (-5 *1 (-367 *4)) + (-5 *3 (-1190 *4))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1190 *1)) (-4 *1 (-1029))))) +(((*1 *2 *3 *4) + (-12 (-4 *5 (-804)) (-4 *6 (-861)) (-4 *3 (-567)) + (-4 *7 (-964 *3 *5 *6)) + (-5 *2 (-2 (|:| -1658 (-782)) (|:| -1754 *8) (|:| |radicand| *8))) + (-5 *1 (-968 *5 *6 *3 *7 *8)) (-5 *4 (-782)) + (-4 *8 + (-13 (-373) + (-10 -8 (-15 -2882 ($ *7)) (-15 -1595 (*7 $)) (-15 -1608 (*7 $)))))))) (((*1 *1 *2) (-12 (-5 *2 (-936)) (-4 *1 (-378)))) ((*1 *2 *3 *3) (-12 (-5 *3 (-936)) (-5 *2 (-1285 *4)) (-5 *1 (-539 *4)) @@ -942,8 +929,8 @@ ((*1 *2 *1) (-12 (-4 *2 (-861)) (-5 *1 (-724 *2 *3 *4)) (-4 *3 (-1117)) (-14 *4 - (-1 (-112) (-2 (|:| -4317 *2) (|:| -2398 *3)) - (-2 (|:| -4317 *2) (|:| -2398 *3))))))) + (-1 (-112) (-2 (|:| -4317 *2) (|:| -1658 *3)) + (-2 (|:| -4317 *2) (|:| -1658 *3))))))) (((*1 *1 *2) (-12 (-5 *2 (-655 (-655 *3))) (-4 *3 (-1066)) (-4 *1 (-698 *3 *4 *5)) (-4 *4 (-383 *3)) (-4 *5 (-383 *3)))) @@ -955,19 +942,39 @@ (-12 (-5 *2 (-655 (-655 *5))) (-4 *5 (-1066)) (-4 *1 (-1070 *3 *4 *5 *6 *7)) (-4 *6 (-243 *4 *5)) (-4 *7 (-243 *3 *5))))) -(((*1 *2 *1) (-12 (-4 *1 (-1012 *2)) (-4 *2 (-1235))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1159 *4 *2)) (-14 *4 (-936)) - (-4 *2 (-13 (-1066) (-10 -7 (-6 (-4462 "*"))))) - (-5 *1 (-917 *4 *2))))) -(((*1 *2 *3 *4 *2 *2 *5) - (|partial| -12 (-5 *2 (-854 *4)) (-5 *3 (-623 *4)) (-5 *5 (-112)) - (-4 *4 (-13 (-1220) (-29 *6))) - (-4 *6 (-13 (-463) (-1055 (-575)) (-650 (-575)))) - (-5 *1 (-226 *6 *4))))) +(((*1 *1 *2 *3) + (-12 + (-5 *3 + (-655 + (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2) + (|:| |xpnt| (-575))))) + (-4 *2 (-567)) (-5 *1 (-429 *2)))) + ((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |contp| (-575)) + (|:| -1366 (-655 (-2 (|:| |irr| *4) (|:| -2205 (-575))))))) + (-4 *4 (-1261 (-575))) (-5 *2 (-429 *4)) (-5 *1 (-453 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-418 (-967 *4))) (-4 *4 (-316)) - (-5 *2 (-418 (-429 (-967 *4)))) (-5 *1 (-1059 *4))))) + (-12 (-4 *4 (-567)) (-4 *5 (-804)) (-4 *6 (-861)) + (-4 *7 (-1082 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-655 *7)) (|:| |badPols| (-655 *7)))) + (-5 *1 (-994 *4 *5 *6 *7)) (-5 *3 (-655 *7))))) +(((*1 *2 *1) + (-12 (-5 *2 (-176 (-418 (-575)))) (-5 *1 (-118 *3)) (-14 *3 (-575)))) + ((*1 *1 *2 *3 *3) + (-12 (-5 *3 (-1174 *2)) (-4 *2 (-316)) (-5 *1 (-176 *2)))) + ((*1 *1 *2) (-12 (-5 *2 (-418 *3)) (-4 *3 (-316)) (-5 *1 (-176 *3)))) + ((*1 *2 *3) + (-12 (-5 *2 (-176 (-575))) (-5 *1 (-776 *3)) (-4 *3 (-415)))) + ((*1 *2 *1) + (-12 (-5 *2 (-176 (-418 (-575)))) (-5 *1 (-882 *3)) (-14 *3 (-575)))) + ((*1 *2 *1) + (-12 (-14 *3 (-575)) (-5 *2 (-176 (-418 (-575)))) + (-5 *1 (-883 *3 *4)) (-4 *4 (-880 *3))))) +(((*1 *2) + (-12 (-4 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(-5 *2 (-655 (-1176))) (-5 *1 (-339)))) ((*1 *1 *2) (-12 (-5 *2 (-1176)) (-5 *1 (-339))))) (((*1 *2 *3) @@ -1172,189 +1144,236 @@ (-5 *1 (-470 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1247 *3 *2)) (-4 *3 (-1066)) (-4 *2 (-1276 *3))))) -(((*1 *2 *1 *1) - (-12 (-4 *1 (-993 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-804)) - (-4 *5 (-861)) (-4 *6 (-1082 *3 *4 *5)) (-4 *3 (-567)) - (-5 *2 (-112))))) -(((*1 *2 *3 *1) - (-12 (-5 *2 (-655 (-1194))) (-5 *1 (-1197)) (-5 *3 (-1194))))) -(((*1 *2 *1) (-12 (-5 *2 (-655 (-655 (-227)))) (-5 *1 (-941))))) -(((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-693 *3)) (-4 *3 (-1117))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) -(((*1 *2 *3 *4 *4 *4) - (-12 (-5 *3 (-655 *8)) (-5 *4 (-112)) (-4 *8 (-1082 *5 *6 *7)) - (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-5 *2 (-655 (-1044 *5 *6 *7 *8))) (-5 *1 (-1044 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4 *4) - (-12 (-5 *3 (-655 *8)) (-5 *4 (-112)) (-4 *8 (-1082 *5 *6 *7)) - (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - 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*1 (-1288))))) +(((*1 *2 *1) (-12 (-4 *1 (-1012 *2)) (-4 *2 (-1235))))) +(((*1 *1 *1) (-12 (-5 *1 (-904 *2)) (-4 *2 (-1117))))) (((*1 *2 *1) (-12 (-5 *2 (-655 (-1199))) (-5 *1 (-185 *3)) (-4 *3 (-187))))) (((*1 *2 *3) @@ -1448,158 +1461,184 @@ (-2 (|:| |f1| (-655 *4)) (|:| |f2| (-655 (-655 (-655 *4)))) (|:| |f3| (-655 (-655 *4))) (|:| |f4| (-655 (-655 (-655 *4)))))) (-5 *1 (-1205 *4)) (-5 *3 (-655 (-655 (-655 *4))))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-904 *3)) (-4 *3 (-1117)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1120 *3 *4 *5 *6 *7)) (-4 *3 (-1117)) (-4 *4 (-1117)) - (-4 *5 (-1117)) (-4 *6 (-1117)) (-4 *7 (-1117)) (-5 *2 (-112))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-4 *3 (-1082 *5 *6 *7)) - (-5 *2 (-655 (-2 (|:| |val| (-112)) (|:| -4270 *4)))) - (-5 *1 (-1125 *5 *6 *7 *3 *4)) (-4 *4 (-1088 *5 *6 *7 *3))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-1285 *4)) (-5 *3 (-575)) (-4 *4 (-359)) - (-5 *1 (-539 *4))))) -(((*1 *2 *1) - (-12 (-4 *1 (-918 *3)) (-4 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finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-570)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-782)) (-4 *1 (-706 *2)) (-4 *2 (-1117)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| -4169 + (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) + (|:| |fn| (-1285 (-325 (-227)))) (|:| |yinit| (-655 (-227))) + (|:| |intvals| (-655 (-227))) (|:| |g| (-325 (-227))) + (|:| |abserr| (-227)) (|:| |relerr| (-227)))) + (|:| -3179 + (-2 (|:| |stiffness| (-389)) (|:| |stability| (-389)) + (|:| |expense| (-389)) (|:| |accuracy| (-389)) + (|:| |intermediateResults| (-389)))))) + (-5 *1 (-814)))) + ((*1 *2 *3 *4) + (-12 (-5 *2 (-1290)) (-5 *1 (-1212 *3 *4)) (-4 *3 (-1117)) + (-4 *4 (-1117))))) +(((*1 *2 *1 *3 *4 *4 *5) + (-12 (-5 *3 (-958 (-227))) (-5 *4 (-885)) (-5 *5 (-936)) + (-5 *2 (-1290)) (-5 *1 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+ (-5 *2 (-1052)) (-5 *1 (-756))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1066)) (-4 *3 (-803)) (-4 *2 (-373)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-575)) (-5 *1 (-227)))) ((*1 *1 *1 *1) - (-3765 (-12 (-5 *1 (-303 *2)) (-4 *2 (-373)) (-4 *2 (-1235))) + (-3763 (-12 (-5 *1 (-303 *2)) (-4 *2 (-373)) (-4 *2 (-1235))) (-12 (-5 *1 (-303 *2)) (-4 *2 (-484)) (-4 *2 (-1235))))) ((*1 *1 *1 *1) (-4 *1 (-373))) ((*1 *1 *1 *2) (-12 (-5 *2 (-575)) (-5 *1 (-389)))) @@ -2272,35 +2404,50 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1308 *2 *3)) (-4 *2 (-373)) (-4 *2 (-1066)) (-4 *3 (-857))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) +(((*1 *2 *3 *4 *4 *4 *4) + (-12 (-5 *3 (-700 (-227))) (-5 *4 (-575)) (-5 *2 (-1052)) + (-5 *1 (-766))))) (((*1 *2 *3) - (-12 (-5 *3 (-1 *5 *5 *5)) (-4 *5 (-1276 *4)) - (-4 *4 (-38 (-418 (-575)))) - (-5 *2 (-1 (-1174 *4) (-1174 *4) (-1174 *4))) (-5 *1 (-1278 *4 *5))))) -(((*1 *2) - (-12 - (-5 *2 (-2 (|:| -4131 (-655 (-1194))) (|:| -4024 (-655 (-1194))))) - 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(-5 *1 (-353 *3 *4)) (-14 *3 (-936)) + (-14 *4 (-936)))) + ((*1 *2) + (-12 (-5 *2 (-973 (-1137))) (-5 *1 (-354 *3 *4)) (-4 *3 (-359)) + (-14 *4 (-1190 *3)))) + ((*1 *2) + (-12 (-5 *2 (-973 (-1137))) (-5 *1 (-355 *3 *4)) (-4 *3 (-359)) + (-14 *4 (-936))))) +(((*1 *2 *3 *3) + (-12 (-4 *3 (-1239)) (-4 *5 (-1261 *3)) (-4 *6 (-1261 (-418 *5))) + (-5 *2 (-112)) (-5 *1 (-351 *4 *3 *5 *6)) (-4 *4 (-352 *3 *5 *6)))) + ((*1 *2 *3 *3) + (-12 (-4 *1 (-352 *3 *4 *5)) (-4 *3 (-1239)) (-4 *4 (-1261 *3)) + (-4 *5 (-1261 (-418 *4))) (-5 *2 (-112))))) (((*1 *1) (-5 *1 (-188)))) (((*1 *2 *3 *4) (-12 (-5 *4 (-936)) (-4 *6 (-567)) (-5 *2 (-655 (-325 *6))) @@ -2769,22 +2861,33 @@ ((*1 *2 *1) (-12 (-5 *2 (-1300 *3 *4)) (-5 *1 (-1309 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1066))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 (-655 *2)) (-4 *2 (-1117)) (-4 *2 (-1235))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-418 (-1190 (-325 *3)))) (-4 *3 (-567)) + (-5 *1 (-1147 *3))))) +(((*1 *2 *2) + (-12 (-5 *2 (-655 *7)) (-4 *7 (-1088 *3 *4 *5 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-(((*1 *2 *3 *4) - (-12 (-5 *4 (-575)) (-5 *2 (-655 (-2 (|:| -2353 *3) (|:| -2645 *4)))) - (-5 *1 (-707 *3)) (-4 *3 (-1261 *4))))) +(((*1 *2 *3 *4 *4 *5 *3 *3 *4 *3 *3 *3) + (-12 (-5 *3 (-575)) (-5 *5 (-700 (-227))) (-5 *4 (-227)) + (-5 *2 (-1052)) (-5 *1 (-763))))) (((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -2801,28 +2904,42 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-418 (-575))) (-5 *1 (-314))))) -(((*1 *2 *3) - (-12 (-4 *3 (-1261 *2)) (-4 *2 (-1261 *4)) - (-5 *1 (-1002 *4 *2 *3 *5)) (-4 *4 (-359)) (-4 *5 (-735 *2 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1137)) (-5 *2 (-112)) (-5 *1 (-832))))) -(((*1 *2 *1) - (-12 (-5 *2 (-418 (-967 *3))) (-5 *1 (-464 *3 *4 *5 *6)) - (-4 *3 (-567)) (-4 *3 (-174)) (-14 *4 (-936)) - (-14 *5 (-655 (-1194))) (-14 *6 (-1285 (-700 *3)))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-540))))) -(((*1 *1) (-5 *1 (-1080)))) 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+2974,6 @@ ((*1 *2 *3 *1) (-12 (-5 *3 (-1 (-112) *4)) (|has| *1 (-6 -4460)) (-4 *1 (-500 *4)) (-4 *4 (-1235)) (-5 *2 (-782))))) -(((*1 *2 *3 *2 *4) - (|partial| -12 (-5 *3 (-655 (-623 *2))) (-5 *4 (-1194)) - (-4 *2 (-13 (-27) (-1220) (-441 *5))) - (-4 *5 (-13 (-567) (-1055 (-575)) (-650 (-575)))) - (-5 *1 (-285 *5 *2))))) (((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -2881,52 +2993,43 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *1 *1 *2 *2) - (-12 (-5 *2 (-575)) (-4 *1 (-698 *3 *4 *5)) (-4 *3 (-1066)) - (-4 *4 (-383 *3)) (-4 *5 (-383 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-1009 *2)) (-4 *2 (-567)) (-4 *2 (-556)))) + ((*1 *1 *1) (-4 *1 (-1077)))) (((*1 *2 *1) (-12 (-4 *3 (-1117)) (-4 *4 (-13 (-1066) (-898 *3) (-625 *2))) (-5 *2 (-904 *3)) (-5 *1 (-1093 *3 *4 *5)) (-4 *5 (-13 (-441 *4) (-898 *3) (-625 *2)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-567) (-1055 (-575)))) (-4 *5 (-441 *4)) - (-5 *2 - (-3 (|:| |overq| (-1190 (-418 (-575)))) - (|:| |overan| (-1190 (-48))) (|:| -3420 (-112)))) - (-5 *1 (-446 *4 *5 *3)) (-4 *3 (-1261 *5))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1111 (-854 (-227)))) (-5 *2 (-227)) (-5 *1 (-194)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1111 (-854 (-227)))) (-5 *2 (-227)) (-5 *1 (-309)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1111 (-854 (-227)))) (-5 *2 (-227)) (-5 *1 (-314))))) -(((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-575)) (-4 *1 (-57 *4 *3 *5)) (-4 *4 (-1235)) - (-4 *3 (-383 *4)) (-4 *5 (-383 *4))))) (((*1 *2 *1) - (-12 (-4 *3 (-463)) (-4 *4 (-861)) (-4 *5 (-804)) (-5 *2 (-655 *6)) - (-5 *1 (-1004 *3 *4 *5 *6)) (-4 *6 (-964 *3 *5 *4))))) + (-12 (-5 *2 (-702 (-884 (-981 *3) (-981 *3)))) (-5 *1 (-981 *3)) + (-4 *3 (-1117))))) +(((*1 *2 *1) (-12 (-5 *2 (-655 (-655 (-227)))) (-5 *1 (-941))))) +(((*1 *1 *2) (-12 (-5 *2 (-325 (-171 (-389)))) (-5 *1 (-339)))) + ((*1 *1 *2) (-12 (-5 *2 (-325 (-575))) (-5 *1 (-339)))) + ((*1 *1 *2) (-12 (-5 *2 (-325 (-389))) (-5 *1 (-339)))) + ((*1 *1 *2) (-12 (-5 *2 (-325 (-705))) (-5 *1 (-339)))) + ((*1 *1 *2) (-12 (-5 *2 (-325 (-712))) (-5 *1 (-339)))) + ((*1 *1 *2) (-12 (-5 *2 (-325 (-710))) (-5 *1 (-339)))) + ((*1 *1) (-5 *1 (-339)))) +(((*1 *2) (-12 (-5 *2 (-1290)) (-5 *1 (-570))))) (((*1 *1) (-5 *1 (-300)))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-373) (-10 -8 (-15 ** ($ $ (-418 (-575))))))) - (-5 *2 (-655 *4)) (-5 *1 (-1145 *3 *4)) (-4 *3 (-1261 *4)))) - ((*1 *2 *3 *3 *3 *3) - (-12 (-4 *3 (-13 (-373) (-10 -8 (-15 ** ($ $ (-418 (-575))))))) - (-5 *2 (-655 *3)) (-5 *1 (-1145 *4 *3)) (-4 *4 (-1261 *3))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-112)))) ((*1 *1 *2 *2) (-12 (-5 *1 (-303 *2)) (-4 *2 (-1235)))) ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-445)))) ((*1 *1 *1 *1) (-5 *1 (-873))) ((*1 *2 *1 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1043 *3)) (-4 *3 (-1235))))) -(((*1 *2 *1 *3) - (-12 (-4 *1 (-871)) (-5 *2 (-702 (-560))) (-5 *3 (-560))))) (((*1 *2 *1) (-12 (-4 *1 (-1117)) (-5 *2 (-1137))))) -(((*1 *2 *1) - (|partial| -12 (-5 *2 (-1078 (-1041 *3) (-1190 (-1041 *3)))) - (-5 *1 (-1041 *3)) (-4 *3 (-13 (-859) (-373) (-1039)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-575)) (-5 *2 (-1052)) (-5 *1 (-769))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-655 *2)) (-4 *2 (-1235))))) +(((*1 *2 *3 *2 *4) + (-12 (-5 *3 (-655 *6)) (-5 *4 (-655 (-252 *5 *6))) (-4 *6 (-463)) + (-5 *2 (-252 *5 *6)) (-14 *5 (-655 (-1194))) (-5 *1 (-642 *5 *6))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-700 *3)) + (-4 *3 (-13 (-316) (-10 -8 (-15 -4281 ((-429 $) $))))) + (-4 *4 (-1261 *3)) (-5 *1 (-510 *3 *4 *5)) (-4 *5 (-420 *3 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-936)) (-5 *2 (-1190 *4)) (-5 *1 (-367 *4)) + (-4 *4 (-359))))) (((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -2946,24 +3049,20 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-655 *2)) (-4 *2 (-1235))))) -(((*1 *2 *3 *3 *4 *5 *5) - (-12 (-5 *5 (-112)) (-4 *6 (-463)) (-4 *7 (-804)) (-4 *8 (-861)) - (-4 *3 (-1082 *6 *7 *8)) - (-5 *2 (-655 (-2 (|:| |val| *3) (|:| -4270 *4)))) - (-5 *1 (-1125 *6 *7 *8 *3 *4)) (-4 *4 (-1088 *6 *7 *8 *3)))) - ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-655 (-2 (|:| |val| (-655 *8)) (|:| -4270 *9)))) - (-5 *5 (-112)) (-4 *8 (-1082 *6 *7 *4)) (-4 *9 (-1088 *6 *7 *4 *8)) - (-4 *6 (-463)) (-4 *7 (-804)) (-4 *4 (-861)) - (-5 *2 (-655 (-2 (|:| |val| *8) (|:| -4270 *9)))) - (-5 *1 (-1125 *6 *7 *4 *8 *9))))) +(((*1 *2 *1) + (-12 (-4 *1 (-345 *3 *4 *5 *6)) (-4 *3 (-373)) (-4 *4 (-1261 *3)) + (-4 *5 (-1261 (-418 *4))) (-4 *6 (-352 *3 *4 *5)) (-5 *2 (-112))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-936)) (-4 *1 (-755 *3)) (-4 *3 (-174))))) +(((*1 *2 *1 *3 *3 *3) + (-12 (-5 *3 (-389)) (-5 *2 (-1290)) (-5 *1 (-1287))))) +(((*1 *2 *2 *3) + (-12 (-4 *4 (-1117)) (-4 *2 (-913 *4)) (-5 *1 (-703 *4 *2 *5 *3)) + (-4 *5 (-383 *2)) (-4 *3 (-13 (-383 *4) (-10 -7 (-6 -4460))))))) (((*1 *2 *3) - (-12 (-5 *3 (-575)) (|has| *1 (-6 -4451)) (-4 *1 (-415)) - (-5 *2 (-936))))) -(((*1 *2 *1) (-12 (-4 *1 (-359)) (-5 *2 (-782)))) - ((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-413)) (-5 *2 (-782))))) -(((*1 *2 *2) (-12 (-5 *2 (-655 *3)) (-4 *3 (-859)) (-5 *1 (-312 *3))))) + (-12 (-5 *3 (-1194)) + (-4 *4 (-13 (-316) (-1055 (-575)) (-650 (-575)) (-148))) + (-5 *2 (-1 *5 *5)) (-5 *1 (-815 *4 *5)) + (-4 *5 (-13 (-29 *4) (-1220) (-974)))))) (((*1 *2 *3 *3) (-12 (-5 *3 (-782)) (-5 *2 (-1285 (-655 (-575)))) (-5 *1 (-491)))) ((*1 *1 *2 *3) @@ -2971,22 +3070,29 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1235)) (-5 *1 (-1174 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1 *3)) (-4 *3 (-1235)) (-5 *1 (-1174 *3))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1119 *3)) (-5 *1 (-920 *3)) (-4 *3 (-378)) - (-4 *3 (-1117))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-700 (-418 (-967 (-575))))) - (-5 *2 (-655 (-700 (-325 (-575))))) (-5 *1 (-1048)) - (-5 *3 (-325 (-575)))))) -(((*1 *2 *3) - (-12 (-5 *3 (-655 (-2 (|:| -4182 *4) (|:| -2807 (-575))))) - (-4 *4 (-1117)) (-5 *2 (-1 *4)) (-5 *1 (-1034 *4))))) -(((*1 *2 *3 *4 *3 *4 *3) - (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *2 (-1052)) - (-5 *1 (-767))))) -(((*1 *2 *3 *4 *3) - (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *2 (-1052)) - (-5 *1 (-758))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-55)))) + ((*1 *2 *1) + (-12 (-4 *3 (-373)) (-4 *4 (-804)) (-4 *5 (-861)) (-5 *2 (-112)) + (-5 *1 (-515 *3 *4 *5 *6)) (-4 *6 (-964 *3 *4 *5)))) + ((*1 *2 *1) (-12 (-4 *1 (-733)) (-5 *2 (-112)))) + ((*1 *2 *1) (-12 (-4 *1 (-737)) (-5 *2 (-112))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-556)))) +(((*1 *1 *2) (-12 (-5 *2 (-1285 *3)) (-4 *3 (-373)) (-4 *1 (-338 *3)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1285 *3)) (-4 *3 (-1261 *4)) (-4 *4 (-1239)) + (-4 *1 (-352 *4 *3 *5)) (-4 *5 (-1261 (-418 *3))))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1285 *4)) (-5 *3 (-1285 *1)) (-4 *4 (-174)) + (-4 *1 (-377 *4)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1285 *4)) (-5 *3 (-1285 *1)) (-4 *4 (-174)) + (-4 *1 (-380 *4 *5)) (-4 *5 (-1261 *4)))) + ((*1 *1 *2) + (-12 (-5 *2 (-1285 *3)) (-4 *3 (-174)) (-4 *1 (-420 *3 *4)) + (-4 *4 (-1261 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1285 *3)) (-4 *3 (-174)) (-4 *1 (-428 *3))))) +(((*1 *2 *1) (-12 (-4 *1 (-1110 *2)) (-4 *2 (-1235))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-793 *2)) (-4 *2 (-1066))))) (((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -3006,29 +3112,13 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-782)) (-5 *2 (-112)))) - ((*1 *2 *3 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-1236 *3)) (-4 *3 (-861)) - (-4 *3 (-1117))))) -(((*1 *2 *3) - (-12 (-4 *4 (-359)) (-5 *2 (-429 (-1190 (-1190 *4)))) - (-5 *1 (-1233 *4)) (-5 *3 (-1190 (-1190 *4)))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-112)) (-4 *6 (-13 (-463) (-1055 (-575)) (-650 (-575)))) - (-4 *3 (-13 (-27) (-1220) (-441 *6) (-10 -8 (-15 -2883 ($ *7))))) - (-4 *7 (-859)) - (-4 *8 - (-13 (-1263 *3 *7) (-373) (-1220) - (-10 -8 (-15 -2389 ($ $)) (-15 -4413 ($ $))))) - (-5 *2 - (-3 (|:| |%series| *8) - (|:| |%problem| (-2 (|:| |func| (-1176)) (|:| |prob| (-1176)))))) - (-5 *1 (-433 *6 *3 *7 *8 *9 *10)) (-5 *5 (-1176)) (-4 *9 (-1000 *8)) - (-14 *10 (-1194))))) -(((*1 *2 *3) - (-12 (-4 *4 (-567)) (-5 *2 (-171 *5)) (-5 *1 (-611 *4 *5 *3)) - (-4 *5 (-13 (-441 *4) (-1019) (-1220))) - (-4 *3 (-13 (-441 (-171 *4)) (-1019) (-1220)))))) +(((*1 *1 *1) + (-12 (-5 *1 (-606 *2)) (-4 *2 (-38 (-418 (-575)))) (-4 *2 (-1066))))) +(((*1 *2 *3 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *2 (-1052)) + (-5 *1 (-766))))) +(((*1 *2 *2) (-12 (-5 *1 (-598 *2)) (-4 *2 (-556))))) +(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-124)))) (((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-138)))) ((*1 *2 *1) (-12 (-5 *2 (-1234)) (-5 *1 (-157)))) ((*1 *2 *1) (-12 (-5 *1 (-303 *2)) (-4 *2 (-1235)))) @@ -3042,22 +3132,28 @@ (-4 *4 (-13 (-1066) (-898 *3) (-625 (-904 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1117)) (-5 *1 (-1183 *3 *2)) (-4 *3 (-1117))))) +(((*1 *2) (-12 (-5 *2 (-1290)) (-5 *1 (-447))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-782)) (-4 *4 (-1066)) + (-5 *2 (-2 (|:| -3262 *1) (|:| -4041 *1))) (-4 *1 (-1261 *4))))) (((*1 *2 *3) - (-12 (-4 *4 (-316)) (-4 *5 (-383 *4)) (-4 *6 (-383 *4)) - (-5 *2 - (-2 (|:| |Smith| *3) (|:| |leftEqMat| *3) (|:| |rightEqMat| *3))) - (-5 *1 (-1141 *4 *5 *6 *3)) (-4 *3 (-698 *4 *5 *6))))) -(((*1 *2 *3) - (-12 (-4 *4 (-804)) (-4 *5 (-861)) (-4 *6 (-316)) - (-5 *2 (-655 (-782))) (-5 *1 (-789 *3 *4 *5 *6 *7)) - (-4 *3 (-1261 *6)) (-4 *7 (-964 *6 *4 *5))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-936)) (-4 *1 (-755 *3)) (-4 *3 (-174))))) -(((*1 *2 *1) (-12 (-4 *1 (-1166 *3)) (-4 *3 (-1235)) (-5 *2 (-112))))) + (-12 + (-5 *3 + (-655 (-2 (|:| -2412 (-418 (-575))) (|:| -2429 (-418 (-575)))))) + (-5 *2 (-655 (-227))) (-5 *1 (-314))))) (((*1 *1 *2) (-12 (-5 *2 (-655 *1)) (-4 *1 (-463)))) ((*1 *1 *1 *1) (-4 *1 (-463)))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1235)) (-5 *1 (-385 *4 *2)) - (-4 *2 (-13 (-383 *4) (-10 -7 (-6 -4461))))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-418 (-967 (-171 (-575))))) (-5 *2 (-655 (-171 *4))) + (-5 *1 (-388 *4)) (-4 *4 (-13 (-373) (-859))))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-655 (-418 (-967 (-171 (-575)))))) + (-5 *4 (-655 (-1194))) (-5 *2 (-655 (-655 (-171 *5)))) + (-5 *1 (-388 *5)) (-4 *5 (-13 (-373) (-859)))))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-376 *3 *4)) + (-4 *3 (-377 *4)))) + ((*1 *2) (-12 (-4 *1 (-377 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -3074,16 +3170,30 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-655 (-655 (-958 (-227))))) (-5 *2 (-655 (-227))) - (-5 *1 (-479))))) +(((*1 *1) + (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-575)) (-14 *3 (-782)) + (-4 *4 (-174))))) +(((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-655 (-967 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-859) (-316) (-148) (-1039))) + (-5 *2 (-655 (-1063 *5 *6))) (-5 *1 (-1312 *5 *6 *7)) + (-14 *6 (-655 (-1194))) (-14 *7 (-655 (-1194))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-655 (-967 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-859) (-316) (-148) (-1039))) + (-5 *2 (-655 (-1063 *5 *6))) (-5 *1 (-1312 *5 *6 *7)) + (-14 *6 (-655 (-1194))) (-14 *7 (-655 (-1194))))) + ((*1 *2 *3) + (-12 (-5 *3 (-655 (-967 *4))) + (-4 *4 (-13 (-859) (-316) (-148) (-1039))) + (-5 *2 (-655 (-1063 *4 *5))) (-5 *1 (-1312 *4 *5 *6)) + (-14 *5 (-655 (-1194))) (-14 *6 (-655 (-1194)))))) (((*1 *2 *2) - (-12 (-5 *2 (-655 (-655 *6))) (-4 *6 (-964 *3 *5 *4)) - (-4 *3 (-13 (-316) (-148))) (-4 *4 (-13 (-861) (-625 (-1194)))) - (-4 *5 (-804)) (-5 *1 (-939 *3 *4 *5 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-1290)) (-5 *1 (-833))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-1235)) (-5 *1 (-184 *3 *2)) (-4 *2 (-685 *3))))) + (-12 (-5 *2 (-655 (-655 *3))) (-4 *3 (-861)) (-5 *1 (-1205 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1190 *4)) (-4 *4 (-359)) + (-5 *2 (-1285 (-655 (-2 (|:| -4181 *4) (|:| -4317 (-1137)))))) + (-5 *1 (-356 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-138)))) ((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-157)))) ((*1 *2 *1) (-12 (-5 *1 (-303 *2)) (-4 *2 (-1235)))) @@ -3097,23 +3207,15 @@ (-4 *4 (-13 (-1066) (-898 *3) (-625 (-904 *3)))))) ((*1 *2 *1) (-12 (-4 *2 (-1117)) (-5 *1 (-1183 *2 *3)) (-4 *3 (-1117))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-1 (-655 *7) *7 (-1190 *7))) (-5 *5 (-1 (-429 *7) *7)) - (-4 *7 (-1261 *6)) (-4 *6 (-13 (-373) (-148) (-1055 (-418 (-575))))) - (-5 *2 (-655 (-2 (|:| |frac| (-418 *7)) (|:| -2571 *3)))) - (-5 *1 (-820 *6 *7 *3 *8)) (-4 *3 (-667 *7)) - (-4 *8 (-667 (-418 *7))))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-429 *6) *6)) (-4 *6 (-1261 *5)) - (-4 *5 (-13 (-373) (-148) (-1055 (-575)) (-1055 (-418 (-575))))) - (-5 *2 - (-655 (-2 (|:| |frac| (-418 *6)) (|:| -2571 (-665 *6 (-418 *6)))))) - (-5 *1 (-823 *5 *6)) (-5 *3 (-665 *6 (-418 *6)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1268 *3 *2)) (-4 *3 (-1066)) (-4 *2 (-1245 *3))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-567)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -4232 *4))) - (-5 *1 (-986 *4 *3)) (-4 *3 (-1261 *4))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-700 *3)) (-4 *3 (-1066)) (-5 *1 (-701 *3)))) + ((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-700 *3)) (-4 *3 (-1066)) (-5 *1 (-701 *3))))) +(((*1 *2 *1) (-12 (-5 *2 (-575)) (-5 *1 (-873))))) +(((*1 *2 *2) + (-12 (-4 *3 (-463)) (-4 *4 (-804)) (-4 *5 (-861)) + (-4 *6 (-1082 *3 *4 *5)) (-5 *1 (-635 *3 *4 *5 *6 *7 *2)) + (-4 *7 (-1088 *3 *4 *5 *6)) (-4 *2 (-1126 *3 *4 *5 *6))))) (((*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-782)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-936)))) ((*1 *1 *1 *1) @@ -3140,10 +3242,10 @@ ((*1 *1 *2 *1) (-12 (-4 *1 (-396 *2)) (-4 *2 (-1117)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-655 (-1194))) (-4 *4 (-174)) - (-4 *6 (-243 (-2871 *3) (-782))) + (-4 *6 (-243 (-2869 *3) (-782))) (-14 *7 - (-1 (-112) (-2 (|:| -4317 *5) (|:| -2398 *6)) - (-2 (|:| -4317 *5) (|:| -2398 *6)))) + (-1 (-112) (-2 (|:| -4317 *5) (|:| -1658 *6)) + (-2 (|:| -4317 *5) (|:| -1658 *6)))) (-5 *1 (-472 *3 *4 *5 *6 *7 *2)) (-4 *5 (-861)) (-4 *2 (-964 *4 *6 (-875 *3))))) ((*1 *1 *1 *2) @@ -3217,16 +3319,19 @@ (-12 (-4 *1 (-1302 *3 *2)) (-4 *3 (-861)) (-4 *2 (-1066)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-1308 *2 *3)) (-4 *2 (-1066)) (-4 *3 (-857))))) -(((*1 *1 *2) - (-12 (-5 *2 (-655 *1)) (-4 *1 (-1151 *3)) (-4 *3 (-1066)))) - ((*1 *2 *2 *1) - (|partial| -12 (-5 *2 (-418 *1)) (-4 *1 (-1261 *3)) (-4 *3 (-1066)) - (-4 *3 (-567)))) - ((*1 *1 *1 *1) - (|partial| -12 (-4 *1 (-1261 *2)) (-4 *2 (-1066)) (-4 *2 (-567))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-332 *2 *3)) (-4 *2 (-1117)) (-4 *3 (-132)) - (-4 *3 (-803))))) +(((*1 *2 *3) + (-12 (-5 *3 (-782)) (-5 *2 (-1290)) (-5 *1 (-877 *4 *5 *6 *7)) + (-4 *4 (-1066)) (-14 *5 (-655 (-1194))) (-14 *6 (-655 *3)) + (-14 *7 *3))) + ((*1 *2 *3) + (-12 (-5 *3 (-782)) (-4 *4 (-1066)) (-4 *5 (-861)) (-4 *6 (-804)) + (-14 *8 (-655 *5)) (-5 *2 (-1290)) + (-5 *1 (-1297 *4 *5 *6 *7 *8 *9 *10)) (-4 *7 (-964 *4 *6 *5)) + (-14 *9 (-655 *3)) (-14 *10 *3)))) +(((*1 *2) + (-12 (-4 *4 (-174)) (-5 *2 (-112)) (-5 *1 (-376 *3 *4)) + (-4 *3 (-377 *4)))) + ((*1 *2) (-12 (-4 *1 (-377 *3)) (-4 *3 (-174)) (-5 *2 (-112))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -3243,57 +3348,28 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *2) (-12 (-5 *2 (-575)) (-5 *1 (-572)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1190 (-418 (-575)))) (-5 *1 (-957)) (-5 *3 (-575))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-863 *2)) (-4 *2 (-1066)) (-4 *2 (-373))))) (((*1 *2 *2) - (-12 (-5 *2 (-1174 *3)) (-4 *3 (-1066)) (-5 *1 (-1178 *3)))) + (-12 (-4 *3 (-463)) (-5 *1 (-1226 *3 *2)) + (-4 *2 (-13 (-441 *3) (-1220)))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1176)) (-5 *1 (-1216))))) +(((*1 *2 *1) (-12 (-4 *1 (-260 *2)) (-4 *2 (-1235))))) +(((*1 *1 *1) + (-12 (-5 *1 (-606 *2)) (-4 *2 (-38 (-418 (-575)))) (-4 *2 (-1066))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-904 *3)) (-4 *3 (-1117))))) +(((*1 *2 *3) (-12 (-5 *3 (-389)) (-5 *2 (-1176)) (-5 *1 (-314))))) +(((*1 *1 *1) (-12 (-4 *1 (-167 *2)) (-4 *2 (-174)) (-4 *2 (-1077)))) ((*1 *1 *1) - (-12 (-5 *1 (-1277 *2 *3 *4)) (-4 *2 (-1066)) (-14 *3 (-1194)) - (-14 *4 *2)))) -(((*1 *2 *3 *3 *4 *4 *4 *4) - (-12 (-5 *3 (-227)) (-5 *4 (-575)) (-5 *2 (-1052)) (-5 *1 (-759))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-575)) (-5 *4 (-429 *2)) (-4 *2 (-964 *7 *5 *6)) - (-5 *1 (-753 *5 *6 *7 *2)) (-4 *5 (-804)) (-4 *6 (-861)) - (-4 *7 (-316))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-567) (-1055 (-575)) (-650 (-575)))) - (-5 *1 (-285 *3 *2)) (-4 *2 (-13 (-27) (-1220) (-441 *3))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1194)) - (-4 *4 (-13 (-567) (-1055 (-575)) (-650 (-575)))) - (-5 *1 (-285 *4 *2)) (-4 *2 (-13 (-27) (-1220) (-441 *4))))) - ((*1 *1 *1) (-5 *1 (-389))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-4 *3 (-1082 *5 *6 *7)) - (-5 *2 (-655 (-2 (|:| |val| *3) (|:| -4270 *4)))) - (-5 *1 (-787 *5 *6 *7 *3 *4)) (-4 *4 (-1088 *5 *6 *7 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1302 *3 *4)) (-4 *3 (-861)) (-4 *4 (-1066)) - (-5 *2 (-2 (|:| |k| (-830 *3)) (|:| |c| *4)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-567) (-148))) (-5 *1 (-548 *3 *2)) - (-4 *2 (-1276 *3)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-373) (-378) (-625 (-575)))) (-4 *4 (-1261 *3)) - (-4 *5 (-735 *3 *4)) (-5 *1 (-552 *3 *4 *5 *2)) (-4 *2 (-1276 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-373) (-378) (-625 (-575)))) (-5 *1 (-553 *3 *2)) - (-4 *2 (-1276 *3)))) + (-12 (-5 *1 (-349 *2 *3 *4)) (-14 *2 (-655 (-1194))) + (-14 *3 (-655 (-1194))) (-4 *4 (-398)))) ((*1 *2 *2) - (-12 (-5 *2 (-1174 *3)) (-4 *3 (-13 (-567) (-148))) - (-5 *1 (-1170 *3))))) -(((*1 *2 *3 *3 *3 *3 *4 *3 *3 *3 *3 *3 *3 *5 *5 *4 *3 *6 *7) - (-12 (-5 *3 (-575)) (-5 *5 (-700 (-227))) - (-5 *6 (-3 (|:| |fn| (-399)) (|:| |fp| (-75 FCN JACOBF JACEPS)))) - (-5 *7 (-3 (|:| |fn| (-399)) (|:| |fp| (-76 G JACOBG JACGEP)))) - (-5 *4 (-227)) (-5 *2 (-1052)) (-5 *1 (-760))))) -(((*1 *2 *3 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-227)) (-5 *4 (-575)) - (-5 *5 (-3 (|:| |fn| (-399)) (|:| |fp| (-64 G)))) (-5 *2 (-1052)) - (-5 *1 (-759))))) + (-12 (-4 *3 (-567)) (-5 *1 (-442 *3 *2)) (-4 *2 (-441 *3)))) + ((*1 *2 *1) (-12 (-4 *1 (-808 *2)) (-4 *2 (-174)) (-4 *2 (-1077)))) + ((*1 *1 *1) (-4 *1 (-859))) + ((*1 *2 *1) (-12 (-4 *1 (-1014 *2)) (-4 *2 (-174)) (-4 *2 (-1077)))) + ((*1 *1 *1) (-4 *1 (-1077))) ((*1 *1 *1) (-4 *1 (-1156)))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-227)) (-5 *4 (-575)) (-5 *2 (-1052)) (-5 *1 (-769))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -3310,104 +3386,35 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1235)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-861)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-861)))) - ((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-575)) (-4 *1 (-291 *3)) (-4 *3 (-1235)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-575)) (-4 *1 (-291 *2)) (-4 *2 (-1235)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -4169 - (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) - (|:| -3437 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) - (|:| |relerr| (-227)))) - (|:| -3179 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1174 (-227))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3437 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))))) - (-5 *1 (-570)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-782)) (-4 *1 (-706 *2)) (-4 *2 (-1117)))) - ((*1 *1 *2) - (-12 - (-5 *2 - (-2 - (|:| -4169 - (-2 (|:| |xinit| (-227)) (|:| |xend| (-227)) - (|:| |fn| (-1285 (-325 (-227)))) (|:| |yinit| (-655 (-227))) - (|:| |intvals| (-655 (-227))) (|:| |g| (-325 (-227))) - (|:| |abserr| (-227)) (|:| |relerr| (-227)))) - (|:| -3179 - (-2 (|:| |stiffness| (-389)) (|:| |stability| (-389)) - (|:| |expense| (-389)) (|:| |accuracy| (-389)) - (|:| |intermediateResults| (-389)))))) - (-5 *1 (-814)))) - ((*1 *2 *3 *4) - (-12 (-5 *2 (-1290)) (-5 *1 (-1212 *3 *4)) (-4 *3 (-1117)) - (-4 *4 (-1117))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *5 (-112)) - (-5 *6 (-227)) (-5 *7 (-3 (|:| |fn| (-399)) (|:| |fp| (-68 APROD)))) - (-5 *8 (-3 (|:| |fn| (-399)) (|:| |fp| (-73 MSOLVE)))) - (-5 *2 (-1052)) (-5 *1 (-767))))) +(((*1 *2 *2) (-12 (-5 *2 (-1176)) (-5 *1 (-1213))))) (((*1 *2 *3) - (-12 (-5 *3 (-1258 *5 *4)) (-4 *4 (-831)) (-14 *5 (-1194)) - (-5 *2 (-575)) (-5 *1 (-1131 *4 *5))))) -(((*1 *2 *3 *2) + (|partial| -12 (-4 *5 (-1055 (-48))) + (-4 *4 (-13 (-567) (-1055 (-575)))) (-4 *5 (-441 *4)) + (-5 *2 (-429 (-1190 (-48)))) (-5 *1 (-446 *4 *5 *3)) + (-4 *3 (-1261 *5))))) +(((*1 *2 *3 *1) (-12 (-5 *2 - (-655 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-782)) (|:| |poli| *3) - (|:| |polj| *3)))) - (-4 *5 (-804)) (-4 *3 (-964 *4 *5 *6)) (-4 *4 (-463)) (-4 *6 (-861)) - (-5 *1 (-460 *4 *5 *6 *3))))) -(((*1 *1 *1 *1 *2) - (-12 (-4 *1 (-1082 *3 *4 *2)) (-4 *3 (-1066)) (-4 *4 (-804)) - (-4 *2 (-861)))) - ((*1 *1 *1 *1) - (-12 (-4 *1 (-1082 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-804)) - (-4 *4 (-861))))) -(((*1 *2 *2) - (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) - (-4 *2 (-13 (-441 *3) (-1019)))))) -(((*1 *2 *3) (-12 (-5 *3 (-852)) (-5 *2 (-1052)) (-5 *1 (-851)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-655 (-325 (-389)))) (-5 *4 (-655 (-389))) - (-5 *2 (-1052)) (-5 *1 (-851))))) -(((*1 *2 *3) - (-12 (-5 *3 (-655 (-2 (|:| -2353 *4) (|:| -2645 (-575))))) - (-4 *4 (-1261 (-575))) (-5 *2 (-748 (-782))) (-5 *1 (-453 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-429 *5)) (-4 *5 (-1261 *4)) (-4 *4 (-1066)) - (-5 *2 (-748 (-782))) (-5 *1 (-455 *4 *5))))) -(((*1 *1 *1) (-5 *1 (-1080)))) + (-2 (|:| |cycle?| (-112)) (|:| -2489 (-782)) (|:| |period| (-782)))) + (-5 *1 (-1174 *4)) (-4 *4 (-1235)) (-5 *3 (-782))))) +(((*1 *1 *2) + (-12 (-5 *2 (-655 (-655 *3))) (-4 *3 (-1117)) (-5 *1 (-920 *3))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-655 *5)) (-5 *4 (-936)) (-4 *5 (-861)) - (-5 *2 (-59 (-655 (-683 *5)))) (-5 *1 (-683 *5))))) + (|partial| -12 (-5 *3 (-1285 *4)) (-4 *4 (-13 (-1066) (-650 (-575)))) + (-5 *2 (-1285 (-418 (-575)))) (-5 *1 (-1313 *4))))) +(((*1 *2 *1 *2) (-12 (-5 *1 (-1043 *2)) (-4 *2 (-1235))))) +(((*1 *2 *2) (-12 (-5 *2 (-389)) (-5 *1 (-1287)))) + ((*1 *2) (-12 (-5 *2 (-389)) (-5 *1 (-1287))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4461)) (-4 *1 (-120 *2)) (-4 *2 (-1235))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-1052))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-655 *6)) (-4 *6 (-1082 *3 *4 *5)) (-4 *3 (-567)) + (-4 *4 (-804)) (-4 *5 (-861)) (-5 *1 (-994 *3 *4 *5 *6)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *2 (-655 *7)) (-5 *3 (-112)) (-4 *7 (-1082 *4 *5 *6)) + (-4 *4 (-567)) (-4 *5 (-804)) (-4 *6 (-861)) + (-5 *1 (-994 *4 *5 *6 *7))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *1 *1 *1) (-5 *1 (-227))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -3428,39 +3435,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-655 (-1285 *5))) (-5 *4 (-575)) (-5 *2 (-1285 *5)) - (-5 *1 (-1046 *5)) (-4 *5 (-373)) (-4 *5 (-378)) (-4 *5 (-1066))))) -(((*1 *2 *1) (-12 (-4 *1 (-538)) (-5 *2 (-702 (-1241)))))) -(((*1 *2 *2) (-12 (-5 *2 (-575)) (-5 *1 (-941))))) -(((*1 *2 *1) (-12 (-4 *1 (-400)) (-5 *2 (-112))))) -(((*1 *2 *2) (-12 (-5 *2 (-700 (-325 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(-12 (-5 *2 (-115)) (-5 *3 (-1 *4 *4)) (-4 *4 (-1117)) + (-5 *1 (-114 *4)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-115)) (-5 *2 (-655 (-1 *4 (-655 *4)))) + (-5 *1 (-114 *4)) (-4 *4 (-1117))))) +(((*1 *1) (-5 *1 (-1197)))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-667 *2)) (-4 *2 (-1066)) (-4 *2 (-373)))) + ((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-1 *4 *4)) (-4 *4 (-373)) (-5 *1 (-670 *4 *2)) + (-4 *2 (-667 *4))))) (((*1 *2 *1) (-12 (-5 *2 (-655 (-2 (|:| -4169 (-1194)) (|:| -3179 *4)))) (-5 *1 (-901 *3 *4)) (-4 *3 (-1117)) (-4 *4 (-1117)))) ((*1 *2 *1) (-12 (-4 *3 (-1117)) (-4 *4 (-1117)) (-4 *5 (-1117)) (-4 *6 (-1117)) (-4 *7 (-1117)) (-5 *2 (-655 *1)) (-4 *1 (-1120 *3 *4 *5 *6 *7))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-2 (|:| -3926 (-793 *3)) (|:| |coef2| (-793 *3)))) - (-5 *1 (-793 *3)) (-4 *3 (-567)) (-4 *3 (-1066)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-567)) (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) - (-5 *2 (-2 (|:| -3926 *1) (|:| |coef2| *1))) - (-4 *1 (-1082 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1199))))) (((*1 *2 *3) (-12 (-5 *2 (-575)) (-5 *1 (-580 *3)) (-4 *3 (-1055 *2)))) ((*1 *2 *1) (-12 (-4 *1 (-1120 *3 *4 *2 *5 *6)) (-4 *3 (-1117)) (-4 *4 (-1117)) (-4 *5 (-1117)) (-4 *6 (-1117)) (-4 *2 (-1117))))) -(((*1 *1 *2) (-12 (-5 *2 (-655 (-339))) (-5 *1 (-339))))) +(((*1 *2 *1) (-12 (-5 *2 (-342)) (-5 *1 (-254))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -3480,36 +3493,34 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-993 *3 *4 *2 *5)) (-4 *3 (-1066)) (-4 *4 (-804)) - (-4 *5 (-1082 *3 *4 *2)) (-4 *2 (-861)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1082 *3 *4 *2)) (-4 *3 (-1066)) (-4 *4 (-804)) - (-4 *2 (-861))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-958 *4)) (-4 *4 (-1066)) (-5 *1 (-1182 *3 *4)) - (-14 *3 (-936))))) +(((*1 *2 *3 *3 *4 *4 *5 *4 *5 *4 *4 *5 *4) + (-12 (-5 *3 (-1176)) (-5 *4 (-575)) (-5 *5 (-700 (-171 (-227)))) + (-5 *2 (-1052)) (-5 *1 (-765))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-575)) (-4 *5 (-359)) (-5 *2 (-429 (-1190 (-1190 *5)))) + (-5 *1 (-1233 *5)) (-5 *3 (-1190 (-1190 *5)))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-133)) (-5 *3 (-782)) (-5 *2 (-1290))))) (((*1 *2 *3) - (-12 (-4 *4 (-1066)) - (-4 *2 (-13 (-415) (-1055 *4) (-373) (-1220) (-293))) - (-5 *1 (-454 *4 *3 *2)) (-4 *3 (-1261 *4))))) -(((*1 *2 *3 *3 *4 *5 *3 *6) - (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *5 (-227)) - (-5 *6 (-3 (|:| |fn| (-399)) (|:| |fp| (-81 FCN)))) (-5 *2 (-1052)) - (-5 *1 (-757))))) -(((*1 *2 *1) (-12 (-5 *2 (-1290)) (-5 *1 (-833))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1082 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-804)) - (-4 *4 (-861)) (-4 *2 (-463))))) -(((*1 *1) (-12 (-4 *1 (-338 *2)) (-4 *2 (-378)) (-4 *2 (-373))))) + (-12 (-4 *4 (-861)) (-5 *2 (-655 (-655 (-655 *4)))) + (-5 *1 (-1205 *4)) (-5 *3 (-655 (-655 *4)))))) +(((*1 *1 *2) + (-12 (-5 *2 (-655 *3)) (-4 *3 (-1235)) (-5 *1 (-1174 *3))))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-567) (-1055 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((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-987)))) @@ -3535,50 +3546,39 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *3 (-115)) (-4 *4 (-1066)) (-5 *1 (-725 *4 *2)) - (-4 *2 (-659 *4)))) - ((*1 *2 *3 *2) (-12 (-5 *3 (-115)) (-5 *1 (-847 *2)) (-4 *2 (-1066))))) -(((*1 *2 *3) - (-12 (-5 *3 (-575)) (-5 *2 (-655 (-655 (-227)))) (-5 *1 (-1231))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-4 *3 (-1082 *5 *6 *7)) (-5 *2 (-112)) - (-5 *1 (-1089 *5 *6 *7 *3 *4)) (-4 *4 (-1088 *5 *6 *7 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-4 *3 (-1082 *5 *6 *7)) - (-5 *2 (-655 (-2 (|:| |val| (-112)) (|:| -4270 *4)))) - (-5 *1 (-1089 *5 *6 *7 *3 *4)) (-4 *4 (-1088 *5 *6 *7 *3))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-782)) (|:| |poli| *2) - (|:| |polj| *2))) - (-4 *5 (-804)) (-4 *2 (-964 *4 *5 *6)) (-5 *1 (-460 *4 *5 *6 *2)) - (-4 *4 (-463)) (-4 *6 (-861))))) -(((*1 *1 *1) - (-12 (-4 *1 (-698 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-383 *2)) - (-4 *4 (-383 *2))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1261 (-418 *2))) (-5 *2 (-575)) (-5 *1 (-928 *4 *3)) - (-4 *3 (-1261 (-418 *4)))))) -(((*1 *2 *3 *2) (-12 (-5 *2 (-1052)) (-5 *3 (-1194)) (-5 *1 (-275))))) -(((*1 *1 *1 *1) (-4 *1 (-144))) +(((*1 *1 *1 *1) + (-12 (-5 *1 (-655 *2)) (-4 *2 (-1117)) (-4 *2 (-1235))))) +(((*1 *2 *1) (-12 (-5 *1 (-176 *2)) (-4 *2 (-316)))) + ((*1 *2 *1) (-12 (-5 *1 (-929 *2)) (-4 *2 (-316)))) + ((*1 *2 *1) (-12 (-4 *1 (-1009 *2)) (-4 *2 (-567)) (-4 *2 (-316)))) + ((*1 *2 *1) (-12 (-4 *1 (-1077)) (-5 *2 (-575))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *5 *5 *5 *3) + (-12 (-5 *3 (-575)) (-5 *5 (-700 (-227))) (-5 *4 (-227)) + (-5 *2 (-1052)) (-5 *1 (-761))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-793 *2)) (-4 *2 (-567)) (-4 *2 (-1066)))) ((*1 *2 *2 *2) - (-12 (-4 *3 (-567)) (-5 *1 (-159 *3 *2)) (-4 *2 (-441 *3)))) - ((*1 *2 *2 *2) (-12 (-5 *1 (-160 *2)) (-4 *2 (-556)))) - 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(-12 (-5 *3 (-1176)) (-5 *5 (-700 (-227))) (-5 *6 (-227)) + (-5 *7 (-700 (-575))) (-5 *4 (-575)) (-5 *2 (-1052)) (-5 *1 (-763))))) +(((*1 *2 *3) (-12 (-5 *3 (-325 (-227))) (-5 *2 (-112)) (-5 *1 (-275))))) +(((*1 *2 *3) + (-12 (-5 *3 (-967 *5)) (-4 *5 (-1066)) (-5 *2 (-492 *4 *5)) + (-5 *1 (-959 *4 *5)) (-14 *4 (-655 (-1194)))))) +(((*1 *2 *3 *2) + (-12 (-5 *2 (-1174 (-655 (-575)))) (-5 *3 (-655 (-575))) + (-5 *1 (-895))))) (((*1 *2 *1) (-12 (-4 *1 (-1120 *3 *2 *4 *5 *6)) (-4 *3 (-1117)) (-4 *4 (-1117)) (-4 *5 (-1117)) (-4 *6 (-1117)) (-4 *2 (-1117))))) @@ -3598,44 +3598,52 @@ (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3)))) ((*1 *1 *1) (-4 *1 (-1223)))) -(((*1 *1 *1) - (-12 (-5 *1 (-606 *2)) (-4 *2 (-38 (-418 (-575)))) (-4 *2 (-1066))))) -(((*1 *2) - (-12 (-5 *2 (-973 (-1137))) (-5 *1 (-353 *3 *4)) (-14 *3 (-936)) - (-14 *4 (-936)))) - ((*1 *2) - (-12 (-5 *2 (-973 (-1137))) (-5 *1 (-354 *3 *4)) (-4 *3 (-359)) - (-14 *4 (-1190 *3)))) - ((*1 *2) - (-12 (-5 *2 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(-5 *1 (-642 *4 *5)) (-5 *3 (-655 (-252 *4 *5)))))) (((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -3652,59 +3660,40 @@ (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3)))) ((*1 *1 *1) (-4 *1 (-1223)))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *5 (-227)) - (-5 *2 (-1052)) (-5 *1 (-763))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-655 *6)) (-4 *1 (-964 *4 *5 *6)) (-4 *4 (-1066)) - (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-782)))) - ((*1 *2 *1) - (-12 (-4 *1 (-964 *3 *4 *5)) (-4 *3 (-1066)) (-4 *4 (-804)) - (-4 *5 (-861)) (-5 *2 (-782))))) -(((*1 *2 *2) - (-12 (-5 *2 (-958 *3)) (-4 *3 (-13 (-373) (-1220) (-1019))) - (-5 *1 (-178 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1063 *4 *5)) (-4 *4 (-13 (-859) (-316) (-148) (-1039))) - (-14 *5 (-655 (-1194))) (-5 *2 (-655 (-655 (-1041 (-418 *4))))) - (-5 *1 (-1312 *4 *5 *6)) (-14 *6 (-655 (-1194))))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-655 (-967 *5))) (-5 *4 (-112)) - 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*2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -3721,50 +3710,33 @@ (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3)))) ((*1 *1 *1) (-4 *1 (-1223)))) -(((*1 *2 *1) - (-12 (-5 *2 (-655 (-655 (-958 (-227))))) (-5 *1 (-1230 *3)) - (-4 *3 (-991))))) -(((*1 *2 *3) (-12 (-5 *3 (-1194)) (-5 *2 (-1290)) (-5 *1 (-1197)))) - ((*1 *2 *1) (-12 (-5 *2 (-1290)) (-5 *1 (-1198))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-383 *2)) (-4 *2 (-1235)) (-4 *2 (-861)))) - ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-383 *3)) (-4 *3 (-1235)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-985 *2)) (-4 *2 (-861)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-1151 *2)) (-4 *2 (-1066)))) - ((*1 *1 *2) - (-12 (-5 *2 (-655 *1)) (-4 *1 (-1151 *3)) (-4 *3 (-1066)))) - ((*1 *1 *2) - (-12 (-5 *2 (-655 (-1182 *3 *4))) (-5 *1 (-1182 *3 *4)) - (-14 *3 (-936)) (-4 *4 (-1066)))) - ((*1 *1 *1 *1) - (-12 (-5 *1 (-1182 *2 *3)) (-14 *2 (-936)) (-4 *3 (-1066))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 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(-873))) (-5 *2 (-1290)) (-5 *1 (-1155))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-844 *3)) (-4 *3 (-1117)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-854 *3)) (-4 *3 (-1117))))) +(((*1 *2 *3 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-575)) + (-5 *5 (-3 (|:| |fn| (-399)) (|:| |fp| (-64 G)))) (-5 *2 (-1052)) + (-5 *1 (-759))))) (((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) @@ -3784,55 +3756,60 @@ (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3)))) ((*1 *1 *1) (-4 *1 (-1223)))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-655 (-2 (|:| -2418 (-418 (-575))) (|:| -2435 (-418 (-575)))))) - (-5 *2 (-655 (-418 (-575)))) (-5 *1 (-1037 *4)) - (-4 *4 (-1261 (-575)))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-655 (-1 (-112) *8))) (-4 *8 (-1082 *5 *6 *7)) - (-4 *5 (-567)) (-4 *6 (-804)) (-4 *7 (-861)) - (-5 *2 (-2 (|:| |goodPols| (-655 *8)) (|:| |badPols| (-655 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((*1 *1 *1 *2) (-12 (-5 *2 (-782)) (-4 *1 (-1273 *3)) (-4 *3 (-1235)))) ((*1 *2 *1) (-12 (-4 *1 (-1273 *2)) (-4 *2 (-1235))))) -(((*1 *2 *3) (-12 (-5 *3 (-1176)) (-5 *2 (-1290)) (-5 *1 (-593))))) -(((*1 *2 *2) - (-12 - (-5 *2 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) - (|:| |xpnt| (-575)))) - (-4 *4 (-13 (-1261 *3) (-567) (-10 -8 (-15 -3926 ($ $ $))))) - (-4 *3 (-567)) (-5 *1 (-1264 *3 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-565 *2)) (-4 *2 (-13 (-415) (-1220)))))) +(((*1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1174 *3)) (-4 *3 (-1117)) + (-4 *3 (-1235))))) (((*1 *2 *1) - (-12 (-4 *1 (-377 *3)) (-4 *3 (-174)) (-4 *3 (-567)) - (-5 *2 (-1190 *3))))) + (-12 (-4 *1 (-1151 *3)) (-4 *3 (-1066)) + (-5 *2 (-655 (-655 (-958 *3)))))) + ((*1 *1 *2 *3 *3) + (-12 (-5 *2 (-655 (-655 (-958 *4)))) (-5 *3 (-112)) (-4 *4 (-1066)) + (-4 *1 (-1151 *4)))) + ((*1 *1 *2) + (-12 (-5 *2 (-655 (-655 (-958 *3)))) (-4 *3 (-1066)) + (-4 *1 (-1151 *3)))) + ((*1 *1 *1 *2 *3 *3) + (-12 (-5 *2 (-655 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*7))))) +(((*1 *2 *2) (-12 (-5 *2 (-575)) (-5 *1 (-263))))) (((*1 *2 *3) - (-12 (-4 *4 (-1066)) (-5 *2 (-575)) (-5 *1 (-454 *4 *3 *5)) - (-4 *3 (-1261 *4)) - (-4 *5 (-13 (-415) (-1055 *4) (-373) (-1220) (-293)))))) + (|partial| -12 (-5 *3 (-700 (-418 (-967 (-575))))) + (-5 *2 (-700 (-325 (-575)))) (-5 *1 (-1048))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-700 *8)) (-5 *4 (-782)) (-4 *8 (-964 *5 *7 *6)) + (-4 *5 (-13 (-316) (-148))) (-4 *6 (-13 (-861) (-625 (-1194)))) + (-4 *7 (-804)) + (-5 *2 + (-655 + (-2 (|:| |det| *8) (|:| |rows| (-655 (-575))) + (|:| |cols| (-655 (-575)))))) + (-5 *1 (-939 *5 *6 *7 *8))))) (((*1 *1 *2 *1) (-12 (|has| *1 (-6 -4460)) (-4 *1 (-152 *2)) (-4 *2 (-1235)) (-4 *2 (-1117)))) @@ -4548,67 +4523,71 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1157 *3 *4)) (-4 *3 (-13 (-1117) (-34))) (-4 *4 (-13 (-1117) (-34))) (-5 *1 (-1158 *3 *4))))) -(((*1 *1 *2) (-12 (-5 *2 (-1137)) (-5 *1 (-832))))) -(((*1 *2 *3) (-12 (-5 *3 (-958 *2)) (-5 *1 (-999 *2)) (-4 *2 (-1066))))) -(((*1 *2 *2 *3) - 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(-13 (-316) (-148))) (-4 *6 (-13 (-861) (-625 (-1194)))) @@ -6064,7 +6220,7 @@ (|:| |wcond| (-655 (-967 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1285 (-418 (-967 *5)))) - (|:| -1624 (-655 (-1285 (-418 (-967 *5)))))))))) + (|:| -2098 (-655 (-1285 (-418 (-967 *5)))))))))) (-5 *1 (-939 *5 *6 *7 *8)) (-5 *4 (-655 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-700 *8)) (-5 *4 (-655 (-1194))) (-4 *8 (-964 *5 *7 *6)) @@ -6076,7 +6232,7 @@ (|:| |wcond| (-655 (-967 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1285 (-418 (-967 *5)))) - (|:| -1624 (-655 (-1285 (-418 (-967 *5)))))))))) + (|:| -2098 (-655 (-1285 (-418 (-967 *5)))))))))) (-5 *1 (-939 *5 *6 *7 *8)))) ((*1 *2 *3) (-12 (-5 *3 (-700 *7)) (-4 *7 (-964 *4 *6 *5)) @@ -6088,7 +6244,7 @@ (|:| |wcond| (-655 (-967 *4))) (|:| |bsoln| (-2 (|:| |partsol| (-1285 (-418 (-967 *4)))) - (|:| -1624 (-655 (-1285 (-418 (-967 *4)))))))))) + (|:| -2098 (-655 (-1285 (-418 (-967 *4)))))))))) (-5 *1 (-939 *4 *5 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-700 *9)) (-5 *5 (-936)) (-4 *9 (-964 *6 *8 *7)) @@ -6100,7 +6256,7 @@ (|:| |wcond| (-655 (-967 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1285 (-418 (-967 *6)))) - (|:| -1624 (-655 (-1285 (-418 (-967 *6)))))))))) + (|:| -2098 (-655 (-1285 (-418 (-967 *6)))))))))) (-5 *1 (-939 *6 *7 *8 *9)) (-5 *4 (-655 *9)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-700 *9)) (-5 *4 (-655 (-1194))) (-5 *5 (-936)) @@ -6112,7 +6268,7 @@ (|:| |wcond| (-655 (-967 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1285 (-418 (-967 *6)))) - (|:| -1624 (-655 (-1285 (-418 (-967 *6)))))))))) + (|:| -2098 (-655 (-1285 (-418 (-967 *6)))))))))) (-5 *1 (-939 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-700 *8)) (-5 *4 (-936)) (-4 *8 (-964 *5 *7 *6)) @@ -6124,7 +6280,7 @@ (|:| |wcond| (-655 (-967 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1285 (-418 (-967 *5)))) - (|:| -1624 (-655 (-1285 (-418 (-967 *5)))))))))) + (|:| -2098 (-655 (-1285 (-418 (-967 *5)))))))))) (-5 *1 (-939 *5 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-700 *9)) (-5 *4 (-655 *9)) (-5 *5 (-1176)) 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(-5 *2 (-2 (|:| |localSymbols| (-1198)) (|:| -2558 (-655 (-339))))) + (-5 *2 (-2 (|:| |localSymbols| (-1198)) (|:| -2553 (-655 (-339))))) (-5 *1 (-409 *3 *4 *5 *6)) (-14 *3 (-1194)) - (-14 *4 (-3 (|:| |fst| (-445)) (|:| -2007 "void"))) + (-14 *4 (-3 (|:| |fst| (-445)) (|:| -2001 "void"))) (-14 *5 (-655 (-1194))) (-14 *6 (-1198)))) ((*1 *1 *2) (-12 (-5 *2 (-655 (-339))) (-5 *1 (-409 *3 *4 *5 *6)) - (-14 *3 (-1194)) (-14 *4 (-3 (|:| |fst| (-445)) (|:| -2007 "void"))) + (-14 *3 (-1194)) (-14 *4 (-3 (|:| |fst| (-445)) (|:| -2001 "void"))) (-14 *5 (-655 (-1194))) (-14 *6 (-1198)))) ((*1 *1 *2) (-12 (-5 *2 (-339)) (-5 *1 (-409 *3 *4 *5 *6)) (-14 *3 (-1194)) - (-14 *4 (-3 (|:| |fst| (-445)) (|:| -2007 "void"))) + (-14 *4 (-3 (|:| |fst| (-445)) (|:| -2001 "void"))) (-14 *5 (-655 (-1194))) (-14 *6 (-1198)))) ((*1 *1 *2) (-12 (-5 *2 (-340 *4)) (-4 *4 (-13 (-861) (-21))) @@ -8269,14 +8673,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-445)) (-5 *1 (-448)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1198)) (|:| -2558 (-655 (-339))))) + (-5 *2 (-2 (|:| |localSymbols| (-1198)) (|:| -2553 (-655 (-339))))) (-4 *1 (-451)))) ((*1 *1 *2) (-12 (-5 *2 (-339)) (-4 *1 (-451)))) ((*1 *1 *2) (-12 (-5 *2 (-655 (-339))) (-4 *1 (-451)))) ((*1 *1 *2) (-12 (-5 *2 (-1285 (-710))) (-4 *1 (-451)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1198)) (|:| -2558 (-655 (-339))))) + (-5 *2 (-2 (|:| |localSymbols| (-1198)) (|:| -2553 (-655 (-339))))) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-339)) (-4 *1 (-452)))) ((*1 *1 *2) (-12 (-5 *2 (-655 (-339))) (-4 *1 (-452)))) @@ -8345,7 +8749,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-655 (-2 (|:| -1754 *3) (|:| -3693 *4)))) + (-12 (-5 *2 (-655 (-2 (|:| -1754 *3) (|:| -3692 *4)))) (-4 *3 (-1066)) (-4 *4 (-737)) (-5 *1 (-746 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-575)) (-4 *1 (-774)))) ((*1 *1 *2) @@ -8354,25 +8758,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) - (|:| -3437 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) + (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (|:| |mdnia| (-2 (|:| |fn| (-325 (-227))) - (|:| -3437 (-655 (-1111 (-854 (-227))))) + (|:| -1974 (-655 (-1111 (-854 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))))) (-5 *1 (-780)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-325 (-227))) - (|:| -3437 (-655 (-1111 (-854 (-227))))) (|:| |abserr| (-227)) + (|:| -1974 (-655 (-1111 (-854 (-227))))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-780)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) - (|:| -3437 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) + (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227)))) (-5 *1 (-780)))) ((*1 *2 *3) (-12 (-5 *2 (-785)) (-5 *1 (-784 *3)) (-4 *3 (-1235)))) @@ -8390,23 +8794,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-325 (-227))) (|:| -3474 (-655 (-227))) + (-2 (|:| |fn| (-325 (-227))) (|:| -3472 (-655 (-227))) (|:| |lb| (-655 (-854 (-227)))) (|:| |cf| (-655 (-325 (-227)))) (|:| |ub| (-655 (-854 (-227)))))) (|:| |lsa| (-2 (|:| |lfn| (-655 (-325 (-227)))) - (|:| -3474 (-655 (-227))))))) + (|:| -3472 (-655 (-227))))))) (-5 *1 (-852)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-655 (-325 (-227)))) (|:| -3474 (-655 (-227))))) + (-2 (|:| |lfn| (-655 (-325 (-227)))) (|:| -3472 (-655 (-227))))) (-5 *1 (-852)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-325 (-227))) (|:| -3474 (-655 (-227))) + (-2 (|:| |fn| (-325 (-227))) (|:| -3472 (-655 (-227))) (|:| |lb| (-655 (-854 (-227)))) (|:| |cf| (-655 (-325 (-227)))) (|:| |ub| (-655 (-854 (-227)))))) (-5 *1 (-852)))) @@ -8507,53 +8911,48 @@ ((*1 *1 *2) (-12 (-5 *2 (-675 *3 *4)) (-4 *3 (-861)) (-4 *4 (-174)) (-5 *1 (-1305 *3 *4))))) -(((*1 *2 *1) - (-12 (-4 *4 (-1117)) (-5 *2 (-901 *3 *4)) (-5 *1 (-897 *3 *4 *5)) - (-4 *3 (-1117)) (-4 *5 (-677 *4)))) - ((*1 *2 *3) - (-12 (-5 *3 (-981 *4)) (-4 *4 (-1117)) (-5 *2 (-1119 *4)) 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(-1235)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-1194)) (-5 *3 (-1176)) (-5 *1 (-1006)))) ((*1 *1 *2 *3) @@ -9553,101 +9812,30 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-1194)) (-5 *3 (-1111 *4)) (-4 *4 (-1235)) (-5 *1 (-1109 *4))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-4 *8 (-1082 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-655 *8)) - (|:| |towers| (-655 (-1044 *5 *6 *7 *8))))) - (-5 *1 (-1044 *5 *6 *7 *8)) (-5 *3 (-655 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-112)) (-4 *5 (-463)) (-4 *6 (-804)) (-4 *7 (-861)) - (-4 *8 (-1082 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-655 *8)) - (|:| |towers| (-655 (-1163 *5 *6 *7 *8))))) - (-5 *1 (-1163 *5 *6 *7 *8)) (-5 *3 (-655 *8))))) -(((*1 *2 *3) - (-12 (-5 *3 (-700 (-418 (-967 (-575))))) (-5 *2 (-655 (-325 (-575)))) - (-5 *1 (-1048))))) -(((*1 *2 *1) - (-12 (-4 *1 (-259 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-861)) - (-4 *5 (-274 *4)) (-4 *6 (-804)) (-5 *2 (-782)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-259 *4 *3 *5 *6)) 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+ (-2 (|:| -4181 *4) (|:| -3082 *4) (|:| |totalpts| (-575)) + (|:| |success| (-112)))) + (-5 *1 (-800)) (-5 *5 (-575))))) +(((*1 *1 *1) + (-12 (-5 *1 (-606 *2)) (-4 *2 (-38 (-418 (-575)))) (-4 *2 (-1066))))) (((*1 *1 *2) (-12 (-5 *2 (-655 (-575))) (-5 *1 (-50 *3 *4)) (-4 *3 (-1066)) (-14 *4 (-655 (-1194))))) @@ -9680,201 +9868,230 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-782)) (-5 *1 (-1305 *3 *4)) (-4 *4 (-728 (-418 (-575)))) (-4 *3 (-861)) (-4 *4 (-174))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-655 + (-2 + (|:| -4169 + (-2 (|:| |var| (-1194)) (|:| |fn| (-325 (-227))) + (|:| -1974 (-1111 (-854 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -3179 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1174 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -1974 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-570))))) +(((*1 *2 *1) (-12 (-4 *1 (-538)) (-5 *2 (-702 (-130)))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1 *6 *5 *4)) (-4 *5 (-1117)) (-4 *4 (-1117)) + (-4 *6 (-1117)) (-5 *2 (-1 *6 *5)) (-5 *1 (-695 *5 *4 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-655 (-325 (-227)))) (-5 *2 (-112)) (-5 *1 (-275)))) - ((*1 *2 *3) (-12 (-5 *3 (-325 (-227))) (-5 *2 (-112)) (-5 *1 (-275)))) - ((*1 *2 *3) - (-12 (-4 *4 (-567)) (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-112)) - (-5 *1 (-994 *4 *5 *6 *3)) (-4 *3 (-1082 *4 *5 *6))))) -(((*1 *2 *3) - (-12 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(-4 *3 (-167 *5)))) @@ -9992,9 +10216,9 @@ (-12 (-5 *2 (-967 *3)) (-4 *3 (-1066)) (-4 *1 (-1082 *3 *4 *5)) (-4 *5 (-625 (-1194))) (-4 *4 (-804)) (-4 *5 (-861)))) ((*1 *1 *2) - (-3765 + (-3763 (-12 (-5 *2 (-967 (-575))) (-4 *1 (-1082 *3 *4 *5)) - (-12 (-3215 (-4 *3 (-38 (-418 (-575))))) (-4 *3 (-38 (-575))) + (-12 (-3213 (-4 *3 (-38 (-418 (-575))))) (-4 *3 (-38 (-575))) (-4 *5 (-625 (-1194)))) (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861))) (-12 (-5 *2 (-967 (-575))) (-4 *1 (-1082 *3 *4 *5)) @@ -10042,36 +10266,35 @@ (-4 *4 (-13 (-859) (-316) (-148) (-1039))) (-14 *6 (-655 (-1194))) (-5 *2 (-655 (-791 *4 (-875 *6)))) (-5 *1 (-1312 *4 *5 *6)) (-14 *5 (-655 (-1194)))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-112)) (-5 *3 (-655 (-269))) (-5 *1 (-267)))) - ((*1 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-269))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-655 (-700 *5))) (-4 *5 (-316)) (-4 *5 (-1066)) - (-5 *2 (-1285 (-1285 *5))) (-5 *1 (-1046 *5)) (-5 *4 (-1285 *5))))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 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*2 *3) - (|partial| -12 (-4 *4 (-1239)) (-4 *5 (-1261 *4)) - (-5 *2 (-2 (|:| |radicand| (-418 *5)) (|:| |deg| (-782)))) - (-5 *1 (-149 *4 *5 *3)) (-4 *3 (-1261 (-418 *5)))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-655 (-875 *5))) (-14 *5 (-655 (-1194))) (-4 *6 (-463)) - (-5 *2 - (-2 (|:| |dpolys| (-655 (-252 *5 *6))) - (|:| |coords| (-655 (-575))))) - (-5 *1 (-482 *5 *6 *7)) (-5 *3 (-655 (-252 *5 *6))) (-4 *7 (-463))))) + (-12 (-5 *3 (-1176)) (-5 *2 (-216 (-513))) (-5 *1 (-848))))) +(((*1 *1 *1) + (-12 (-5 *1 (-1182 *2 *3)) (-14 *2 (-936)) (-4 *3 (-1066))))) +(((*1 *2) + (-12 (-4 *1 (-352 *3 *4 *5)) (-4 *3 (-1239)) (-4 *4 (-1261 *3)) + (-4 *5 (-1261 (-418 *4))) (-5 *2 (-700 (-418 *4)))))) (((*1 *2 *3) - (-12 (-4 *4 (-316)) (-4 *5 (-383 *4)) (-4 *6 (-383 *4)) - (-5 *2 (-2 (|:| |Hermite| *3) (|:| |eqMat| *3))) - (-5 *1 (-1141 *4 *5 *6 *3)) (-4 *3 (-698 *4 *5 *6))))) -(((*1 *2 *3 *3 *4 *5) - (-12 (-5 *3 (-1176)) (-4 *6 (-463)) (-4 *7 (-804)) (-4 *8 (-861)) - (-4 *4 (-1082 *6 *7 *8)) (-5 *2 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*4))))) (((*1 *1 *2) (-12 (-5 *2 (-399)) (-5 *1 (-643))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-655 *2)) (-4 *2 (-964 *4 *5 *6)) (-4 *4 (-316)) + (-4 *5 (-804)) (-4 *6 (-861)) (-5 *1 (-458 *4 *5 *6 *2))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) +(((*1 *2 *3 *4 *4 *4 *3 *5 *3 *4 *6 *7) + (-12 (-5 *4 (-575)) (-5 *5 (-700 (-227))) + (-5 *6 (-3 (|:| |fn| (-399)) (|:| |fp| (-86 FCN)))) + (-5 *7 (-3 (|:| |fn| (-399)) (|:| |fp| (-88 OUTPUT)))) + (-5 *3 (-227)) (-5 *2 (-1052)) (-5 *1 (-760))))) (((*1 *2 *1) (-12 (-5 *2 @@ -10329,7 +10480,7 @@ (-2 (|:| |var| (-1194)) (|:| |arrayIndex| (-655 (-967 (-575)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-112)) (|:| -1400 (-873)))))) + (-2 (|:| |ints2Floats?| (-112)) (|:| -1401 (-873)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1194)) (|:| |rand| (-873)) (|:| |ints2Floats?| (-112)))) @@ -10337,13 +10488,13 @@ (-2 (|:| |switch| (-1193)) (|:| |thenClause| (-339)) (|:| |elseClause| (-339)))) (|:| |returnBranch| - (-2 (|:| -4076 (-112)) - (|:| -4182 - (-2 (|:| |ints2Floats?| (-112)) (|:| -1400 (-873)))))) + (-2 (|:| -2017 (-112)) + (|:| -4181 + (-2 (|:| |ints2Floats?| (-112)) (|:| -1401 (-873)))))) (|:| |blockBranch| (-655 (-339))) (|:| |commentBranch| (-655 (-1176))) (|:| |callBranch| (-1176)) (|:| |forBranch| - (-2 (|:| -3437 (-1109 (-967 (-575)))) + (-2 (|:| -1974 (-1109 (-967 (-575)))) (|:| |span| (-967 (-575))) (|:| -1788 (-339)))) (|:| |labelBranch| (-1137)) (|:| |loopBranch| (-2 (|:| |switch| (-1193)) (|:| -1788 (-339)))) @@ -10351,57 +10502,26 @@ (-2 (|:| -1777 (-1194)) (|:| |contents| (-655 (-1194))))) (|:| |printBranch| (-655 (-873))))) (-5 *1 (-339))))) +(((*1 *1 *2) (-12 (-5 *2 (-655 *3)) (-4 *3 (-1117)) (-5 *1 (-224 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-655 *3)) (-4 *3 (-1235)) (-4 *1 (-260 *3)))) + ((*1 *1) (-12 (-4 *1 (-260 *2)) (-4 *2 (-1235))))) (((*1 *2 *1) (-12 (-5 *2 (-655 (-623 *1))) (-4 *1 (-311))))) (((*1 *1 *2) (-12 (-5 *2 (-655 (-873))) (-5 *1 (-873)))) ((*1 *1 *1) (-5 *1 (-873))) 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(-2 (|:| |eqzro| (-655 *7)) (|:| |neqzro| (-655 *7)) + (|:| |wcond| (-655 (-967 *4))) + (|:| |bsoln| + (-2 (|:| |partsol| (-1285 (-418 (-967 *4)))) + (|:| -2098 (-655 (-1285 (-418 (-967 *4)))))))))) + (-5 *1 (-939 *4 *5 *6 *7)) (-4 *7 (-964 *4 *6 *5))))) (((*1 *2 *3 *4) (-12 (-5 *3 (-655 *8)) (-5 *4 (-137 *5 *6 *7)) (-14 *5 (-575)) (-14 *6 (-782)) (-4 *7 (-174)) (-4 *8 (-174)) @@ -10935,45 +11007,47 @@ (-4 *8 (-1066)) (-4 *2 (-964 *9 *7 *5)) (-5 *1 (-739 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-804)) (-4 *4 (-964 *8 *6 *5))))) -(((*1 *2 *3 *1) (-12 (-5 *3 (-1194)) (-5 *2 (-448)) (-5 *1 (-1198))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-936)) (-5 *4 (-1176)) (-5 *2 (-1290)) (-5 *1 (-1286))))) +(((*1 *2 *2 *3 *4) + (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-861)) (-4 *5 (-804)) + (-4 *6 (-567)) (-4 *7 (-964 *6 *5 *3)) + (-5 *1 (-473 *5 *3 *6 *7 *2)) + (-4 *2 + (-13 (-1055 (-418 (-575))) (-373) + (-10 -8 (-15 -2882 ($ *7)) (-15 -1595 (*7 $)) + (-15 -1608 (*7 $)))))))) +(((*1 *2 *3) + (-12 (-4 *4 (-316)) (-4 *5 (-383 *4)) (-4 *6 (-383 *4)) + (-5 *2 (-2 (|:| |Hermite| *3) (|:| |eqMat| *3))) + (-5 *1 (-1141 *4 *5 *6 *3)) (-4 *3 (-698 *4 *5 *6))))) +(((*1 *2) + (-12 (-4 *3 (-567)) (-5 *2 (-655 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-428 *3))))) +(((*1 *1 *2) (-12 (-5 *2 (-1176)) (-5 *1 (-540)))) + ((*1 *1 *2) (-12 (-5 *2 (-399)) (-5 *1 (-540))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-575)) (-4 *1 (-1245 *4)) (-4 *4 (-1066)) (-4 *4 (-567)) + (-5 *2 (-418 (-967 *4))))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-575)) (-4 *1 (-1245 *4)) (-4 *4 (-1066)) (-4 *4 (-567)) + (-5 *2 (-418 (-967 *4)))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-575)) (-5 *1 (-1127))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1235)) (-5 *1 (-1149 *4 *2)) + (-4 *2 (-13 (-615 (-575) *4) (-10 -7 (-6 -4460) (-6 -4461)))))) + ((*1 *2 *2) + (-12 (-4 *3 (-861)) (-4 *3 (-1235)) (-5 *1 (-1149 *3 *2)) + (-4 *2 (-13 (-615 (-575) *3) (-10 -7 (-6 -4460) (-6 -4461))))))) (((*1 *2 *1 *1) (-12 (-5 *2 - (-2 (|:| -3926 (-793 *3)) (|:| |coef1| (-793 *3)) - (|:| |coef2| (-793 *3)))) - (-5 *1 (-793 *3)) (-4 *3 (-567)) (-4 *3 (-1066)))) + (-2 (|:| |polnum| (-793 *3)) (|:| |polden| *3) (|:| -2515 (-782)))) + (-5 *1 (-793 *3)) (-4 *3 (-1066)))) ((*1 *2 *1 *1) - (-12 (-4 *3 (-567)) (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) - (-5 *2 (-2 (|:| -3926 *1) (|:| |coef1| *1) (|:| |coef2| *1))) + (-12 (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) + (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -2515 (-782)))) (-4 *1 (-1082 *3 *4 *5))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-700 *3)) (-4 *3 (-1066)) (-5 *1 (-701 *3))))) -(((*1 *2 *3) - (-12 (-5 *3 (-325 (-389))) (-5 *2 (-325 (-227))) (-5 *1 (-314))))) -(((*1 *2 *1) - (-12 (-4 *1 (-335 *3 *4)) (-4 *3 (-1066)) (-4 *4 (-803)) - (-5 *2 (-655 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-392 *3 *4)) (-4 *3 (-1066)) (-4 *4 (-1117)) - (-5 *2 (-655 *3)))) - ((*1 *2 *1) - (-12 (-5 *2 (-1174 *3)) (-5 *1 (-607 *3)) (-4 *3 (-1066)))) - ((*1 *2 *1) - (-12 (-5 *2 (-655 *3)) (-5 *1 (-746 *3 *4)) (-4 *3 (-1066)) - (-4 *4 (-737)))) - ((*1 *2 *1) (-12 (-4 *1 (-863 *3)) (-4 *3 (-1066)) (-5 *2 (-655 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1276 *3)) (-4 *3 (-1066)) (-5 *2 (-1174 *3))))) -(((*1 *1 *1 *2) - (|partial| -12 (-4 *1 (-1228 *3 *4 *5 *2)) (-4 *3 (-567)) - (-4 *4 (-804)) (-4 *5 (-861)) (-4 *2 (-1082 *3 *4 *5))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-655 (-873))) (-5 *1 (-873))))) -(((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-782)) (-4 *4 (-13 (-1066) (-728 (-418 (-575))))) - (-4 *5 (-861)) (-5 *1 (-1301 *4 *5 *2)) (-4 *2 (-1306 *5 *4))))) -(((*1 *2 *3 *4 *3) - (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *2 (-1052)) - (-5 *1 (-758))))) (((*1 *2 *3 *2) (-12 (-5 *2 (-655 (-389))) (-5 *3 (-655 (-269))) (-5 *1 (-267)))) ((*1 *2 *1 *2) (-12 (-5 *2 (-655 (-389))) (-5 *1 (-479)))) @@ -10982,23 +11056,29 @@ (-12 (-5 *3 (-936)) (-5 *4 (-885)) (-5 *2 (-1290)) (-5 *1 (-1286)))) ((*1 *2 *1 *3 *4) (-12 (-5 *3 (-936)) (-5 *4 (-1176)) (-5 *2 (-1290)) (-5 *1 (-1286))))) -(((*1 *2) - (-12 (-4 *3 (-567)) (-5 *2 (-655 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-428 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1261 (-418 (-575)))) (-5 *1 (-928 *3 *2)) - (-4 *2 (-1261 (-418 *3)))))) -(((*1 *1 *1 *1) (-12 (-5 *1 (-606 *2)) (-4 *2 (-1066))))) -(((*1 *2 *1) - (-12 (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) (-5 *2 (-655 *1)) - (-4 *1 (-1082 *3 *4 *5))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-655 (-873))) (-5 *1 (-873))))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-623 *2)) (-4 *2 (-13 (-27) (-1220) (-441 *4))) - (-4 *4 (-13 (-567) (-1055 (-575)) (-650 (-575)))) - (-5 *1 (-285 *4 *2))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-920 *4)) (-4 *4 (-1117)) (-5 *2 (-655 (-782))) - (-5 *1 (-919 *4))))) + (-12 (-5 *3 (-655 (-655 (-655 *4)))) (-5 *2 (-655 (-655 *4))) + (-4 *4 (-861)) (-5 *1 (-1205 *4))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-832)) (-5 *4 (-52)) (-5 *2 (-1290)) (-5 *1 (-842))))) +(((*1 *2 *3) + (-12 (-4 *4 (-373)) (-4 *4 (-567)) (-4 *5 (-1261 *4)) + (-5 *2 (-2 (|:| -3320 (-634 *4 *5)) (|:| -2792 (-418 *5)))) + (-5 *1 (-634 *4 *5)) (-5 *3 (-418 *5)))) + ((*1 *2 *1) + (-12 (-5 *2 (-655 (-1182 *3 *4))) (-5 *1 (-1182 *3 *4)) + (-14 *3 (-936)) (-4 *4 (-1066)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-463)) (-4 *3 (-1066)) + (-5 *2 (-2 (|:| |primePart| *1) (|:| |commonPart| *1))) + (-4 *1 (-1261 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-700 (-418 (-967 *4)))) (-4 *4 (-463)) + (-5 *2 (-655 (-3 (-418 (-967 *4)) (-1183 (-1194) (-967 *4))))) + (-5 *1 (-301 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-885)) (-5 *1 (-269)))) + ((*1 *1 *2) (-12 (-5 *2 (-389)) (-5 *1 (-269))))) (((*1 *2 *1) (-12 (-5 *2 (-655 *5)) (-5 *1 (-137 *3 *4 *5)) (-14 *3 (-575)) (-14 *4 (-782)) (-4 *5 (-174))))) @@ -11016,9 +11096,7 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-463) (-1055 (-575)) (-650 (-575)))) (-5 *1 (-1224 *3 *2)) (-4 *2 (-13 (-27) (-1220) (-441 *3)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-463)) (-5 *1 (-1226 *3 *2)) - (-4 *2 (-13 (-441 *3) (-1220)))))) +(((*1 *2 *1) (-12 (-4 *1 (-1110 *2)) (-4 *2 (-1235))))) (((*1 *2 *1 *3 *3) (-12 (-5 *3 (-782)) (-4 *1 (-751 *4 *5)) (-4 *4 (-1066)) (-4 *5 (-861)) (-5 *2 (-967 *4)))) @@ -11039,38 +11117,46 @@ (-12 (-5 *2 (-1290)) (-5 *1 (-216 *3)) (-4 *3 (-13 (-861) - (-10 -8 (-15 -2070 ((-1176) $ (-1194))) (-15 -2484 (*2 $)) - (-15 -2514 (*2 $))))))) + (-10 -8 (-15 -2065 ((-1176) $ (-1194))) (-15 -2478 (*2 $)) + (-15 -3411 (*2 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1290)) (-5 *1 (-405)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-575)) (-5 *2 (-1290)) (-5 *1 (-405)))) ((*1 *2 *1) (-12 (-5 *2 (-1290)) (-5 *1 (-513)))) ((*1 *2 *3) (-12 (-5 *3 (-1176)) (-5 *2 (-1290)) (-5 *1 (-721)))) ((*1 *2 *1) (-12 (-5 *2 (-1290)) (-5 *1 (-1215)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-575)) (-5 *2 (-1290)) (-5 *1 (-1215))))) -(((*1 *2 *2) (-12 (-5 *2 (-1176)) (-5 *1 (-873))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-13 (-316) (-148))) (-4 *5 (-13 (-861) (-625 (-1194)))) + (-4 *6 (-804)) (-4 *7 (-964 *4 *6 *5)) + (-5 *2 + (-2 (|:| |sysok| (-112)) (|:| |z0| (-655 *7)) (|:| |n0| (-655 *7)))) + (-5 *1 (-939 *4 *5 *6 *7)) (-5 *3 (-655 *7))))) (((*1 *2 *1) (-12 (-4 *1 (-1027 *3)) (-4 *3 (-1235)) (-5 *2 (-655 *3))))) -(((*1 *2 *2 *3 *4 *4) - (-12 (-5 *4 (-575)) (-4 *3 (-174)) (-4 *5 (-383 *3)) - (-4 *6 (-383 *3)) (-5 *1 (-699 *3 *5 *6 *2)) - (-4 *2 (-698 *3 *5 *6))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1285 *5)) (-4 *5 (-13 (-1066) (-650 *4))) - (-4 *4 (-567)) (-5 *2 (-112)) (-5 *1 (-649 *4 *5))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-782)) (-5 *1 (-59 *3)) (-4 *3 (-1235)))) - ((*1 *1 *2) (-12 (-5 *2 (-655 *3)) (-4 *3 (-1235)) (-5 *1 (-59 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) -(((*1 *1) (-5 *1 (-158)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-418 (-967 *5))) (-5 *4 (-1194)) - (-4 *5 (-13 (-316) (-148))) (-5 *2 (-655 (-325 *5))) - (-5 *1 (-1146 *5)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-655 (-418 (-967 *5)))) (-5 *4 (-655 (-1194))) - (-4 *5 (-13 (-316) (-148))) (-5 *2 (-655 (-655 (-325 *5)))) - (-5 *1 (-1146 *5))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-942))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1176)) (-5 *2 (-321)) (-5 *1 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(-12 (-5 *2 (-1152)) (-5 *1 (-528))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1230 *3)) (-4 *3 (-991))))) +(((*1 *2) (-12 (-5 *2 (-131)) (-5 *1 (-1204))))) +(((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-479)) (-5 *4 (-936)) (-5 *2 (-1290)) (-5 *1 (-1286))))) (((*1 *2 *2 *3) (-12 (-5 *2 (-904 *4)) (-5 *3 (-1 (-112) *5)) (-4 *4 (-1117)) (-4 *5 (-1235)) (-5 *1 (-902 *4 *5)))) @@ -15480,83 +15692,36 @@ (-4 *6 (-13 (-441 *5) (-898 *4) (-625 (-904 *4)))) (-4 *4 (-1117)) (-4 *5 (-13 (-1066) (-898 *4) (-625 (-904 *4)))) (-5 *1 (-1093 *4 *5 *6))))) -(((*1 *1 *1 *1) - (|partial| -12 (-4 *2 (-174)) (-5 *1 (-298 *2 *3 *4 *5 *6 *7)) - (-4 *3 (-1261 *2)) (-4 *4 (-23)) (-14 *5 (-1 *3 *3 *4)) - (-14 *6 (-1 (-3 *4 "failed") *4 *4)) - (-14 *7 (-1 (-3 *3 "failed") *3 *3 *4)))) - ((*1 *1 *1 *1) - (|partial| -12 (-5 *1 (-722 *2 *3 *4 *5 *6)) (-4 *2 (-174)) - (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) - (-14 *5 (-1 (-3 *3 "failed") *3 *3)) - (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) - ((*1 *1 *1 *1) - (|partial| -12 (-5 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(-936)) - (-14 *6 (-655 (-1194))) (-14 *7 (-1285 (-700 *4))))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1194)) (-5 *3 (-1285 (-464 *4 *5 *6 *7))) - (-5 *1 (-464 *4 *5 *6 *7)) (-4 *4 (-174)) (-14 *5 (-936)) - (-14 *6 (-655 *2)) (-14 *7 (-1285 (-700 *4))))) - ((*1 *1 *2) - (-12 (-5 *2 (-1285 (-464 *3 *4 *5 *6))) (-5 *1 (-464 *3 *4 *5 *6)) - (-4 *3 (-174)) (-14 *4 (-936)) (-14 *5 (-655 (-1194))) - (-14 *6 (-1285 (-700 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-1285 (-1194))) (-5 *1 (-464 *3 *4 *5 *6)) - (-4 *3 (-174)) (-14 *4 (-936)) (-14 *5 (-655 (-1194))) - (-14 *6 (-1285 (-700 *3))))) - ((*1 *1 *2) - (-12 (-5 *2 (-1194)) (-5 *1 (-464 *3 *4 *5 *6)) (-4 *3 (-174)) - (-14 *4 (-936)) (-14 *5 (-655 *2)) (-14 *6 (-1285 (-700 *3))))) - ((*1 *1) - (-12 (-5 *1 (-464 *2 *3 *4 *5)) (-4 *2 (-174)) (-14 *3 (-936)) - (-14 *4 (-655 (-1194))) (-14 *5 (-1285 (-700 *2)))))) -(((*1 *2 *3 *4 *4 *3 *4 *5 *4 *4 *3 *3 *3 *3 *6 *3 *7) - (-12 (-5 *3 (-575)) (-5 *5 (-112)) (-5 *6 (-700 (-227))) - (-5 *7 (-3 (|:| |fn| (-399)) (|:| |fp| (-77 OBJFUN)))) - (-5 *4 (-227)) (-5 *2 (-1052)) (-5 *1 (-764))))) -(((*1 *2 *3) - (|partial| -12 (-5 *3 (-936)) - (-5 *2 (-1285 (-655 (-2 (|:| -4182 *4) (|:| -4317 (-1137)))))) - (-5 *1 (-356 *4)) (-4 *4 (-359))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-967 (-418 (-575)))) (-5 *4 (-1194)) - (-5 *5 (-1111 (-854 (-227)))) (-5 *2 (-655 (-227))) (-5 *1 (-309))))) -(((*1 *1 *1) - (-12 (-4 *1 (-259 *2 *3 *4 *5)) (-4 *2 (-1066)) (-4 *3 (-861)) - (-4 *4 (-274 *3)) (-4 *5 (-804))))) -(((*1 *2) - (-12 (-4 *1 (-352 *3 *4 *5)) (-4 *3 (-1239)) (-4 *4 (-1261 *3)) - (-4 *5 (-1261 (-418 *4))) (-5 *2 (-112))))) -(((*1 *1) (-5 *1 (-142)))) +(((*1 *2 *1) (-12 (-4 *1 (-970)) (-5 *2 (-655 (-655 (-958 (-227))))))) + ((*1 *2 *1) (-12 (-4 *1 (-991)) (-5 *2 (-655 (-655 (-958 (-227)))))))) +(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) + (-12 (-5 *3 (-227)) (-5 *4 (-575)) + (-5 *5 (-3 (|:| |fn| (-399)) (|:| |fp| (-64 G)))) (-5 *2 (-1052)) + (-5 *1 (-759))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-227)) (-5 *1 (-228)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-171 (-227))) (-5 *1 (-228)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-567)) (-5 *1 (-442 *3 *2)) (-4 *2 (-441 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1156)))) +(((*1 *2) (-12 (-5 *2 (-1176)) (-5 *1 (-402))))) (((*1 *2 *1) (-12 (-5 *2 (-1142 (-575) (-623 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-1009 *2)) (-4 *4 (-1261 *3)) (-4 *2 (-316)) @@ -15934,16 +16150,13 @@ (-12 (-4 *4 (-174)) (-4 *2 (|SubsetCategory| (-737) *4)) (-5 *1 (-673 *3 *4 *2)) (-4 *3 (-728 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-1009 *2)) (-4 *2 (-567))))) -(((*1 *2 *3) - (-12 (-4 *1 (-352 *4 *3 *5)) (-4 *4 (-1239)) (-4 *3 (-1261 *4)) - (-4 *5 (-1261 (-418 *3))) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-4 *1 (-352 *3 *4 *5)) (-4 *3 (-1239)) (-4 *4 (-1261 *3)) - (-4 *5 (-1261 (-418 *4))) (-5 *2 (-112))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-418 (-575))) (-5 *1 (-606 *3)) (-4 *3 (-38 *2)) + (-4 *3 (-1066))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-655 (-325 (-227)))) (|:| -3474 (-655 (-227))))) + (-2 (|:| |lfn| (-655 (-325 (-227)))) (|:| -3472 (-655 (-227))))) (-5 *2 (-655 (-1194))) (-5 *1 (-275)))) ((*1 *2 *3) (-12 (-5 *3 (-1190 *7)) (-4 *7 (-964 *6 *4 *5)) (-4 *4 (-804)) @@ -15965,7 +16178,7 @@ (-5 *1 (-965 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-373) - (-10 -8 (-15 -2883 ($ *7)) (-15 -1595 (*7 $)) (-15 -1608 (*7 $))))))) + (-10 -8 (-15 -2882 ($ *7)) (-15 -1595 (*7 $)) (-15 -1608 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-990 *3 *4 *5)) (-4 *3 (-1066)) (-4 *4 (-803)) (-4 *5 (-861)) (-5 *2 (-655 *5)))) @@ -15975,31 +16188,52 @@ ((*1 *2 *3) (-12 (-5 *3 (-418 (-967 *4))) (-4 *4 (-567)) (-5 *2 (-655 (-1194))) (-5 *1 (-1060 *4))))) -(((*1 *1 *1) (-4 *1 (-1161)))) -(((*1 *1 *1 *1) (-5 *1 (-873)))) -(((*1 *2 *3) - (-12 (-5 *2 (-1174 (-575))) (-5 *1 (-1178 *4)) (-4 *4 (-1066)) - (-5 *3 (-575))))) +(((*1 *2) + (-12 (-14 *4 (-782)) (-4 *5 (-1235)) (-5 *2 (-135)) + (-5 *1 (-242 *3 *4 *5)) (-4 *3 (-243 *4 *5)))) + ((*1 *2) + (-12 (-4 *4 (-373)) (-5 *2 (-135)) (-5 *1 (-337 *3 *4)) + (-4 *3 (-338 *4)))) + ((*1 *2) + (-12 (-5 *2 (-782)) (-5 *1 (-401 *3 *4 *5)) (-14 *3 *2) (-14 *4 *2) + (-4 *5 (-174)))) + ((*1 *2 *1) + (-12 (-4 *3 (-373)) (-4 *4 (-804)) (-4 *5 (-861)) (-5 *2 (-575)) + (-5 *1 (-515 *3 *4 *5 *6)) (-4 *6 (-964 *3 *4 *5)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-655 *6)) (-4 *6 (-861)) (-4 *4 (-373)) (-4 *5 (-804)) + (-5 *2 (-575)) (-5 *1 (-515 *4 *5 *6 *7)) (-4 *7 (-964 *4 *5 *6)))) + ((*1 *2 *1) (-12 (-4 *1 (-997 *3)) (-4 *3 (-1066)) (-5 *2 (-936)))) + ((*1 *2) (-12 (-4 *1 (-1292 *3)) (-4 *3 (-373)) (-5 *2 (-135))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1194)) (-4 *5 (-373)) (-5 *2 (-1174 (-1174 (-967 *5)))) + (-5 *1 (-1293 *5)) (-5 *4 (-1174 (-967 *5)))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1066)) (-4 *4 (-804)) (-4 *5 (-861)) (-5 *2 (-655 *1)) + (-4 *1 (-1082 *3 *4 *5))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-655 (-1194))) (-5 *3 (-52)) (-5 *1 (-904 *4)) + (-4 *4 (-1117))))) (((*1 *2 *1) (-12 (-5 *2 (-655 *4)) (-5 *1 (-1158 *3 *4)) (-4 *3 (-13 (-1117) (-34))) (-4 *4 (-13 (-1117) (-34)))))) -(((*1 *2 *3 *4 *5 *6 *7 *8 *9) - (|partial| -12 (-5 *4 (-655 *11)) (-5 *5 (-655 (-1190 *9))) - (-5 *6 (-655 *9)) (-5 *7 (-655 *12)) (-5 *8 (-655 (-782))) - (-4 *11 (-861)) (-4 *9 (-316)) (-4 *12 (-964 *9 *10 *11)) - (-4 *10 (-804)) (-5 *2 (-655 (-1190 *12))) - (-5 *1 (-718 *10 *11 *9 *12)) (-5 *3 (-1190 *12))))) -(((*1 *2 *3) (-12 (-5 *3 (-782)) (-5 *2 (-389)) (-5 *1 (-1057))))) -(((*1 *2) - (-12 (-4 *3 (-567)) (-5 *2 (-655 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-428 *3))))) -(((*1 *1 *2 *3 *3 *4 *4) - (-12 (-5 *2 (-967 (-575))) (-5 *3 (-1194)) - (-5 *4 (-1111 (-418 (-575)))) (-5 *1 (-30))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-567)) (-5 *2 (-655 *3)) (-5 *1 (-986 *4 *3)) - (-4 *3 (-1261 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-260 *2)) (-4 *2 (-1235))))) +(((*1 *2 *1 *1) + (-12 (-4 *1 (-993 *3 *4 *5 *6)) (-4 *3 (-1066)) (-4 *4 (-804)) + (-4 *5 (-861)) (-4 *6 (-1082 *3 *4 *5)) (-4 *3 (-567)) + (-5 *2 (-112))))) +(((*1 *2 *3 *4 *4 *3 *5) + (-12 (-5 *4 (-623 *3)) (-5 *5 (-1190 *3)) + (-4 *3 (-13 (-441 *6) (-27) (-1220))) + (-4 *6 (-13 (-463) (-1055 (-575)) (-148) (-650 (-575)))) + (-5 *2 (-597 *3)) (-5 *1 (-571 *6 *3 *7)) (-4 *7 (-1117)))) + ((*1 *2 *3 *4 *4 *4 *3 *5) + (-12 (-5 *4 (-623 *3)) (-5 *5 (-418 (-1190 *3))) + (-4 *3 (-13 (-441 *6) (-27) (-1220))) + (-4 *6 (-13 (-463) (-1055 (-575)) (-148) (-650 (-575)))) + (-5 *2 (-597 *3)) (-5 *1 (-571 *6 *3 *7)) (-4 *7 (-1117))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-556)))) +(((*1 *2 *1) (-12 (-4 *1 (-1138 *2)) (-4 *2 (-1235))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-871)) (-5 *3 (-129)) (-5 *2 (-782))))) (((*1 *2 *1) (-12 (-5 *2 (-1142 (-575) (-623 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-316)) (-4 *4 (-1009 *3)) (-4 *5 (-1261 *4)) @@ -16016,12 +16250,11 @@ (-12 (-4 *3 (-174)) (-4 *2 (-728 *3)) (-5 *1 (-673 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-737) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1009 *2)) (-4 *2 (-567))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-517)) (-5 *2 (-655 (-980))) (-5 *1 (-300))))) -(((*1 *2 *1 *3 *3 *4 *4) - (-12 (-5 *3 (-782)) (-5 *4 (-936)) (-5 *2 (-1290)) (-5 *1 (-1286)))) - ((*1 *2 *1 *3 *3 *4 *4) - (-12 (-5 *3 (-782)) (-5 *4 (-936)) (-5 *2 (-1290)) (-5 *1 (-1287))))) +(((*1 *2 *3 *3 *3 *3 *3 *3 *3 *3 *4 *5 *5 *5 *5 *5 *5 *6 *6 *6 *3 *3 *5 + *7 *3 *8) + (-12 (-5 *5 (-700 (-227))) (-5 *6 (-112)) (-5 *7 (-700 (-575))) + (-5 *8 (-3 (|:| |fn| (-399)) (|:| |fp| (-65 QPHESS)))) + (-5 *3 (-575)) (-5 *4 (-227)) (-5 *2 (-1052)) (-5 *1 (-764))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -16038,35 +16271,45 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-1228 *4 *5 *3 *6)) (-4 *4 (-567)) (-4 *5 (-804)) - (-4 *3 (-861)) (-4 *6 (-1082 *4 *5 *3)) (-5 *2 (-112)))) - ((*1 *2 *1) (-12 (-4 *1 (-1304 *3)) (-4 *3 (-373)) (-5 *2 (-112))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1228 *3 *4 *5 *6)) (-4 *3 (-567)) (-4 *4 (-804)) - (-4 *5 (-861)) (-4 *6 (-1082 *3 *4 *5)) (-5 *2 (-655 *6))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-782)) (-5 *1 (-598 *2)) (-4 *2 (-556)))) - ((*1 *2 *3) - (-12 (-5 *2 (-2 (|:| -1548 *3) (|:| -2398 (-782)))) (-5 *1 (-598 *3)) - (-4 *3 (-556))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-655 *6)) (-4 *6 (-1082 *3 *4 *5)) (-4 *3 (-567)) - (-4 *4 (-804)) (-4 *5 (-861)) (-5 *1 (-994 *3 *4 *5 *6)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *2 (-655 *7)) (-5 *3 (-112)) (-4 *7 (-1082 *4 *5 *6)) +(((*1 *2 *3) (-12 (-5 *3 (-936)) (-5 *2 (-1176)) (-5 *1 (-797))))) +(((*1 *2 *1 *3) + (-12 (-4 *1 (-871)) (-5 *2 (-702 (-560))) (-5 *3 (-560))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-1300 *3 *4)) (-4 *3 (-861)) (-4 *4 (-174)) + (-5 *1 (-675 *3 *4)))) + ((*1 *2 *1) + (|partial| -12 (-5 *2 (-675 *3 *4)) (-5 *1 (-1305 *3 *4)) + (-4 *3 (-861)) (-4 *4 (-174))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1 (-112) *7 (-655 *7))) (-4 *1 (-1228 *4 *5 *6 *7)) (-4 *4 (-567)) (-4 *5 (-804)) (-4 *6 (-861)) - (-5 *1 (-994 *4 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-597 *3)) (-4 *3 (-373))))) -(((*1 *2 *3) - (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-575))) (-5 *1 (-1064))))) -(((*1 *1) (-5 *1 (-1080)))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-13 (-463) (-148))) (-5 *2 (-429 *3)) - (-5 *1 (-100 *4 *3)) (-4 *3 (-1261 *4)))) + (-4 *7 (-1082 *4 *5 *6)) (-5 *2 (-112))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1261 *5)) (-4 *5 (-373)) + (-4 *7 (-1261 (-418 *6))) + (-5 *2 (-2 (|:| |answer| *3) (|:| -3660 *3))) + (-5 *1 (-573 *5 *6 *7 *3)) (-4 *3 (-352 *5 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-655 *3)) (-4 *3 (-1261 *5)) (-4 *5 (-13 (-463) (-148))) - (-5 *2 (-429 *3)) (-5 *1 (-100 *5 *3))))) + (-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1261 *5)) (-4 *5 (-373)) + (-5 *2 + (-2 (|:| |answer| (-418 *6)) (|:| -3660 (-418 *6)) + (|:| |specpart| (-418 *6)) (|:| |polypart| *6))) + (-5 *1 (-574 *5 *6)) (-5 *3 (-418 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-655 (-849))) (-5 *1 (-141))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-655 (-873))) (-5 *1 (-1194))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-920 (-575))) (-5 *4 (-575)) (-5 *2 (-700 *4)) + (-5 *1 (-1045 *5)) (-4 *5 (-1066)))) + ((*1 *2 *3) + (-12 (-5 *3 (-655 (-575))) (-5 *2 (-700 (-575))) (-5 *1 (-1045 *4)) + (-4 *4 (-1066)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-655 (-920 (-575)))) (-5 *4 (-575)) + (-5 *2 (-655 (-700 *4))) (-5 *1 (-1045 *5)) (-4 *5 (-1066)))) + ((*1 *2 *3) + (-12 (-5 *3 (-655 (-655 (-575)))) (-5 *2 (-655 (-700 (-575)))) + (-5 *1 (-1045 *4)) (-4 *4 (-1066))))) +(((*1 *1 *2) (-12 (-5 *2 (-655 (-873))) (-5 *1 (-873))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -16083,47 +16326,44 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) +(((*1 *2 *3 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-575)) (-5 *4 (-700 (-227))) (-5 *2 (-1052)) + (-5 *1 (-766))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) (((*1 *2 *3 *2) (-12 (-5 *1 (-690 *3 *2)) (-4 *3 (-1117)) (-4 *2 (-1117))))) -(((*1 *2 *3 *4 *3 *5) - (-12 (-5 *3 (-1176)) (-5 *4 (-171 (-227))) (-5 *5 (-575)) - (-5 *2 (-1052)) (-5 *1 (-769))))) -(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-336 *3)) (-4 *3 (-1235)))) - ((*1 *2 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-527 *3 *4)) (-4 *3 (-1235)) - (-14 *4 (-575))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1151 *3)) (-4 *3 (-1066)) - (-5 *2 (-655 (-655 (-655 (-958 *3)))))))) -(((*1 *2 *1) (-12 (-4 *1 (-808 *2)) (-4 *2 (-174))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-145))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-655 *7)) (-4 *7 (-1082 *4 *5 *6)) (-4 *4 (-463)) + (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-112)) + (-5 *1 (-1005 *4 *5 *6 *7 *8)) (-4 *8 (-1088 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-655 *7)) (-4 *7 (-1082 *4 *5 *6)) (-4 *4 (-463)) + (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-112)) + (-5 *1 (-1124 *4 *5 *6 *7 *8)) (-4 *8 (-1088 *4 *5 *6 *7))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-575)) (-5 *1 (-572))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-112) (-115) (-115))) (-5 *1 (-115))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-936)) (-5 *2 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+ (-12 (-5 *3 (-575)) (-4 *2 (-23)) (-5 *1 (-660 *4 *2 *5)) + (-4 *4 (-1117)) (-14 *5 *2)))) +(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) + (-12 (-5 *3 (-1176)) (-5 *4 (-575)) (-5 *5 (-700 (-171 (-227)))) + (-5 *2 (-1052)) (-5 *1 (-765))))) (((*1 *2 *1) - (-12 (-5 *2 (-702 (-884 (-981 *3) (-981 *3)))) (-5 *1 (-981 *3)) - (-4 *3 (-1117))))) -(((*1 *2) - (-12 (-5 *2 (-1290)) (-5 *1 (-1212 *3 *4)) (-4 *3 (-1117)) - (-4 *4 (-1117))))) + (-12 (-5 *2 (-873)) (-5 *1 (-401 *3 *4 *5)) (-14 *3 (-782)) + (-14 *4 (-782)) (-4 *5 (-174))))) +(((*1 *2 *3 *1) + (|partial| -12 (-5 *3 (-904 *4)) (-4 *4 (-1117)) (-4 *2 (-1117)) + (-5 *1 (-901 *4 *2))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-1066)) (-4 *2 (-698 *4 *5 *6)) + (-5 *1 (-104 *4 *3 *2 *5 *6)) (-4 *3 (-1261 *4)) (-4 *5 (-383 *4)) + (-4 *6 (-383 *4))))) (((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) @@ -16140,60 +16380,63 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *1 *1 *2) - 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-4461))))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1082 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-804)) - (-4 *4 (-861)) (-4 *2 (-567)))) - ((*1 *1 *1 *2) +(((*1 *1) (-5 *1 (-589)))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-373)) (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-112)) + (-5 *1 (-515 *4 *5 *6 *3)) (-4 *3 (-964 *4 *5 *6))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1199))))) +(((*1 *2 *2) + (-12 (-4 *3 (-463)) (-5 *1 (-1226 *3 *2)) + (-4 *2 (-13 (-441 *3) (-1220)))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-1082 *3 *4 *2)) (-4 *3 (-1066)) (-4 *4 (-804)) + (-4 *2 (-861)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-1082 *2 *3 *4)) (-4 *2 (-1066)) (-4 *3 (-804)) - (-4 *4 (-861)) (-4 *2 (-567))))) + (-4 *4 (-861))))) (((*1 *2 *1) (-12 (-5 *2 @@ -16604,11 +16540,6 @@ (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print"))) (-5 *1 (-339))))) (((*1 *2 *2) - (-12 (-5 *2 (-1174 *3)) (-4 *3 (-1066)) (-5 *1 (-1178 *3)))) - ((*1 *1 *1) - (-12 (-5 *1 (-1277 *2 *3 *4)) (-4 *2 (-1066)) (-14 *3 (-1194)) - (-14 *4 *2)))) -(((*1 *2 *2) (-12 (-4 *3 (-567)) (-5 *1 (-284 *3 *2)) (-4 *2 (-13 (-441 *3) (-1019))))) ((*1 *2 *2) @@ -16624,31 +16555,43 @@ ((*1 *2 *2) (-12 (-5 *2 (-1174 *3)) (-4 *3 (-38 (-418 (-575)))) (-5 *1 (-1180 *3))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-1000 *2)) (-4 *2 (-1220))))) +(((*1 *1 *2 *1) + (-12 (-5 *1 (-660 *2 *3 *4)) (-4 *2 (-1117)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *1 *2 *3) (-12 (-5 *2 (-782)) (-5 *1 (-59 *3)) (-4 *3 (-1235)))) + ((*1 *1 *2) (-12 (-5 *2 (-655 *3)) (-4 *3 (-1235)) (-5 *1 (-59 *3))))) +(((*1 *2) (-12 (-5 *2 (-655 (-1176))) (-5 *1 (-1288)))) + ((*1 *2 *2) (-12 (-5 *2 (-655 (-1176))) (-5 *1 (-1288))))) +(((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1176)) (-5 *1 (-194)))) + ((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1176)) (-5 *1 (-309)))) + ((*1 *2 *3) (-12 (-5 *3 (-227)) (-5 *2 (-1176)) (-5 *1 (-314))))) +(((*1 *1 *2) (-12 (-5 *2 (-655 (-873))) (-5 *1 (-873)))) + ((*1 *1 *1) (-5 *1 (-873)))) +(((*1 *1) (-5 *1 (-142)))) (((*1 *2 *3) - (-12 (-4 *4 (-567)) (-4 *5 (-804)) (-4 *6 (-861)) (-5 *2 (-112)) - (-5 *1 (-994 *4 *5 *6 *3)) (-4 *3 (-1082 *4 *5 *6))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-453 *3)) (-4 *3 (-1261 (-575)))))) -(((*1 *2 *1) (-12 (-4 *1 (-1027 *3)) (-4 *3 (-1235)) (-5 *2 (-112)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1182 *3 *4)) (-14 *3 (-936)) - (-4 *4 (-1066))))) -(((*1 *1 *2) (-12 (-5 *2 (-782)) (-5 *1 (-135))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-112)) (-4 *6 (-13 (-463) (-1055 (-575)) (-650 (-575)))) - (-4 *3 (-13 (-27) (-1220) (-441 *6) (-10 -8 (-15 -2883 ($ *7))))) - (-4 *7 (-859)) - (-4 *8 - (-13 (-1263 *3 *7) (-373) (-1220) - (-10 -8 (-15 -2389 ($ $)) (-15 -4413 ($ $))))) + (-12 (-5 *3 (-655 (-1194))) (-4 *4 (-13 (-316) (-148))) + (-4 *5 (-13 (-861) (-625 (-1194)))) (-4 *6 (-804)) + (-5 *2 (-655 (-418 (-967 *4)))) (-5 *1 (-939 *4 *5 *6 *7)) + (-4 *7 (-964 *4 *6 *5))))) +(((*1 *2 *3 *4 *5 *6 *7 *7 *8) + (-12 + (-5 *3 + (-2 (|:| |det| *12) (|:| |rows| (-655 (-575))) + (|:| |cols| (-655 (-575))))) + 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\ No newline at end of file |